When a semipermeable vesicle is exposed to a solute concentration gradient, it experiences a nonuniform osmotic pressure distribution. This distribution, incompatible with static equilibrium, induces inward osmosis on the low-concentration side and outward osmosis on the high-concentration side. The resulting imbalance drives the vesicle to drift down the gradient—a phenomenon known as osmophoresis. While osmophoresis may superficially resemble other phoretic mechanisms (such as diffusiophoresis or thermophoresis) driven by scalar field gradients, it is fundamentally distinct due to its essential dependence on the absolute value of the (strictly non-negative) concentration field itself. In this work, we revisit the osmophoresis problem, identifying the appropriate limiting process that consistently represents an imposed macroscale concentration gradient, and clarifying the distinction between the concentration and pressure fields and their dynamic counterparts. Our scrutiny resolves the longstanding anomaly of significant advective transport at low Péclet numbers, as originally reported by Anderson [Phys. Fluids 26, 2871 (1983)], and yields a closed-form expression for the drift velocity, valid for all Péclet numbers. We demonstrate how previous efforts to go beyond leading-order approximation at small Péclet numbers have led to inconsistent perturbation schemes.

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• Complex fluids
• Stokes equations