An analytical flux decline model for membrane distillation
Deposit of suspended solids and scale formation of dissolved solids on the membrane surface result in decline of flux that is a major problem in a membrane distillation (MD) process. The descending flux rate is modeled by incorporating the scaling and/or intermediate pore blocking followed by cake formation concepts into the normal flux equation. The aim of this paper is to investigate the mass transfer phenomena and provide a detailed mathematical model of fouling in MD. The force balance and pore blockage theories explain open area reduction on the membrane surface. Equilibrium of hydrodynamic-forces on solutes yields a differential equation to determine the function of membrane roughness. The pore blockage theory is illustrated via a modified expression of clogging. Subsequently, combination of derived equations results in permeate flux reduction model. The developed model is validated through a set of observations and provided excellent fits of a range of experimental flux data. The effect of operating conditions, particle size, crystal shapes and concentration of feed solution on the decline of flux is investigated using the proposed model. It is observed that the moment of rapid decline of flux is dependent significantly on density, size of the particles and flow-rate.