We use theory to study the distribution of spherical emulsion oil droplets in water near a lipophilic surface as a guideline for designing membranes for oil/water phase separation. Heterogeneous phase separations are shown in our laboratory using hydrophilic and hydrophobic membrane designs, where the affinity of the membrane surface to one of the phases in the mixture locally increases its concentration. Considering a colloidal emulsion (nano- to microemulsions) of spherical and noncoalescing droplets, we assess the contribution of colloidal forces, i.e., van der Waals, electrical double layer, and hydrophobic interactions and the finite size of the droplets to the accumulation of spherical emulsion droplets near a surface. We use our theory to study an experiment-inspired case study and find that an isolated lipophilic membrane surface in contact with an oil-in-water emulsion supports the oil-enriched emulsion phase in a thin layer near the membrane surface, suggesting that a membrane pore size comparable to this thickness should support oil-enriched emulsion in the membrane pores and hence past the membrane.
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