osmotic virial expansion

Module: solid

Category: material

Type string: "osmotic virial expansion"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
phiw0	phiw0	-6.27744e+66	[]
cr	cr	-6.27744e+66	[]
c1	c1	0	[]
c2	c2	0	[]
c3	c3	0	[]

Description

The material type for osmotic pressure from virial expansion is osmotic virial expansion.

The Cauchy stress for this material is

\[ \boldsymbol{\sigma}=-\pi\mathbf{I}, \]

where \(\pi\) is the osmotic pressure, given by

\[ \pi=c_{1}c+c_{2}c^{2}+c_{3}c^{3},\quad c=\frac{\varphi_{r}^{w}c_{r}}{J-1+\varphi_{r}^{w}}\,, \]

\(c\) is the solute concentration in the current configuration, and \(J=\det\mathbf{F}\) is the relative volume.

This osmotic swelling pressure in the interstitial fluid of a porous material represents an entropic mechanism whose magnitude is independent of the external bath osmolarity. Typically, this material should be used in a solid mixture where the swelling pressure is resisted by a solid matrix in tension.

Example:

<Material>
  <material id="1" type="solid mixture">
    <solid type="osmotic virial expansion">
      <phiw0>0.8</phiw0>
      <cr lc="1">100</cr>
      <c1>2.436e-6</c1>
      <c2>0</c2>
      <c3>0</c3>
    </solid>
    <solid type="spherical fiber distribution"/>
  </material>
</Material>
<LoadData>
  <loadcurve id="1" type="smooth">
    <loadpoint>0,0</loadpoint>
    <loadpoint>1,1</loadpoint>
  </loadcurve>
</LoadData>