http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Chakraborty&feedformat=atomSoft-Matter - User contributions [en]2022-09-29T19:55:50ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=14055Rupak Chakraborty2009-12-06T21:58:28Z<p>Chakraborty: </p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (Length scales part)<br />
<br />
[[Vane rheometry]]<br />
<br />
[[Herschel-Bulkley fluid]]<br />
<br />
[[Navier-Stokes equation]]<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]<br />
<br />
[[Dilatant shear bands in solidifying metals]]<br />
<br />
[[Spatial cooperativity in soft glassy flows]]<br />
<br />
[[Partial coalescence of drops at liquid interfaces]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Navier-Stokes_equation&diff=14054Navier-Stokes equation2009-12-06T21:57:33Z<p>Chakraborty: </p>
<hr />
<div>The Navier-Stokes equation describes the motion of fluids. It is derived from applying Newton's second law to fluid systems, and assumes that the fluid stress is the sum of a viscous term and a pressure term. The general form of the equations of fluid motion is<br />
<br />
:<math>\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},</math><br />
<br />
where <math>\mathbf{v}</math> is the flow velocity, <math>\rho</math> is the fluid density, ''p'' is the pressure, <math>\mathbb{T}</math> is the stress tensor, and <math>\mathbf{f} </math> represents body forces per unit volume acting on the fluid.<br />
<br />
==References==<br />
[http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations Wikipedia article]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Navier-Stokes_equation&diff=14053Navier-Stokes equation2009-12-06T21:56:58Z<p>Chakraborty: </p>
<hr />
<div>The Navier-Stokes equation describes the motion of fluids. It is derived from applying Newton's second law to fluid systems, and assumes that the fluid stress is the sum of a viscous term and a pressure term. The general form of the equations of fluid motion is<br />
<br />
:<math>\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},</math><br />
<br />
where <math>\mathbf{v}</math> is the flow velocity, <math>\rho</math> is the fluid density, ''p'' is the pressure, <math>\mathbb{T}</math> is the stress tensor, and <math>\mathbf{f} </math> represents body forces per unit volume acting on the fluid and <math>\nabla</math> is the del operator.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Navier-Stokes_equation&diff=14052Navier-Stokes equation2009-12-06T21:56:06Z<p>Chakraborty: New page: The Navier-Stokes equation describes the motion of fluids. It is derived from applying Newton's second law to fluid systems, and assumes that the fluid stress is the sum of a viscous term...</p>
<hr />
<div>The Navier-Stokes equation describes the motion of fluids. It is derived from applying Newton's second law to fluid systems, and assumes that the fluid stress is the sum of a viscous term and a pressure term. The general form of the equations of fluid motion is<br />
<br />
:<math>\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},</math><br />
<br />
where <math>\mathbf{v}</math> is the flow velocity, <math>\rho</math> is the fluid density, ''p'' is the pressure, <math>\mathbb{T}</math> is the ([[Stress (physics)#Stress deviator tensor|deviatoric]]) stress [[tensor field|tensor]], and <math>\mathbf{f} </math> represents [[body force]]s (per unit volume) acting on the fluid and <math>\nabla</math> is the [[del]] operator.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Partial_coalescence_of_drops_at_liquid_interfaces&diff=14051Partial coalescence of drops at liquid interfaces2009-12-06T21:53:15Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Blanchette, F., Bigioni, T., Nature 2 (2006).<br />
<br />
==Keywords==<br />
[[Navier-Stokes equation]], pinch-off, surface tension<br />
<br />
==Summary==<br />
<br />
[[Image:drop_1.jpg |right| |200px| |thumb| Figure 1. Evolution of drop as it makes contact with the surface, with simulation results below it.]]<br />
<br />
Coalescence occurs when two separate masses of the same fluid are brought into contact; to minimize surface energy, they combine into a single larger mass. However, this does not always occur when a drop of fluid comes into contact with a large reservoir of the same fluid. Sometimes, the drop partially coalesces, "pinches off" in the process of merging, and leaves behind a smaller droplet. The authors study the mechanism of this effect.<br />
<br />
The authors deposited a liquid onto an identical liquid in air and filmed the process with a high-speed camera. The results are shown in Figure 1. As shown, the drop comes into contact and forms a smaller daughter droplet. The shape of the droplet was numerically simulated by solving the Navier-Stokes equations, including surface tension as a force on the localized interface. The simulation shapes matched well with the experimental results as shown in Figure 1. The authors ruled out static Rayleigh-Plateau instability as a cause for the pinch-off by modifying simulation parameters.<br />
