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2.9.1 Perfect Osmometer
Consider a porous medium with an interstitial fluid that consists of a solvent and one or more solutes, whose boundary is permeable to the solvent but not to the solutes (e.g., a biological cell). Since solutes are trapped within such a medium, is a constant in this type of problem. Since the boundary is permeable to the solvent, must be continuous across the boundary. Assuming ideal physicochemical conditions, , and zero ambient pressure, this continuity requirement implies that , where is the osmolarity of the external environment. Using (2.9-2), it follows that The reference configuration (the stress-free configuration of the solid) is achieved when and , from which it follows that , where is the value of in the reference state. Therefore (2.9.1-1) may also be written as and this expression may be substituted into (2.9-3) to evaluate the corresponding elasticity tensor.
A perfect osmometer is a porous material whose interstitial fluid behaves ideally and whose solid matrix exhibits negligible resistance to swelling ( . In that case and (2.9.1-2) may be rearranged to yield This equation is known as the Boyle-van't Hoff relation for a perfect osmometer. It predicts that variations in the relative volume of such as medium with changes in external osmolarity is an affine function of , with the intercept at the origin representing the solid volume fraction and the slope representing the fluid volume fraction, in the reference configuration.
FEBio implements the relation of (2.9.1-2) for the purpose of modeling equilibrium swelling even when solid matrix stresses are not negligible. The name “perfect osmometer” is adopted for this model because it reproduces the Boyle-van't Hoff response in the special case when .