Time necessary to reach equilibrium in a membrane transport

Example 10.3 Time necessary to reach equilibrium in a membrane transport Consider two containers of volumes Iand I 2 and the initial solute concentrations of c, and c2 (c, c2) separated by a permeable membrane. We want to know the time necessary to reach the equilibrium at which cx = c2. The changes in the number of moles of solute in containers 1 and 2 are calculated as a function of the area. 1 of the membrane and the solute flow J% 

In practice, after a time of 4t0, the concentration differences between the two containers will vanish, and t0 is considered the characteristic time. This approximation may be useful in cellular transport, and artificial kidneys and lungs. 

6 Frictional Forces and Resistance-Type Phenomenological Coefficients 

We can express the phenomenological coefficients in terms of the frictional forces assuming that for a steady-state flow, the thermodynamic forces Xare counterbalanced by a sum of suitable frictional forces F. Thus, for a solute in an aqueous solution, we have 

The terms Fsm and comprise complex hydrodynamic interactions within the membrane matrix and should be regarded as macroscopic averages. For sufficiently swollen membranes, however, Fsw, which indicates the interactions of solute and solvent, may approach free diffusion. 

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