<br />
Instead, they suggest that the pinch-off depends on the inward momentum of the collapsing neck as the drop merges. The downward pull of surface tension at the drop's summit is generally larger than the inward horizontal pull of the neck. However, the horizontal collapse may induce pinch-off if the vertical collapse is retarded. The authors suggest that capillary waves generated by the opening of the neck provide the retarding force. The capillary waves stretch the drop by focusing energy on its summit and thereby reduce the vertical collapse. Numerical simulations seem to support this claim, and the phase boundary between partial and total coalescence is found to be characterized by a critical Ohnesorge number of 0.026.<br />
<br />
However, these results only apply to systems where gravitational effects are negligible. When the drops are significantly deformed due to gravity, the merging dynamics are more complicated. Furthermore, these experiments were carried out in air; when the same experiment is done in a liquid (different from that of the drop), the critical Ohnesorge number changes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Partial_coalescence_of_drops_at_liquid_interfaces&diff=14050Partial coalescence of drops at liquid interfaces2009-12-06T21:50:53Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Blanchette, F., Bigioni, T., Nature 2 (2006).<br />
<br />
==Keywords==<br />
Navier-Stokes equation, pinch-off, surface tension<br />
<br />
==Summary==<br />
<br />
[[Image:drop_1.jpg |right| |200px| |thumb| Figure 1. Evolution of drop as it makes contact with the surface, with simulation results below it.]]<br />
<br />
Coalescence occurs when two separate masses of the same fluid are brought into contact; to minimize surface energy, they combine into a single larger mass. However, this does not always occur when a drop of fluid comes into contact with a large reservoir of the same fluid. Sometimes, the drop partially coalesces, "pinches off" in the process of merging, and leaves behind a smaller droplet. The authors study the mechanism of this effect.<br />
<br />
The authors deposited a liquid onto an identical liquid in air and filmed the process with a high-speed camera. The results are shown in Figure 1. As shown, the drop comes into contact and forms a smaller daughter droplet. The shape of the droplet was numerically simulated by solving the Navier-Stokes equations, including surface tension as a force on the localized interface. The simulation shapes matched well with the experimental results as shown in Figure 1. The authors ruled out static Rayleigh-Plateau instability as a cause for the pinch-off by modifying simulation parameters.<br />
<br />
Instead, they suggest that the pinch-off depends on the inward momentum of the collapsing neck as the drop merges. The downward pull of surface tension at the drop's summit is generally larger than the inward horizontal pull of the neck. However, the horizontal collapse may induce pinch-off if the vertical collapse is retarded. The authors suggest that capillary waves generated by the opening of the neck provide the retarding force. The capillary waves stretch the drop by focusing energy on its summit and thereby reduce the vertical collapse. Numerical simulations seem to support this claim, and the phase boundary between partial and total coalescence is found to be characterized by a critical Ohnesorge number of 0.026.<br />
<br />
However, these results only apply to systems where gravitational effects are negligible. When the drops are significantly deformed due to gravity, the merging dynamics are more complicated. Furthermore, these experiments were carried out in air; when the same experiment is done in a liquid (different from that of the drop), the critical Ohnesorge number changes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Drop_1.jpg&diff=14049File:Drop 1.jpg2009-12-06T21:49:38Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Partial_coalescence_of_drops_at_liquid_interfaces&diff=14048Partial coalescence of drops at liquid interfaces2009-12-06T21:48:04Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Blanchette, F., Bigioni, T., Nature 2 (2006).<br />
<br />
==Keywords==<br />
<br />
<br />
==Summary==<br />
<br />
[[Image:glassy_1.jpg |right| |200px| |thumb| Figure 1. Different colors represent different rotation velocities.]]<br />
<br />
[[Image:glassy_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
Coalescence occurs when two separate masses of the same fluid are brought into contact; to minimize surface energy, they combine into a single larger mass. However, this does not always occur when a drop of fluid comes into contact with a large reservoir of the same fluid. Sometimes, the drop partially coalesces, "pinches off" in the process of merging, and leaves behind a smaller droplet. The authors study the mechanism of this effect.<br />
<br />
