Spontaneous motion of droplets during the demixing transition in binary fluids

The convective interaction between a pair of droplets coarsening during the demixing transition of a binary fluid is examined. The starting point is the model H equation for binary fluids, and the droplet sizes are considered to be large enough that thermal fluctuations are neglected. Droplet motion is induced by the convective coupling in the concentration equation, where there is a flux of concentration due to the fluid velocity, and a reciprocal effect in the momentum equation. The effect of the convective force density is separated into two parts—one due to the sharp concentration gradients at the droplet interface, and the other due to the variation in the matrix. It is shown that the dominant contribution to the fluid velocity field is due to the sharp concentration variation at the interface, and this is proportional to the square of the droplet flux at the surface. The surface flux is determined by solving the diffusion equation in the matrix between the droplets, and matching the solution to that...