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The study of particle transport in liquid filled membranes is of significant importance in membrane separation processes. It is frequently observed that a particle experiences extra resistance to its motion in a bound region (pore space) compared to an unbound region which is called “hindrance phenomena”. In the current research, the effect of the convective hindrance factor on the rejection coefficient of a rod-shaped particle in a membrane is theoretically studied.
Computational Fluid Dynamics (CFD) calculations were performed to predict the lag coefficient of a rod-shaped particle within a narrow channel. Initial simulations involved solving the Navier Stokes equation defined in an Arbitrary Lagrangian Eulerian frame (moving mesh) to predict the translational motion of a rod-shaped particle at a fixed orientation where the rotational motion of the particle was neglected. The reflection coefficients were determined using a centerline approximation by integrating the lag coefficient over all sterically allowed particle orientations.
Reflection coefficient data are reported for particles with aspect ratios of 2 and 4 with various relative particle radii. The results indicate that including hydrodynamic wall interactions (convective hindrance factor) in theoretical predictions increases the reflection coefficient by for 20-25% particles with aspect ratio equal to 2.
CFD simulations were also performed to study the effect of channel walls on the rotational and translational motion of a rod-shaped particle at low Reynolds number (Re<1). Predictions were made by fixing the initial particle orientation at 45o with respect to the pore axis with the particle at two different locations: the pore centerline and half the distance between the pore wall and the centerline. The particle translational and angular velocities obtained from the simulation results are used to predict the reflection coefficient of the particle in a membrane.