The authors deposited a liquid onto an identical liquid in air and filmed the process with a high-speed camera. The results are shown in Figure 1. As shown, the drop comes into contact and forms a smaller daughter droplet. The shape of the droplet was numerically simulated by solving the Navier-Stokes equations, including surface tension as a force on the localized interface. The simulation shapes matched well with the experimental results as shown in Figure 1. The authors ruled out static Rayleigh-Plateau instability as a cause for the pinch-off by modifying simulation parameters.<br />
<br />
Instead, they suggest that the pinch-off depends on the inward momentum of the collapsing neck as the drop merges. The downward pull of surface tension at the drop's summit is generally larger than the inward horizontal pull of the neck. However, the horizontal collapse may induce pinch-off if the vertical collapse is retarded. The authors suggest that capillary waves generated by the opening of the neck provide the retarding force. The capillary waves stretch the drop by focusing energy on its summit and thereby reduce the vertical collapse. Numerical simulations seem to support this claim, and the phase boundary between partial and total coalescence is found to be characterized by a critical Ohnesorge number of 0.026.<br />
<br />
However, these results only apply to systems where gravitational effects are negligible. When the drops are significantly deformed due to gravity, the merging dynamics are more complicated. Furthermore, these experiments were carried out in air; when the same experiment is done in a liquid (different from that of the drop), the critical Ohnesorge number changes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Partial_coalescence_of_drops_at_liquid_interfaces&diff=14047Partial coalescence of drops at liquid interfaces2009-12-06T21:34:45Z<p>Chakraborty: New page: ==Reference== Blanchette, F., Bigioni, T., Nature 2 (2006). ==Keywords== ==Summary== [[Image:glassy_1.jpg |right| |200px| |thumb| Figure 1. Different colors represent different rotati...</p>
<hr />
<div>==Reference==<br />
Blanchette, F., Bigioni, T., Nature 2 (2006).<br />
<br />
==Keywords==<br />
<br />
<br />
==Summary==<br />
<br />
[[Image:glassy_1.jpg |right| |200px| |thumb| Figure 1. Different colors represent different rotation velocities.]]<br />
<br />
[[Image:glassy_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
Coalescence occurs when two separate masses of teh same fluid are brought into contact; to minimize surface energy, they combine into a single larger mass. However, this does not always occur when a drop of fluid comes into contact with a large reservoir of the same fluid. Sometimes, the drop partially coalesces, "pinches off" in the process of merging, and leaves behind a smaller droplet. The authors study the mechanism of this effect.<br />
<br />
The authors deposited a liquid onto an identical liquid in air and filmed the process with a high-speed camera. The results are shown in Figure 1. As shown, the drop comes into contact and forms a smaller daughter droplet. The shape of the droplet was numerically simulated by solving the Navier-Stokes equations, including surface tension as a force on the localized interface. The simulation shapes matched well with the experimental results as shown in Figure 1. The authors ruled out static Rayleigh-Plateau instability as a cause for the pinch-off by modifying simulation parameters.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=14046Rupak Chakraborty2009-12-06T20:18:18Z<p>Chakraborty: /* Papers */</p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (Length scales part)<br />
<br />
[[Vane rheometry]]<br />
<br />
[[Herschel-Bulkley fluid]]<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]<br />
<br />
[[Dilatant shear bands in solidifying metals]]<br />
<br />
[[Spatial cooperativity in soft glassy flows]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=14045Rupak Chakraborty2009-12-06T20:17:47Z<p>Chakraborty: /* Keywords */</p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (Length scales part)<br />
<br />
[[Vane rheometry]]<br />
<br />
[[Herschel-Bulkley fluid]]<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]<br />
<br />
[[Dilatant shear bands in solidifying metals]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Herschel-Bulkley_fluid&diff=14044Herschel-Bulkley fluid2009-12-06T20:17:19Z<p>Chakraborty: /* References */</p>
<hr />
<div>The Herschel-Bulkley fluid is a generalized model of a non-Newtonian fluid. Generally, the stress of the fluid is related to the strain in a nonlinear way. In the Herschel-Bulkley model, the fluid is characterized by the consistency <math>k</math>, the flow index <math>n</math>, and yield shear stress <math>\tau_0</math>. The consistency is a constant of proportionality, and the flow index is a measure of non-linearity in the stress-strain curve - that is, how shear-thinning or shear-thickening the fluid is. The yield stress is the amount of stress the fluid must experience before it begins to flow.<br />
<br />
== References ==<br />
