Concentration Polarization at the RO Membrane (2D)

A reverse-osmosis membrane does not see a single, uniform salt boundary layer — the layer is thin right at the feed inlet and grows thicker as the water travels down the membrane, because the mass-transfer coefficient that sweeps salt back into the bulk falls off with distance in the classic Lévêque entrance-region solution. This 2D simulator resolves that development directly: it reuses the same channel-averaged solution-diffusion and film-theory solve as the 3D version of this sim for the overall flux, wall concentration and rejection, then spreads the same physics along the membrane length using k(x) ∝ x^−1/3, drawing the exact steady-state advection-diffusion concentration profile above the membrane and animating a drift–diffusion ion field whose local jitter rate depends on where each ion currently sits. Watch the boundary layer visibly thicken from inlet to outlet, and see how pressure, crossflow, salinity and fouling reshape that growth curve in the β(x) chart below.