The segregation of sheared binary fluids in the Bray-Humayun model

The phase separation process which follows a sudden quench inside the coexistence region is considered for a binary fluid subjected to an applied shear flow. This issue is studied in the framework of the convection-diffusion equation based on a Ginzburg-Landau free energy functional in the approximation scheme introduced by Bray and Humayun [Plays. Rev. Lett. 68, 1559 (1992)]. After an early stage where domains furin and shear effects become effective the system enters a scaling regime where the typical domains sizes L-parallel to, L-perpendicular to along the flow and perpendicular to it grow as t(5/4) and t(1/4). The structure factor is characterized by the existence of four peaks, similarly to previous theoretical and experimental observations, and by exponential tails at large wavevectors.