Free swelling/shrinking

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  • kingina
    Junior Member
    • Feb 2015
    • 11

    Free swelling/shrinking

    Hi,

    I'm trying to simulate a free shrinking/swelling of a tissue submerged in an infinite bath using biphasic-solute model. I know that the pressure prescribed at the boundary for swelling is equivalent to p=R*T*c and p=-R*T*c for shrinking, but I'm not sure how to simulate the bath itself. Can I prescribe the pressure and concentration straight at the bath/tissue boundary, or should I create an infinite bath that sits on top of the tissue and apply biphasic-solute contact to obtain the solution? I've got both versions running but both produce different results in terms of displacements and strains, and I'm not sure what is the correct path/solution for this?

    Regards,

    Kinga
  • ateshian
    Developer
    • Dec 2007
    • 1824

    #2
    Hi Kinga,

    In a biphasic-solute analysis the porous material may include one neutral solute, let's call it A. In any analysis you can choose to prescribe the initial concentration cA0 of that solute inside the material.

    Osmotic shrinking/swelling can be performed in two ways: (1) Assume that the infinite bath contains solute A at a different concentration than cA0 (e.g., cA>cA0 for osmotic shrinking and cA<cA0 for osmotic swelling). However, for this option the shrinking/swelling will be transient and the tissue volume may return to its initial value after the diffusion of solute A into or out of the tissue has ended. For this type of analysis you need to prescribe the concentration cA and the pressure (-R*T*cA) as boundary conditions. (2) Assume that the infinite bath contains some other solute B at a concentration cB. This solute cannot transport into the tissue (remember that a biphasic-solute model only allows one solute, which we chose to be A). When cB > cA0 the tissue will shrink, when cB<cA0 the tissue will swell. At steady state the change in volume will persist. For this analysis you only prescribe a pressure boundary condition (-R*T*cB).

    For both cases you don't need to model the infinite bath explicitly. You only need to prescribe boundary conditions on the biphasic-solute material.

    Finally, for case (2) above, you can choose the special case cA0 = 0, in which case prescribing p=-R*T*cB will always produce shrinking (you can't swell the biphasic-solute material if it does not contain a solute).

    Let me know if you need further clarifications.

    Best,

    Gerard

    Comment

    • kingina
      Junior Member
      • Feb 2015
      • 11

      #3
      Dear Gerard,

      Thank you very much for clarifying this for me. I think I understand it now.

      Best regards,

      Kinga

      Comment

      • kingina
        Junior Member
        • Feb 2015
        • 11

        #4
        Dear Gerard,

        Just to clarify something. If my biphasic solute model is at the initial concentration C_A0=500mM, do I need to prescribe both Initial Concentration and Initial pressure? In this case C_A0=500mM and Initial Fluid Pressure =-RTC_A0=-1.238786.
        And then submerge in a bathing solution of smaller concentration C_B=100mM to induce swelling, therefore my Boundary Conditions at the face exposed to the bathing solution would be p=-RTC_B=0.2477572.

        I was going through the user manual and read the part about Prescribing Initial Conditions which says: 'When a multiphasic material is initially exposed to a given external environment with effective pressure p* and effective concentrations c*, the initial conditions inside the material should be set to p=p* and c=c* in order to expedite the evaluation of the initial state of swelling.'

        Previously I only prescribed the Initial concentration, which also induced swelling, so it hasn't crossed my mind that it could be wrong.

        Many thanks,

        Kinga

        Comment

        • ateshian
          Developer
          • Dec 2007
          • 1824

          #5
          Hi Kinga,

          Just to clarify something. If my biphasic solute model is at the initial concentration C_A0=500mM, do I need to prescribe both Initial Concentration and Initial pressure? In this case C_A0=500mM and Initial Fluid Pressure =-RTC_A0=-1.238786.
          Yes, both should be applied to reproduce that initial equilibrium state.

          Let me know if you need further clarifications.

          Best,

          Gerard

          Comment

          • kingina
            Junior Member
            • Feb 2015
            • 11

            #6
            Dear Gerard,

            I’ve conducted free swelling experiments that allowed me to measure the through thickness strain of the cartilage tissue. They show high strain at the cartilage surface and, I’m trying to create a biphasic-solute model that can replicate that. At the start of the experiments, the tissue is equilibrated in saline solution of c=2500mM and then submerged in c=150mM solution to induce free swelling. As mentioned above, I used the free swelling approach (2) where two different solutes are used. The reason for this is that the displacement seen experimentally is not transient and is visible for the duration of the experiments.
            The model is a simple 1x1mm cube, constrained on all sides and only the top surface is allowed to swell. My initial conditions are C_A0=2500mM and p0=2500*298*8.314*10^-6=-6.19393, and my boundary conditions are p* that goes from -6.19393 to -0.371636 (-R*T*C_B). I’ve got the model up and running, however, I’m still unsure if this is the right approach. Is using two different solutes for the free swelling realistic for the comparison to my experiment? Or would you recommend a different approach to this? The overall pattern of the strain and surface displacement seems reasonable in comparison with the experiment. Any insight into this would be greatly appreciated.
            Surface_displacement.pngStrain.png

            Best regards,
            Kinga

            Comment

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