Nanofiltration mass transfer at the entrance region of a slit laminar flow

A numerical model to predict laminar flows hydrodynamics and concentration polarization of salt aqueous solutions in a slit is proposed and experiment ally validated. Physical modeling for the flow and for the mass transfer pr ocess is incorporated, in association with the osmotic pressure constitutiv e equation and a variation law for the membrane intrinsic rejection coeffic ient. The finite volume formulation is used with the SIMPLE algorithm to so lve the discretized equations derived from the partial nonlinear differenti al equations of the mathematical model. The convection terms of the transpo rt equations are discretized by the second-order hybrid central differences /upwind scheme. The experimental cell is a slit 200 mm x 30 mm x 2 mm that simulates the two-dimensional hydrodynamic flow conditions of the open feed channel of a spiral wound module. The predicted values at the hydrodynamic ; entrance region for different permeation velocities and rejection coeffic ients for sodium sulfate solutions, and for a single Schmidt number of 850, are compared against the corresponding experimental values and exhibit an excellent agreement. A new mass transfer correlation St(p) = 1 + 3.68 x 10( -4)(x/ h)(-1.11)Re(0.95)Rep(-1.79) is proposed.