[http://en.wikipedia.org/wiki/Herschel%E2%80%93Bulkley_fluid Wikipedia entry]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Herschel-Bulkley_fluid&diff=14043Herschel-Bulkley fluid2009-12-06T20:17:00Z<p>Chakraborty: New page: The Herschel-Bulkley fluid is a generalized model of a non-Newtonian fluid. Generally, the stress of the fluid is related to the strain in a nonlinear way. In the Herschel-Bulkley model,...</p>
<hr />
<div>The Herschel-Bulkley fluid is a generalized model of a non-Newtonian fluid. Generally, the stress of the fluid is related to the strain in a nonlinear way. In the Herschel-Bulkley model, the fluid is characterized by the consistency <math>k</math>, the flow index <math>n</math>, and yield shear stress <math>\tau_0</math>. The consistency is a constant of proportionality, and the flow index is a measure of non-linearity in the stress-strain curve - that is, how shear-thinning or shear-thickening the fluid is. The yield stress is the amount of stress the fluid must experience before it begins to flow.<br />
<br />
== References ==<br />
[http://en.wikipedia.org/wiki/Herschel%E2%80%93Bulkley_fluid]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14042Spatial cooperativity in soft glassy flows2009-12-06T20:07:45Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, [[Herschel-Bulkley fluid]]<br />
<br />
==Summary==<br />
<br />
[[Image:glassy_1.jpg |right| |200px| |thumb| Figure 1. Different colors represent different rotation velocities.]]<br />
<br />
[[Image:glassy_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_{bulk} = \dot{\gamma}/\sigma_{bulk}</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_{bulk}+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly, the authors found that a unique flow cooperativity length accurately describes all the microchannel data, even across different shear velocities. The predictions are shown as dashed lines in Figure 2. Furthermore, the authors applied the model at different volume fractions, finding a unique cooperativity length for each that matched the data similarly well. It is noted that the cooperativity length is on the same order as dynamical heterogeneities, and that the two might be related. However, whereas dynamical heterogeneities have a maximum at the glass transition, the cooperativity length has a very different behavior, only being nonzero above the transition and increasing from there. Instead of the size of mobile regions, perhaps the the cooperativity length is the characteristic length for plastic events.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14041Spatial cooperativity in soft glassy flows2009-12-06T20:07:03Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, [[Herschel-Bulkley fluid]]<br />
<br />
==Summary==<br />
<br />
[[Image:glassy_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:glassy_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_{bulk} = \dot{\gamma}/\sigma_{bulk}</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_{bulk}+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly, the authors found that a unique flow cooperativity length accurately describes all the microchannel data, even across different shear velocities. The predictions are shown as dashed lines in Figure 2. Furthermore, the authors applied the model at different volume fractions, finding a unique cooperativity length for each that matched the data similarly well. It is noted that the cooperativity length is on the same order as dynamical heterogeneities, and that the two might be related. However, whereas dynamical heterogeneities have a maximum at the glass transition, the cooperativity length has a very different behavior, only being nonzero above the transition and increasing from there. Instead of the size of mobile regions, perhaps the the cooperativity length is the characteristic length for plastic events.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Glassy_2.jpg&diff=14040File:Glassy 2.jpg2009-12-06T20:06:08Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Glassy_1.jpg&diff=14039File:Glassy 1.jpg2009-12-06T20:05:57Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14038Spatial cooperativity in soft glassy flows2009-12-06T19:47:25Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_{bulk} = \dot{\gamma}/\sigma_{bulk}</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_{bulk}+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly, the authors found that a unique flow cooperativity length accurately describes all the microchannel data, even across different shear velocities.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14037Spatial cooperativity in soft glassy flows2009-12-06T09:42:45Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_bulk = \dot{\gamma}/\sigma_bulk</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_{bulk}+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly, the authors found that a unique flow cooperativity length accurately describes all the microchannel data, even across different shear velocities.