Transport coefficients in n membranes systems

The nonlinear equations for water and solute transport across a series array of two membranes have been extended to a series array of n membranes, in order to account for the complex structure of epithelia. The general equations have the same form as those found for the double array and also show a nonlinear dependence on the initial solute concentration C', above which a solute concentration difference is eventually built up. Thus the volume flow equation consists of three different nonlinear addends, containing respectively the hydrostatic pressure difference, the osmotic pressure difference and C'. From this equation the hydraulic permeability and osmotic flow coefficients can be derived, also depending on C'. Around zero hydrostatic pressure difference the hydraulic permeability is lower than predicted by the classical law by Darcy, but tends to the predicted value for high flow values. The ratio between the osmotic flow and filtration coefficients gives a C' independent solute reflection coefficient.