Capillary mass transfer

Abstract

Makiya (1970) has derived the following equations for capillary mass transfer of a nonelectrolyte based on irreversible thermodynamics : Solute d dz Specifying the initial conditions of concentration, volumetric 00w rate, and pressure, he solved these equations for selected membrane parameters using the IBM-CSMP program (1969). In this note simplifications of the above equations are made which permit analytical solutions in dimensionless form for ideal semipermeable membranes and for pure water transport.An ideal semipermeable membrane transfers no solute. This condition requires that the phenomenological coefficients be equal Lp = LPD = LD as shown by Katchalsky and Curran (1965). Equation ( 1 ) is consistent with this definition since it shows that QWCA is constant (= QwoCAo) down the capillary indicating no solute mass transfer in the radial direction.Since the kinetic energy of a fluid flowing in a capillary is small (low Reynolds number) compared to frictional effects, Equation ( 3 ) can be simplified toUpon substitution of Equation (5) for P and CA = (QwoCAO)/QW into Equation ( 2 ) one getsThe term 1/Qw is nonlinear, and no solutions were found. Therefore 1/Qw was expanded in a Taylor series, and the first two terms were taken to give tho following equation: