A semi-permeable membrane forms part of a vertical plane boundary which separates pure solvent from a solution of bulk concentration $C_b $. The osmotic flux J is given by $J = P\Delta C$ where P is the osmotic permeability of the membrane and $\Delta C$ is the concentration difference across it, less than $C_b $ because the osmotic flow tends to sweep solute away from the membrane and a boundary layer is set up. This boundary layer is analysed on the assumption that there is no stirring in the bulk solution so the only motion is the natural convection driven by the relative buoyancy of the solute-poor fluid near the membrane. The flow and concentration distribution are taken to be steady and two-dimensional. The key dimensionless longitudinal coordinate is $x = P^4 C_b^3 \sigma X/g'D^2 $, where X is distance from the leading edge of the membrane, $g'$ is the buoyancy force per unit mass and concentration difference, and $D,\sigma ( \sigma \gg 1 )$ are the solute diffusivity and Schmidt number of the flui...