A two-interface transport model with pore-size distribution for predicting the performance of direct contact membrane distillation (DCMD)

We investigated fundamental aspects of heat and mass transfer of direct contact membrane distillation. Molar flux of water vapor through a membrane pore was analytically obtained by solving Fickʹs law in the original differential form. Axial variation of the temperature profile was derived as exponentially decreasing, and was found to be linear due to small membrane thickness and dominant heat conduction through the solid part of the membrane. An alternative expression of water vapor pressure at a constant temperature was developed using experimental data of water latent heat for evaporation, and was used to calculate the concentration of water vapor in the membrane pore. The effective diffusion coefficient was obtained by combining Knudsen and Brownian diffusion coefficients with Bosanquetʹs assumption. The effective diffusivity and mean free path of water vapor slowly decrease in the axial direction, and the vapor concentration increases along the membrane pore primarily due to the linearly decreasing temperature. We found that the required heat flux monotonously increases with the vapor flux through membrane pores. Finite variance of a pore size distribution provides less vapor flux than that of mono-dispersed pores. This is because a number of smaller pores than the average pore size significantly hinders the vapor transport across the porous membrane. Theoretical prediction of permeate flux agrees very well with experimental observations reported in the literature.