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14036Spatial cooperativity in soft glassy flows2009-12-06T08:21:47Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_bulk = \dot{\gamma}/\sigma_bulk</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_{bulk}+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly, the authors found that a unique flow cooperativity length</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14035Spatial cooperativity in soft glassy flows2009-12-06T07:48:52Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_bulk = \dot{\gamma}/\sigma_bulk</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_bulk+\xi^2 \frac{\partial^2f(z)}{\partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly,</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14034Spatial cooperativity in soft glassy flows2009-12-06T07:48:27Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_bulk = \dot{\gamma}/\sigma_bulk</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_bulk+\xi^2 \frac{\partial^2f(z), \partial^2 z}</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly,</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14033Spatial cooperativity in soft glassy flows2009-12-06T07:47:58Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. In Conceptually, localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system. The rate of plastic rearrangements <math>v</math> is equivalent to a fluidity <math>f</math> defined as <math>\sigma = (1/f)\dot{\gamma}</math>. In the absence of non-local effects, the fluidity reduces to the bulk fluidity <math>f_bulk = \dot{\gamma}/\sigma_bulk</math>, but to take into account the non-local effects, the fluidity is assumed to be of the form<br />
<br />
<math>f(z)=f_bulk+\xi^2 \frac{\partial^2f(z), \partial^2 z</math>.<br />
<br />
In the above, <math>\xi</math> denotes a "flow cooperativity length." This equation was solved numerically using appropriate boundary conditions. Surprisingly,</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14032Spatial cooperativity in soft glassy flows2009-12-06T07:31:33Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell, Herschel-Bulkley model<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model. However, in the microchannel setup, the data does not follow a single rheological curve. The finite-size effect in the microchannel setup which did not appear in the wide-gap setup suggests that there are extended spatial correlations in the system.<br />
<br />
The authors checked that the change in rheology is not caused by a structural change in the emulsion, nor a change in density, nor boundary effects. In order to explain this finite-size effect, they developed a model considering the plastic rearrangements that occur in concentrated emulsions. Localized plastic events induce a non-local, long-range elastic relaxation of the stress over the system.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14031Spatial cooperativity in soft glassy flows2009-12-06T04:23:17Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dot{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14030Spatial cooperativity in soft glassy flows2009-12-06T04:23:06Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow in a narrow microchannel (tens of hundreds micrometers in width). The substance tested was an emulsion of silicone droplets (6.5um in diameter) in a glycerine-water mixture. The local flow curves, which relate the local shear stress <math>\sigma</math> to the local shear rate <math>\dor{\gamma}</math>, are obtained from the measured velocity profiles of both geometries. Figure 1 shows the results for the wide-gap Couette cell, and Figure 2 shows the results for the narrow microchannel. Evidently, the flow curve is highly dependent on the geometry. In the wide-gap case, the curve follows the Herschel-Bulkley model.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14029Spatial cooperativity in soft glassy flows2009-12-06T04:13:05Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but how these heterogeneities affect flow remains unclear. Using a local velocity measurement technique, the authors study the local flow of a film of confined glassy material.<br />
<br />
The authors test flow in two main geometries: shear planar flow in a wide gap Couette cell, and pressure driven planar flow</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14028Spatial cooperativity in soft glassy flows2009-12-06T00:14:37Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. Many have tried to understand the glass transition by studying the dynamical heterogeneities in glass-forming materials, but Using a local velocity measurement technique, the authors measure the local flow of a film of confined glassy material.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Spatial_cooperativity_in_soft_glassy_flows&diff=14027Spatial cooperativity in soft glassy flows2009-12-06T00:10:54Z<p>Chakraborty: New page: ==Reference== Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008). ==Keywords== spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couet...</p>
