Hi:
if you are familiar with the cartilage free swelling problem, you must have seen the boundray condition on cartilage-solution boundary where Mu=Mu*. Does this mean or imply that concentrations (or densities) of the components as well as the pressure on the boundary are the same as of those in the solution, i.e. does it mean that apparent density of water and ions are equal to the free solution and therefore are constant on the boundary. because that means the boundary is in equilibrium with solution and therefore the strain value on the boundary is set to zero.
Is that right?
Thank you,
Alireza
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Chemical potential and concentration
Hi Alireza,
By definition, the chemical potential of a species in a block of material is the work needed to squeze in one more molecule of that kind into the material. In general, it could be a function of the concentrations, the deformation state, temperature, etc. And different materials may have different functional forms for mu.
In equilibrium, just as you say, mu = mu*, so that the molecules can migrate in two directions of the interface freely. However, the deformation states on the two sides need not to be the same, also the materials are totally different. As a result, there is almost no chance for the concentrations to be the same on the two sides.
To speak of the pressure, it is really not a well defined quantity inside a soft tissue. If you think of it as mechanical pressure, then how are you going to measure it? If you define it just as a measure of chemical potential, say p = p0 + exp(mu/kT), then ofcourse p=p* at the interface, because mu=mu*.
Hope this answers your question.
Wei
In reply to Chemical potential and concentration by Wei Hong
Hi Wei:Thank you very much
Hi Wei:
Thank you very much for your response. By reviewing your papers, I found them very interesting, and it apears that your understanting of the thermodynamic phenomena of these kind of problems is far better than me. So please explain a little bit more about these points that you made in your response:
1-"the deformation states on the two sides need not to be the same". I always relate the deformation state with chemical potenial through pressure. what is not clear for me is: how the deformation state can be different while the chemical potential is the same reminding that there is a pressure term in the chemical potential?
2-"also the materials are totally different". Just as a reminder, the boundary we speak of, according to Lai 1991 to my understanding, is in the domain which is all cartilage, and there is no talk of solution AND cartilage, so that there is no concern about different materails.
I appreciate your comments.
Thank you very much,
Alireza