Multiscale Modeling of Membrane Distillation: Some Theoretical Considerations

First, it is shown that the effective thickness of the membrane is the sum of the actual thickness, k(0)/U-L, and lambda C/(U-L) where k(0) is the thermal conductivity of the membrane matrix, lambda is the latent of vaporization of water, C is a parameter (defined as flux per unit thickness of membrane per unit of temperature driving force), and U-L is a coefficient combining the heat transfer coefficients on the feed side and the permeate side film. For typical conditions, the sum of the additional terms exceeds 100 mu m, which clearly shows that the flux is not inversely proportional to membrane thickness. Also, to a first approximation, the thermal efficiency is independent of membrane thickness. This work and the development of an overall mass-transfer coefficient for direct contact membrane distillation build upon the pioneering work of Giulio Sarti. Second, a reassessment of the traditional method for combining the Knudsen diffusion coefficient and the molecular diffusion coefficient suggests that the traditional sum of resistances approach engages in some double counting and thereby overestimates the resistance and consequently underestimates the flux.