Cross fluid: Difference between revisions

Revision as of 13:00, 16 July 2006

A Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the following equation:

<math> \mu_{\operatorname{eff}}(\dot \gamma) = \frac {\mu_0}{1 + ({\frac {\mu_0 \dot \gamma} {\tau ^ *}})^{1-n} } </math>

where

<math> \mu_{\operatorname{eff}}(\dot \gamma) </math> is viscosity as a function of shear rate,

<math> \mu_0 </math>, <math> \tau ^ * </math> and n are coefficients.

At low shear rate (<math> \mu_0 \dot \gamma \ll \tau^* </math>), cross fluids behave as Newtonian fluids and at high shear rate (<math> \mu_0 \dot \gamma \gg \tau^* </math>) as power-law fluids.

@@ Line 2: / Line 2: @@
 <math>
-\mu_\mbox{eff}(\dot \gamma) = \frac {\mu_0}{1 + ({\frac {\mu_0 \dot \gamma} {\tau ^ *}})^{1-n}  }
+\mu_{\operatorname{eff}}(\dot \gamma) = \frac {\mu_0}{1 + ({\frac {\mu_0 \dot \gamma} {\tau ^ *}})^{1-n}  }
 </math>
 where
-:<math> \mu_\mbox{eff}(\dot \gamma) </math> is [[viscosity]] as a function of [[shear rate]],
+:<math> \mu_{\operatorname{eff}}(\dot \gamma) </math> is [[viscosity]] as a function of [[shear rate]],
 :<math> \mu_0 </math>, <math> \tau ^ * </math> and ''n'' are coefficients.
-At low [[shear rate]] (<math> \mu_0 \dot \gamma <\ <\ \tau^* </math>), cross fluids behave as [[Newtonian fluid]]s and at high [[shear rate]] (<math> \mu_0 \dot \gamma >\ >\ \tau^* </math>) as [[power-law fluid]]s.
+At low [[shear rate]] (<math> \mu_0 \dot \gamma \ll \tau^* </math>), cross fluids behave as [[Newtonian fluid]]s and at high [[shear rate]] (<math> \mu_0 \dot \gamma \gg \tau^* </math>) as [[power-law fluid]]s.
 ==See also==
 *[[Navier-Stokes equations]]
-*[[Fluids]]
+*[[Fluid]]
 *[[Carreau fluid]]
 *[[Power-law fluid]]
-*[[Generalized Newtonian fluids]]
+*[[Generalized Newtonian fluid]]
 [[Category: Non-Newtonian fluids]]