<hr />
<div>==Reference==<br />
Goyon, J., Colin, A., Ovarlez, G., Ajdari, A., Bocquet, L., Nature 454 (2008).<br />
<br />
==Keywords==<br />
spatial cooperativity, glass, velocity profile, shear stress, shear strain, Couette cell<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
This paper deals with studying non-local effects at and above the glass transition in an emulsion. A general feature of glassy materials is a strong nonlinear flow rule relating stress and strain. This feature is no well-documented and poorly understood. The authors develop a law governing flows of glassy materials, using a local velocity measurement technique to measure the local flow of a film of confined glassy material.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=14026Rupak Chakraborty2009-12-05T22:43:40Z<p>Chakraborty: /* Keywords */</p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (Length scales part)<br />
<br />
[[Vane rheometry]]<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]<br />
<br />
[[Dilatant shear bands in solidifying metals]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=14025Rupak Chakraborty2009-12-05T22:43:13Z<p>Chakraborty: /* Papers */</p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (length scales)<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]<br />
<br />
[[Dilatant shear bands in solidifying metals]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Vane_rheometry&diff=14024Vane rheometry2009-12-05T22:38:16Z<p>Chakraborty: </p>
<hr />
<div>[[Image:vane_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
Vane rheometry refers to measuring rheological parameters of a liquid or dispersion using a rotating vane immersed in the substance. The torque required to rotate the vane is measured as a function of the shear strain, and from this data, the viscosity and other properties can be extracted. Originally, the vane geometry was used to measure the yield stresses of inorganic dispersions, but recently has been used to measure several other rheological properties including the low-strain modulus and the steady-state flow-curves of substances. In addition to simple fabrication and ease of cleaning, the main advantage of the vane geometry is the elimination of wall-slip effects. A typical vane-and-basket geometry is shown in the figure.<br />
<br />
== References ==<br />
Barnes, H.A., Nguyen, Q.D., "Rotating vane rheometry - a review," Journal of Non-Newtonian Fluid Mechanics, 98 (2001).</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Vane_rheometry&diff=14023Vane rheometry2009-12-05T22:36:47Z<p>Chakraborty: </p>
<hr />
<div>[[Image:vane_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
Vane rheometry refers to measuring rheological parameters of a liquid or dispersion using a rotating vane immersed in the substance. The torque required to rotate the vane is measured as a function of the shear strain, and from this data, the viscosity and other properties can be extracted. Originally, the vane geometry was used to measure the yield stresses of inorganic dispersions, but recently has been used to measure several other rheological properties including the low-strain modulus and the steady-state flow-curves of substances. In addition to simple fabrication and ease of cleaning, the main advantage of the vane geometry is the elimination of wall-slip effects. A typical vane-and-basket geometry is shown in the figure.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Vane_1.jpg&diff=14022File:Vane 1.jpg2009-12-05T22:36:38Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Vane_rheometry&diff=14021Vane rheometry2009-12-05T22:32:53Z<p>Chakraborty: New page: Vane rheometry refers to measuring rheological parameters of a liquid or dispersion using a rotating vane immersed in the substance. By measuring the torque required to rotate the vane, v...</p>
<hr />
<div>Vane rheometry refers to measuring rheological parameters of a liquid or dispersion using a rotating vane immersed in the substance. By measuring the torque required to rotate the vane, various rheological parameters can be extracted. Originally, the vane geometry was used to measure the yield stresses of inorganic dispersions, but recently has been used to measure several other rheological properties including the low-strain modulus and the steady-state flow-curves of substances. In addition to simple fabrication and ease of cleaning, the main advantage of the vane geometry is the elimination of wall-slip effects. A typical vane-and-basket geometry</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14020Dilatant shear bands in solidifying metals2009-12-05T22:19:37Z<p>Chakraborty: /* Keywords */</p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, [[Granular Matter]], [[Vane rheometry]]<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the similar rheology holds only in a certain range above the cohesion volume fraction. For the Mg alloy in the experiment, this range was <math>0.2<f_s<0.35</math>. This suggests that