Thermophoresis in a near-critical binary fluid mixture

We consider a rigid spherical particle immersed in a binary non-electrolyte fluid mixture which lies in the one-phase region near the demixing critical point. Mixture components differently interact with the particle surface, which generates preferential adsorption of one component onto the surface. The resultant inhomogeneity in composition, significant owing to the near criticality, causes particle motion under an imposed temperature gradient, i.e., thermophoresis. Using hydrodynamics based on a coarse-grained free-energy density, we calculate the thermophoretic mobility of the particle, far from which the critical composition is assumed. As expected from the recently predicted direction of thermoosmosis of a mixture, our numerical results show that the particle moves toward the colder side in a mixture near the upper consolute point and toward the warmer side in a mixture near the lower consolute point regardless of which mixture component is adsorbed onto the surface. This property, stemming from the requirement of the free-energy density for describing the phase separation, should hold in general and be able to be examined experimentally.