Thermocapillary interaction between a solid particle and a liquid-gas interface

When a hot solid particle is submerged into an ambient fluid near a free liquid-gas interface, a non-uniform temperature field around the particle produces surface tension gradients at the interface and generates thermocapillary flow in the surrounding fluid. This flow sets the particle itself in motion towards or away from the interface. In the first part of the paper, the interaction between a hot spherical solid particle and a plane undeformable liquid-gas interface is studied. The velocity of the thermocapillary induced motion of the solid particle is proportional to the surface tension gradient at the liquid-gas interface, and is calculated in the approximation of the Stokes flow and a zero Peclet number as a function of the separation distance between the particle and the interface. The asymptotic cases of both small and large separation distances are studied. In the second part of the paper, the interaction between a hot solid sphere and a gas bubble submerged into an ambient fluid is studied in the limiting case when the separation distance between them tends to zero. The velocity of a pairwise migration of a particle and a bubble in contact is calculated as a function of their radius ratio. The asymptotic values of the individual velocities of a solid particle and a gas bubble in near contact are also computed. The relative velocity of their motion towards each other is found to be proportional to the separation distance between them. In the third part of the paper, we investigate the effect of gravity on the thermocapillary driven motion of a solid particle for the two cases. It is shown that due to the thermocapillary interaction, a particle can move against the buoyancy forces.