The surface force pore-¯ow (SFPF) model is based on solute-membrane material interactions at the membrane-solution interface. It has been used to model the transport of solute and solvent through membranes under the in¯uence of such forces and to determine separation ef®ciency based on the assumption of circular pores. It is evident from the model that the pore diameter has a strong bearing upon the separation ef®ciency and the mean separation ef®ciency can be determined from the pore size distribution. In this work a Monte Carlo simulation technique has been employed to generate a large number of sample pores from the mean and the standard deviation. The Gaussian distribution has been used to determine the separation ef®ciency in the SFPF model. The results have been compared with the available data for isopropanol/cellulose acetate/water system and the predicted values agree well with the published data.
List of symbolsA constant characterizing electrostatic repulsive force, m B constant characterizing van der Waals attractive force, m 3 b frictional function, dimensionless C A dimensionless solute concentration at the pore outlet c A molar solute concentration, mol/m 3 D constant characterizing steric repulsion at the interface, m D w Stokes radius of water, m D AB diffusivity of solute in water, m 2 /s f solute separation based on the solute concentration in the bulk feed, dimensionless f H true value of solute separation by membrane pore, dimensionless f H areav as de®ned in Eq. (26) f H diav as de®ned in Eq. (27) k mass transfer coef®cient, m/s k H random variate R a radius of the water channel in the membrane pore, m R b membrane pore radius, m R blo pore radius, m as de®ned in Eq. (20) R bhi pore radius, m as de®ned in Eq. (21) R bmean average pore radius, m m s permeation velocity, m/sGreek letters aq dimensionless solution velocity pro®le in a cylindrical pore b 1 dimensionless solution velocity b 2 dimensionless operating pressure k f DaR b q solution density, kgam 3 , or dimensionless radial distance r standard deviation of the normal pore size distribution, m g viscosity of the solution in the pore, Pa s / potential in the interfacial force ®eld, J/mol