Thermo-osmotic coefficients in membrane distillation: Experiments and theory for three types of membranes

The thermo-osmotic coefficient of a porous medium is the ratio of the mass flow rate and the temperature difference that drives the flow. Thermo-osmotic coefficients of the Millipore DuraPore HVHP, GVHP and VVHP membranes have been measured using a new apparatus designed to provide accurate mass flux measurements with tightly controlled temperatures, pressures, and compositions on the feed and distillate side. To properly analyze the experimental data, recommendations on data reduction procedures anchored in non-equilibrium thermodynamics are discussed. An expression is presented for the apparent energy of activation of the transport process in terms of the derivative of the thermo-osmotic coefficient with respect to the inverse mean temperature. The expression is shown to accurately predict the temperature dependence of the thermo-osmotic coefficients from experiments. The expression is next used to explain observations in similar porous systems from the literature. Based on this, an optimization scheme to find the optimal mean pore radius to maximize the power density of a pressure-retarded membrane distillation (PRMD) process is presented. For membranes with properties similar to the Durapore XXHP series membranes, the optimal pore radius is found to be between 1 and 10 nm. It is shown that the power density can benefit greatly from a narrow pore size distribution and from membrane surface treatments that increase the liquid-solid contact angle, potentially exceeding a benchmark minimum power density of 5 W/m2 (set for the feasibility of pressure-retarded osmosis). An assessment of the second law efficiency of the PRMD process is also presented. A critical part of the process is due to the inevitably smaller water flux through smaller pores, required to maintain a high pressure difference and a feasible power density. This can only be alleviated by increasing the temperature difference across the membrane. We conclude that membranes designed for the PRMD process need increased overall thermal resistance to enhance performance.