Difference between revisions of "Viscosity"

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== Introduction ==
 
== Introduction ==
Viscosity is a measure of the fluid's internal resistance to flow. Formally, for Newtonian fluids, the shear stress is related to the shear strain via:
+
Viscosity is a measure of the fluid's internal resistance to flow. Formally, for Newtonian fluids, the shear stress is related to the shear strain via (where p is the pressure):
<math>\tau_{ij} = \mu (\frac{\del u_i}{\del x_j} + \frac{\del u_j}{\del x_i})</math>
+
<math> \tau _{ij} = -p \delta _{ij} + \mu (\frac{\delta u_i}{\delta x_j} + \frac{\delta u_j}{\delta x_i})</math>
  
Stress is a 2nd rank tensor, where we keep the standard convention that <math>\tau_{ij} </math> refers to the stress on the 'i' face in the 'j' direction (when doing force balances) and is related to the shear strain via the dynamic viscosity. Note that inviscid fluids cannot support shear stress, as evient by the above relation.  
+
Stress is a 2nd rank tensor, where we keep the standard convention that <math>\tau_{ij} </math> refers to the stress on the 'i' face in the 'j' direction (when doing force balances) and is related to the shear strain via the dynamic viscosity. Note that inviscid fluids cannot support shear stress, as evident by the above relation.  
  
 
For non-Newtonian fluids, this relationship can be nonlinear. Some fluids can exhibit shear thinning (viscosity deacreases with shear rate) and shear thickening. Viscosity can be measured using a rheometer, such as the cone an plate viscometer which creates a relatively uniform value of shear stress.  
 
For non-Newtonian fluids, this relationship can be nonlinear. Some fluids can exhibit shear thinning (viscosity deacreases with shear rate) and shear thickening. Viscosity can be measured using a rheometer, such as the cone an plate viscometer which creates a relatively uniform value of shear stress.  
  
 
Kinematic viscosity is useful for characterizing the ratio of the intertial to viscous forces (via the Reynold's number), where the kinematic viscosity is  
 
Kinematic viscosity is useful for characterizing the ratio of the intertial to viscous forces (via the Reynold's number), where the kinematic viscosity is  
<math>\nu = \mu / \rho</math>
+
<math> \nu = \mu / \rho</math>
 
and the Reynold's number is
 
and the Reynold's number is
<math> Re =
 
 
  
 +
<math> Re = Lv/ \nu</math> where L is the characteristic length of the systems, and v is the flow velocity.
  
 +
The viscosity of a fluid can be estimated from the elastic modulus, G (Energy per volume) and the characteristic time of the system
 +
<math> \tau </math> via
 +
<math> \mu = G \tau /2 </math>
  
 +
== References ==
 +
[[Viscosity and molecular properties#Viscosity|Viscosity]] in [[Viscosity and molecular properties]] in the [[General Introduction]] from [[Main Page#Lectures for AP225|Lectures for AP225]].
  
 +
[[Elasticity and viscosity#What is the meaning of viscosity?|Viscosity]] in  [[Viscosity, elasticity, and viscoelasticity]] from [[Main Page#Lectures for AP225|Lectures for AP225]].
  
 +
http://en.wikipedia.org/wiki/Viscosity
  
 +
http://en.wikipedia.org/wiki/Reynolds_number
  
  
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[[Elasticity and viscosity#What is the meaning of viscosity?|Viscosity]] in  [[Viscosity, elasticity, and viscoelasticity]] from [[Main Page#Lectures for AP225|Lectures for AP225]].
 
[[Elasticity and viscosity#What is the meaning of viscosity?|Viscosity]] in  [[Viscosity, elasticity, and viscoelasticity]] from [[Main Page#Lectures for AP225|Lectures for AP225]].
 
 
 
 
  
 
== Keyword in references: ==
 
== Keyword in references: ==

Latest revision as of 16:37, 13 December 2011

Entry by Robin Kirkpatrick


Introduction

Viscosity is a measure of the fluid's internal resistance to flow. Formally, for Newtonian fluids, the shear stress is related to the shear strain via (where p is the pressure): <math> \tau _{ij} = -p \delta _{ij} + \mu (\frac{\delta u_i}{\delta x_j} + \frac{\delta u_j}{\delta x_i})</math>

Stress is a 2nd rank tensor, where we keep the standard convention that <math>\tau_{ij} </math> refers to the stress on the 'i' face in the 'j' direction (when doing force balances) and is related to the shear strain via the dynamic viscosity. Note that inviscid fluids cannot support shear stress, as evident by the above relation.

For non-Newtonian fluids, this relationship can be nonlinear. Some fluids can exhibit shear thinning (viscosity deacreases with shear rate) and shear thickening. Viscosity can be measured using a rheometer, such as the cone an plate viscometer which creates a relatively uniform value of shear stress.

Kinematic viscosity is useful for characterizing the ratio of the intertial to viscous forces (via the Reynold's number), where the kinematic viscosity is <math> \nu = \mu / \rho</math> and the Reynold's number is

<math> Re = Lv/ \nu</math> where L is the characteristic length of the systems, and v is the flow velocity.

The viscosity of a fluid can be estimated from the elastic modulus, G (Energy per volume) and the characteristic time of the system <math> \tau </math> via <math> \mu = G \tau /2 </math>

References

Viscosity in Viscosity and molecular properties in the General Introduction from Lectures for AP225.

Viscosity in Viscosity, elasticity, and viscoelasticity from Lectures for AP225.

http://en.wikipedia.org/wiki/Viscosity

http://en.wikipedia.org/wiki/Reynolds_number



See also:

Viscosity in Viscosity and molecular properties in the General Introduction from Lectures for AP225.

Viscosity in Viscosity, elasticity, and viscoelasticity from Lectures for AP225.

Keyword in references:

An active biopolymer network controlled by molecular motors

A Cascade of Structure in a Drop Falling from a Faucet

David Turnbull (1915-2007). Pioneer of the kinetics of phase transformations in condensed matter

Homogeneous flow of metallic glasses: A free volume perspective

Multiscale approach to link red blood cell dynamics, shear viscosity, and ATP release

Painting with drops, jets, and sheets

Stress Enhancement in the Delayed Yielding of Colloidal Gels