the models developed for granular materials can be applied to partially solid alloys. This is significant because understanding the mechanics and microstructure of solidifying alloys is essential to enhancing industrial casting processes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14019Dilatant shear bands in solidifying metals2009-12-05T22:09:45Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:dilatant_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:dilatant_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the similar rheology holds only in a certain range above the cohesion volume fraction. For the Mg alloy in the experiment, this range was <math>0.2<f_s<0.35</math>. This suggests that the models developed for granular materials can be applied to partially solid alloys. This is significant because understanding the mechanics and microstructure of solidifying alloys is essential to enhancing industrial casting processes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Dilatant_2.jpg&diff=14018File:Dilatant 2.jpg2009-12-05T22:07:08Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Dilatant_1.jpg&diff=14017File:Dilatant 1.jpg2009-12-05T22:06:59Z<p>Chakraborty: </p>
<hr />
<div></div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14016Dilatant shear bands in solidifying metals2009-12-05T22:03:38Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the similar rheology holds only in a certain range above the cohesion volume fraction. For the Mg alloy in the experiment, this range was <math>0.2<f_s<0.35</math>. This suggests that the models developed for granular materials can be applied to partially solid alloys. This is significant because understanding the mechanics and microstructure of solidifying alloys is essential to enhancing industrial casting processes.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14015Dilatant shear bands in solidifying metals2009-12-05T21:46:36Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the similar rheology holds only in a certain range above the cohesion volume fraction. For the Mg alloy in the experiment, this range was <math>0.2<f_s<0.35</math>.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14014Dilatant shear bands in solidifying metals2009-12-05T21:23:16Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the similar characteristics</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14013Dilatant shear bands in solidifying metals2009-12-05T21:22:37Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that the solidifying alloy has a similar rheology to a cohesionless granular material. However, the</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14012Dilatant shear bands in solidifying metals2009-12-05T21:16:20Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.<br />
<br />
It is thus shown that</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14011Dilatant shear bands in solidifying metals2009-12-05T21:15:13Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K., Nature 445 (2007).<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in solidifying metal alloys in this low volume fraction regime.<br />
<br />
In the main set of experiments, an Mg alloy was deformed during solidification using a four-bladed vane. Figure 1 shows the torque versus vane response; it shows an increase in torque to a peak value, then a sharp decrease, and finally deformation continues at a lower torque than the initial torque. Figure 2 is a macrograph of one-quarter of the cross-section of the sample, and it shows a porous band just outside the radius of the vane. The authors note that the torque-vane curve shown in Figure 1 and the shear band shown in Figure 2 are characteristic of compacted cohesionless granular material. Compacted granular materials exhibit Reynolds dilatancy - that is, they expand when sheared because particles must increase the space between themselves in order to rearrange.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=14010Dilatant shear bands in solidifying metals2009-12-05T20:50:15Z<p>Chakraborty: </p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K.<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. During the solidification of a metallic alloy, it has been shown that after nucleation, crystals are initially dispersed in the liquid and the material behaves as a suspension. As the crystals grow, the volume fraction of solid, <math>f_s</math> increases, and at a critical value <math>f_s^{Coh}</math>, there is a sharp increase in viscosity due to the formation of a loose solid. As the metal continues to solidify, partial cohesion between solids develops, allowing the solid to transmit shear, compressive, and tensile strains. Although metals at high volume fraction have been studied extensively, metals at relatively low volume fractions (<math>f_s^{Coh} \leq f_s \leq 0.5</math>) have not. This paper deals with dilatancy in this low volume fraction regime.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Dilatant_shear_bands_in_solidifying_metals&diff=13860Dilatant shear bands in solidifying metals2009-12-05T01:29:47Z<p>Chakraborty: New page: ==Reference== Gourlay, C.M., Dahle, A.K. ==Keywords== dilatancy, shear, granular media ==Summary== Figure 1. [[Image:Nonlinear_2.jpg |...</p>
