How to perform a simple solute transport analysis using a multiphasic material

[ateshian]

FEBio's multiphasic material and analysis module were developed to accommodate a host of complex behaviors that may be found in biological tissues, including solute and solvent transport, osmotic effects, solid matrix deformation, chemical reactions, etc. To accommodate these complex behaviors, FEBio uses the "effective fluid pressure" and "effective solute concentration" as nodal variables. These are related to the actual "fluid pressure" and "solute concentration" via relations described in the User's Manual.

However, in some cases, users may be interested in conducting a simple solute transport analysis without worrying about these complex behaviors. One option is to use the FEBioChem plugin. Alternatively, one can use a multiphasic analysis that can be suitably simplified to analyze a solute transport problem without these added complexities. Just follow these steps:

1. In the multiphasic material, set the osmotic_coefficient material to type "osm-coef-const" and set its value to 0. This will eliminate osmotic effects.
2. Fix the x,y,z-displacement components of the entire multiphasic domain to zero. (In FEBioStudio, use 'Select nodes' and 'Select backfacing' to rubber-band over the entire domain.) This means that any constitutive model can be used for the solid matrix of the multiphasic material (e.g., neo-Hookean), but this solid matrix will not deform.
3. Similarly, fix the fluid pressure to zero. This means that any constitutive model can be used for the permeability of the multiphasic material (e.g., perm-const-iso), but the solvent will not flow.

By fixing the displacement and pressure degrees of freedom, the only degrees of freedom that remain are those of the solute(s) defined in the multiphasic material. This means that the computational analysis is not burdened by having to solve for solid displacements or effective fluid pressure. The multiphasic analysis only solves for the effective solute concentrations. As usual for a multiphasic analysis, if the solutes are neutrally charged, their effective concentration is the same as their actual concentration.

The attached axisymmetric diffusion problem in a cylindrical disk illustrates this type of analysis (DiffusionNoOsmoticEffects.feb).

Gerard Ateshian

[apaz]

Dear Professor Ateshian,

I ran the problem you shared (DifussionNoOsmotic.feb) on FFEBioStudio 1.6, and the concentration field looks quite unstable, with very large values. Where would the error be in the file?

Regards,
Alex

[ateshian]

Hi Alex,

I just downloaded this file and ran it on FEBioStudio 1.6.1.48b2fcdd9 on a Mac running OS 10.15.7 and it ran fine, with expected outcomes for solute concentrations. Which operating system are you using? Can you share the log and xplt files of your results? I have attached mine.

Best,

Gerard

Archive.zip

[Wojtek]

Dear Professor Ateshian

I understand that concentration should be imposed in mM as the boundary condition. My question concerns now the difference between
<vartype="effective solute concentration"/>
<vartype="solute concentration"/>
in the provided example

Best,
Wojtek

[ateshian]

Hi Wojtek,

In general, "effective solute concentration" takes into account the molar concentration of a solute, the ambient electric potential, and non-ideal physico-chemical response within the solution, so that the effective solute concentration is really a measure of the electrochemical potential of the solute. In FEBio the "effective solute concentration" is a nodal degree of freedom, which means that the code solves for this nodal value at each time step. The "solute concentration" is the actual solute molar concentration (number of moles of solute per fluid volume). It is evaluated at integration points within an element.

In the example problem provided above we assume that solutes have neutral electrical charge (so the electric potential is zero) and we assume ideal physico-chemical conditions. In that case the "effective solute concentration" represents the same physical quantity as "solute concentration". However, since the former is evaluated at the nodes and the latter at element integration points, their values will not be exactly the same.

Best,

Gerard

[Wojtek]

Hello
Thank you for prompt answer

So this is the same case as in
https://forums.febio.org/forum/febio...sults#post4420.

The thing that bothers me though is the kappa with upper tilde in equation (3) of

https://help.febio.org/FEBio/FEBio_um_2_9/FEBio_um_2-9-Section-4.8.html#prev

It seems that this effective solubility is set to unity by default in https://help.febio.org/FebioUser/FEBio_um_3-4-4.9.4.1.html
Am I right?

[ateshian]

The effective solubility is a user-defined parameter. In the example file I shared, this parameter is specified in the material definition, under

<solubility type="solub-const">
    <solub>1</solub>
</solubility>

The default value in FEBioStudio is 1, but you can change it to anything you want.

Best,

Gerard