Expression for the Film Mass-Transfer Coefficient of Charged Solutes in a Liquid Stream Flowing in Packed Beds of Charged Particles and Charged Porous Monoliths

Numerous biochemical and chemical separation and reaction systems have low Reynolds and high Peclet numbers and involve mass transfer of charged solutes between a pressure-driven flowing liquid stream and packed beds of charged particles or charged porous monoliths. For such systems, an expression for determining the film mass-transfer coefficient of a charged solute in a pore (channel) was derived from fundamental expressions of physics. In the derivation of the expression for the film mass-transfer coefficient, mass transport by the mechanisms of convection, diffusion, and electrophoretic migration was taken into account. by considering geometrical (physical) similarity between all pores in a packed bed of charged particles or in a charged porous monolith and the existence of a macroscopic pressure field with uniform gradient, the film mass-transfer coefficient is found to be the same over all pores regardless of size. The values of the parameters in the derived expression for the film mass-transfer coefficient depend on the value of the size of the electrical double layer (Debye length), the magnitude of the zeta potential on the surface of the pores, the relative concentrations of the cations and anions of the supporting electrolyte and of the charged solute, the interaction (adsorption) isotherm of the charged analyte with the charged pore surface, and the values of the charge and Peclet numbers of the charged analyte and the cations and anions of the background/buffer electrolyte. The expression for the film mass-transfer coefficient presented in this work could be used to analyze and correlate experimental data on the rate of mass transfer between charged porous monoliths or packed beds of particles having charged pore surfaces and a flowing liquid stream containing charged species