Ring formation by competition between entropic effect and thermophoresis

We have theoretically investigated colloidal distribution in a polymer solution under a temperature gradient, inspired by the recent experiments on trapping of colloids in the hot region against their own thermophoretic properties. In the theory, both the thermophoresis of colloids and the diffusiophoresis originating from entropic (finite volume) effects are taken into account. The model reproduces three different phases of colloidal distribution, such as depletion, accumulation, and ring-like distribution, observed in the experiments. The conditions of the ring formation and other patterns are discussed. We show that the condition of the ring formation depends on the size of colloids as found in the experiments.