| Abstract: | Using Kedem-Katchalsky thermodynamic formalism, the mathematical model describing concentration difference through a membrane (Ci-Ce) in concentration polarization conditions was elaborated. Concentration polarization is connected with concentration boundary layers (l(l), l(h)) creation on both sides of a polymeric membrane (M). These layers both with membrane are the complex l(1)/M/l(h). Obtaining expression, which is square equation considering volume flux (Jvm), contain the transport parameters of membrane (omega m), concentration boundary layers (omega l, omega h) and solution concentration in initial moment (Ch, Cl). Calculations performed on the basis of obtained square equation show that for a polymeric membrane with fixed transport properties, concentration difference (Ci-Ce) is nonlinear function of solution concentration (Ch-Cl). The nonlinearity is connected with appearance of the convection instability for (Ci-Ce) > 0.015 mol l(-1), breaking symmetry of complex l(h)/M/l(l) in relation to gravitational direction, what is the reason of increase (Ci-Ce) and volume and solute fluxes. |