<hr />
<div>==Reference==<br />
Gourlay, C.M., Dahle, A.K.<br />
<br />
==Keywords==<br />
dilatancy, shear, granular media<br />
<br />
==Summary==<br />
<br />
[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
<br />
[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
<br />
[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
<br />
The authors study the microstructure of partially solidified alloys under shear. It is found that these alloys behave similarly to a cohensionless granular material, exhibiting Reynold's dilatancy and strain localization in dilatant shear bands.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Rupak_Chakraborty&diff=13834Rupak Chakraborty2009-12-04T22:56:15Z<p>Chakraborty: </p>
<hr />
<div>==Keywords==<br />
[[Ostwald's rule of stages]]<br />
<br />
[[Granular matter]]<br />
<br />
[[Gecko foot structure]]<br />
<br />
[[Poisson-Boltzmann equation]]<br />
<br />
[[Nanofluid]]<br />
<br />
[[Polymer forces]] (length scales)<br />
<br />
==Papers==<br />
[[Multiphase transformation and Ostwald’s rule of stages during crystallization of a metal phosphate]]<br />
<br />
[[Liquid–solid-like transition in quasi-one-dimensional driven granular media]]<br />
<br />
[[Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements]]<br />
<br />
[[Ion distributions near a liquid-liquid interface]]<br />
<br />
[[Spreading of nanofluids on solids]]<br />
<br />
[[Nonlinear elasticity in biological gels]]</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=Nonlinear_elasticity_in_biological_gels&diff=13833Nonlinear elasticity in biological gels2009-12-04T22:55:13Z<p>Chakraborty: </p>
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<div>==Reference==<br />
Storm, C., Pastore, J.J., et al., Nature 435 (2005).<br />
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==Keywords==<br />
elasticity, polymer gel, [[Polymer forces | polymer length scales]]<br />
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==Summary==<br />
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[[Image:Nonlinear_1.jpg |right| |200px| |thumb| Figure 1.]]<br />
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[[Image:Nonlinear_2.jpg |right| |200px| |thumb| Figure 2.]]<br />
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[[Image:Nonlinear_3.jpg |right| |200px| |thumb| Figure 3.]]<br />
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This paper deals with elucidating the nonlinear elastic properties common to biological gels. As shown in Fig. 1, the shear moduli of various biological networks vary over orders of magnitude as a function of applied strain. The molecular structures responsible for the nonlinear elasticity are unknown, but the paper reports a molecular theory that accounts for the strain-stiffening in these biological networks.<br />
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The proposed model starts with the force of a single filament. To get from there to the bulk elastic properties of a network of filaments, several assumptions are made. First, the network is assumed to be isotropic, in which a pair of nodes are connected by independent semi-flexible filaments. It is also assumed that no torques are exerted at nodes, so that filaments can stretch or compress but cannot bend. In addition, the deformations are assumed to be affine. Lastly, all filament end-to-end lengths are assumed to be equal.<br />
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The experimental shear moduli along with the theoretical prediction is shown in Figure 2. Although the theoretical prediction agrees for low strains, it quickly becomes invalid at higher strains. To correct this, the authors eliminated the restriction that all filament end-to-end lengths are equal. Instead, they take a the distribution of end-to-end lengths to be the equilibrium distribution of end-to-end lengths of filaments of a given (constant) contour length. The results of this extended theory are shown in Figure 3, along with experimental results. <br />
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The extended theory shows better agreement with experiment, but there is still significant deviation, especially at higher strains. One could imagine that the reason for disagreement is the simplifying assumption that no torques are exerted at nodes. This assumption does not seem realistic, as TEM images have shown that filaments do indeed bend in response to external forces. Taking this into account would be difficult, but would probably give more accurate predictions of real biological systems.</div>Chakrabortyhttp://soft-matter.seas.harvard.edu/index.php?title=File:Nonlinear_3.jpg&diff=13832File:Nonlinear 3.jpg2009-12-04T22:54:41Z<p>Chakraborty: </p>
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<div></div>Chakraborty