Quemada¶

Module: fluid

Category: materialprop

Type string: "Quemada"

Parameters¶

Name	Description	Default	Units
`mu0`	zero shear rate viscosity	0	[P.t]
`H`	suspension volume fraction	0	[]
`k0`	k0	0	[]
`kinf`	kinf	0	[]
`gc`	criticial shear rate	1	[1/t]

The material type for a Quemada model ¹ is Quemada.

The viscous shear stress for this material model is

\[ \boldsymbol{\tau}=2\mu\mathbf{D} \]

where

\[ \mu=\frac{\mu_{0}}{\left(1-k\frac{H}{2}\right)^{2}} \]

and

\[ k=\frac{k_{0}+k_{\infty}\sqrt{\dot{\gamma}_{r}}}{1+\sqrt{\dot{\gamma}_{r}}}\,,\quad\dot{\gamma}_{r}=\frac{\dot{\gamma}}{\dot{\gamma}_{c}} \]

Here, \(\dot{\gamma}=\sqrt{2\mathbf{D}:\mathbf{D}}\) is the engineering shear rate.

Example:

<viscous type="Quemada">
    <mu0>0.03</mu0>
    <H>0.5</H>
    <k0>3.691</k0>
    <kinf>1.778</kinf>
    <gc>2.30</gc>
</viscous>

Quemada, DJRA, "Rheology of concentrated disperse systems II. A model for non-newtonian shear viscosity in steady flows", Rheologica Acta 17, 6 (1978), pp. 632--642. ↩