Bilayer Couette flow over a profiled plate

Abstract The shear–driven, bilayer flow of two immiscible liquids sandwiched between a moving planar and stationary corrugated plate, in parallel alignment under Stokes conditions, is explored. motivation, partly inspired by biomimetic considerations, the use surface texturing/topography to reduce friction wear while increasing load carrying capacity lubrication problems. starting point associated mathematical formulation variational principle which, addition classical fluid mechanical field quantities, includes potential fields enabling an elegant reformulation dynamic condition at interface separating layers. Two methods solution are utilised: (i) analytic one equations, boundary conditions invoking long–wave approximation; (ii) exact semi–analytic one, obtained after transformation complex variables application spectral method. For validation comparison purposes FE continuity Navier–Stokes equations solved for. Resulting streamline patterns, shapes wall shear stresses discussed.