Lattice Boltzmann Study of Velocity Behaviour in Binary Mixtures Under Shear

We apply lattice Boltzmann methods to study the relaxation of the velocity profile in binary fluids under shear during spinodal decomposition. In simple fluids, when a shear flow is applied on the boundaries of the system, the time required to obtain a triangular profile is inversely proportional to the viscosity and proportional to the square of the size of the system. We find that the same behaviour also occurs for binary mixtures, for any component ratio in the mixture and independently from the time when shear flow is switched on during phase separation.