Rough or wiggly? Membrane topology and morphology for fouling control

During filtration in reverse osmosis membranes (ROM), the system performance is dramatically affected by membrane fouling which causes a significant decrease in permeate flux as well as an increase in the energy input required to operate the system. In this work, we develop a model, able to dynamically capture foulant evolution, that couples the transient Navier-Stokes and the advection-diffusion equations, with an adsorption-desorption equation for the foulant accumulation. The model is validated against unsteady measurements of permeate flux as well as steady-state spatial fouling patterns. For a straight channel, we derive a universal scaling relationship between the Sherwood and Bejan numbers, i.e. the dimensionless permeate flux through the membrane and the pressure drop along the channel, respectively, and generalize this result to membranes subject to morphological and/or topological modifications, i.e. whose shape (wiggliness) or surface roughness is altered from the rectangular and flat reference case. We demonstrate that a universal scaling can be identified through the definition of a modified Reynolds number, Re*, that accounts for the additional length scales introduced by the membrane modifications, and a membrane performance index, xi, an aggregate efficiency measure with respect to both clean permeate flux and energy input required to operate the system. Our numerical simulations demonstrate that 'wiggly' membranes outperform 'rough' membranes for smaller values of Re*, while the trend is reversed at higher Re*. The proposed approach is able to quantitatively investigate, optimize and guide the design of both morphologically and topologically altered membranes under the same framework, while providing insights into the physical mechanisms controlling the overall system performance.