Statistical theory of vapor transport through hollow fiber membranes in vacuum membrane distillation: Effusion analogy

Abstract

This paper developed a new theory of vacuum membrane distillation, which can be readily applicable to other membrane distillation processes. Using the molecular kinetic theory and statistical mechanics, we derived that the driving force of the vapor flux is the gradient of the incidence rate, which is defined as the number of molecules colliding a flat wall per unit surface area per unit time. Knudsen and Brownian diffusion are seamlessly combined into one governing equation without any forceful assumptions. More importantly, the effect of the vacuum temperature on the mass and the heat flux is studied using the dependence of the incidence rate on temperature. It is concluded that the insensitiveness of the vapor flux on saline concentration and recycling of hot feed stream can be systematically used to design of membrane crystallization processes in the future. (C) 2017 Elsevier B.V. All rights reserved.