Pattern formation in liquid-vapor systems under periodic potential and shear

In this paper the phase behavior and pattern formation in a sheared non-ideal uid under a periodic potential is studied. An isothermal two-dimensional formulation of a lattice Boltzmann scheme for a liquid-vapor system with the van der Waals equation of state is presented and validated. Shear is applied by moving walls and the periodic potential will vary along the ow direction. A region of the parameter space, where in absence of ow a striped phase with oscillating density is stable, will be considered. At low shear rates the periodic patterns are preserved and slightly distorted by the ow. At high shear rates the striped phase looses its stability and a new phase with interface waves between the liquid and vapor regions will appear. Velocity eld patterns will