Pore size distributions have been obtained for three hydrophobic porous membranes from air-liquid displacement measurements, assuming the common model of cylindrical capillaries for the membrane and using flux equations which includes both diffusive and viscous mechanisms for transport in the gas phase in pores. The pore size distribution so obtained arid the same flux equations are used in order to predict the water vapour permeability through the membranes, characterised when employed in different membrane distillation configurations and operating conditions. In membrane distillation applications, where no viscous flux exists, the role of both Knudsen and molecular diffusion resistances is analysed. In membrane distillation applications which include diffusive and viscous transport, the contribution of both mechanisms is analysed.