Self-adjusting, combined diffusion in direct contact and vacuum membrane distillation

Coupled effects of two representative mass transfer phenomena in membrane distillation, i.e., Brownian and Knudsen diffusion, are investigated using molecular kinetics and statistical mechanics. Diffusive mass transfer along the membrane pore is analogously solved using the conventional theory of effusion phenomena, having both pressure and temperature gradients as driving forces. We quantitatively found that the molecular mean speed slightly increases in the presence of a temperature gradient, and the curvature effects of hollow fiber membranes are small if the inner radius is larger than the membrane thickness. In vacuum membrane distillation and direct contact membrane distillation, discarding the smaller of the Brownian or Knudsen diffusion may cause noticeable error in predicting the production rate of freshwater. When both the diffusion mechanisms are present, their coupling hinders the migration of the water vapor through pore spaces. Vapor molecules seem to take routes that minimize the diffusive coupling.