Irreversible thermodynamics solute flux density

Our final objective in this chapter is to obtain an expression for the solute flux density, Js> that takes into consideration the coupling of forces and fluxes introduced by irreversible thermodynamics. Using Equations 3.34b and 3.35, we note that... 

Equation 3.48 indicates that not only does Js depend on An, as expected from classical thermodynamics, but also that the solute flux density can be affected by the overall volume flux density, Jv. In particular, the classical expression for Js for a neutral solute is P Ac (Eq. 1.8), which equals (Pj/RT)ATlj using the Van t Hoff relation (Eq. 2.10 II, = PT Cj). Thus to, is analogous to P/RT of the classical thermodynamic description (Fig. 3-19). The classical treatment indicates that Js is zero if An is zero. On the other hand, when An is zero, Equation 3.48 indicates that Js is then equal to c,(l - cr,)/y solute molecules are thus dragged across the membrane by the moving solvent, leading to a solute flux density proportional to the local solute concentration and to the deviation of the reflection coefficient from 1. Hence, Pj may not always be an adequate parameter by which to describe the flux of species , because the interdependence of forces and fluxes introduced by irreversible thermodynamics indicates that water and solute flow can interact with respect to solute movement across membranes. 

We can profitably reexamine certain aspects of the movement of solutes into and out of cells and organelles by using the more general equations from irreversible thermodynamics. One particularly important situation amenable to relatively uncomplicated analysis occurs when the total volume flux density Jv is zero, an example of a stationary state. This stationary state, in which the volume of the cell or organelle does not change over the time period of interest, can be brought about by having the net volume flux... 

Measurements of incipient plasmolysis can be made for zero volume flux density (Jv = 0) and for a simple external solution (x° = 0) at atmospheric pressure (P° = 0). In this case, Equation 3.41 is the appropriate expression from irreversible thermodynamics, instead of the less realistic condition of water equilibrium that we used previously. For this stationary state condition, the following expression describes incipient plasmolysis (P1 = 0) when the solutes can cross the cell membrane ... 

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