# Difference between revisions of "Hydrodynamic metamaterials: Microfabricated arrays to steer, refract and focus streams of biomaterials"

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The parameters, which uniquely define an array of posts determine the angle, at which large particles are deflected, and also the critical size of particles, which are deflected. | The parameters, which uniquely define an array of posts determine the angle, at which large particles are deflected, and also the critical size of particles, which are deflected. | ||

The authors define four parameters, the horizontal spacing <math>\lambda</math>, the vertical gap between posts, G, the vertical offset between rows, <math>\delta</math>, and the obstacle size, D. | The authors define four parameters, the horizontal spacing <math>\lambda</math>, the vertical gap between posts, G, the vertical offset between rows, <math>\delta</math>, and the obstacle size, D. | ||

+ | |||

Qualitatively, for a given G, the critical particle size decreases as the angle is increased | Qualitatively, for a given G, the critical particle size decreases as the angle is increased | ||

+ | |||

<math>\alpha = tan^{-1}\frac{\delta}{\lambda}</math> | <math>\alpha = tan^{-1}\frac{\delta}{\lambda}</math> | ||

− | For a fixed particle size, the critical particle size decreases with G. | + | |

+ | For a fixed particle size and angle, the critical particle size decreases with G. | ||

+ | These behave more or less what as we would expect. | ||

+ | |||

+ | The likely cause of the observed results is that the hydraulic object is much larger than the cross-sectional gap between the posts. | ||

+ | Objects with large hydraulic diameters are less likely to fit through the space between the post. | ||

+ | We would also expect the critical size to change as a function of flow rate. | ||

+ | The inertia of particles in the flow is a parameter that we expect to contribute to which mode the particle finds itself in. | ||

+ | This dependence is not addressed in the paper. | ||

== Applications == | == Applications == |

## Revision as of 18:15, 16 November 2009

Original entry: Warren Lloyd Ung, APPHY 225, Fall 2009

"Hydrodynamic metamaterials: Microfabricated arrays to steer, refractt, and focus streams of biomaterials"

Keith J. Morton, Kevin Loutherback, David W. Inglis, Ophelia K. Tsui, James C. Sturm, Stephen Y. Chou, and Robert H. Austin.

Proceedings of the National Academy of Science.

## Soft Matter Keywords

Hydrodynamic metamaterials, microfluidics, biomaterials, separation

## Summary

Hydrodynamic metamaterials are microfabricated structures that have can be used to manipulate particles to flow along particular paths. In many ways, they are analogous to traditional optical materials, except rather than modifying the propagation of electromagnetic light waves, these metamaterials modify the propagation of particles through a microfluidic channel.

The hydrodynamic metamaterial discussed in here is an asymmetric array of posts. The asymmetry arises, because each subsequent column of posts is vertically offset from the previous column by a small distance. As a result, the rows of posts are at an angle, <math>\alpha</math>, relative to the direction of flow (Figure 1). Small particles and molecules follow the streamlines of fluid through the channel, and as such, they simply follow the direction of bulk fluid flow through the channel, while moving around any posts in their way. On the other hand, particles larger than some critical size cannot do the same, they cannot fully move around the posts, so each time they encounter a new post, they are deflected it. The large particles, thus, follow the asymmetry of the channel, and propagate at the angle <math>\alpha</math> relative to the flow direction. This ability to segregate particles according to their sizes can be compared with the ability of birefringent crystals to separate different polarizations of light in space.

These metamaterials offer exquisite control over the flow direction of particles in solution. By putting metamaterials with different parameters next to one another, it is possible to create devices to control the direction, along which particles of different sizes move. It is also possible to place several different arrays within a single channel to achieve complex devices. The authors showcase a range of possible applications for these simple microstructures, each time demonstrating its analogy in optics.

## Soft Matter Discussion

The parameters, which uniquely define an array of posts determine the angle, at which large particles are deflected, and also the critical size of particles, which are deflected. The authors define four parameters, the horizontal spacing <math>\lambda</math>, the vertical gap between posts, G, the vertical offset between rows, <math>\delta</math>, and the obstacle size, D.

Qualitatively, for a given G, the critical particle size decreases as the angle is increased

<math>\alpha = tan^{-1}\frac{\delta}{\lambda}</math>

For a fixed particle size and angle, the critical particle size decreases with G. These behave more or less what as we would expect.

The likely cause of the observed results is that the hydraulic object is much larger than the cross-sectional gap between the posts. Objects with large hydraulic diameters are less likely to fit through the space between the post. We would also expect the critical size to change as a function of flow rate. The inertia of particles in the flow is a parameter that we expect to contribute to which mode the particle finds itself in. This dependence is not addressed in the paper.

## Applications

Using these asymmetric arrays of posts as building blocks, it is possible to create devices which refract, focus or disperse particles selectively based on size.

Because these posts are already within a microfluidic channel, this is a powerful tool, which can already be integrated directly with many of the other complex microfluidic systems. For instance, one can imagine a system for studying mitotic cells, in which we separate cells based on their size, interrogate them with optical methods such as fluorescence, and then culture them to examine the resulting daughter cells all integrated in a single device.

This can also be used to create parallel monodisperse flows of particles.