Response of a Compliant Slab to Viscous Incompressible Fluid Flow

The interaction of a compliant slab and the flow of a viscous fluid is explored theoretically. Both laminar and turbulent boundary-layer flow cases are considered. The slab is treated as an infinite, elastic or viscoelastic solid of finite thickness, bonded to a rigid half-space. The two media are coupled through stresses and velocities, in both tangential and normal directions, on the deformed surface of the slab. The proposed mathematical model is used to predict the appearance of unstable surface waves of the coating. According to the model, instabilities of a highly viscoelastic slab originate in the form of waves with phase speeds at about 2.3 percent of the flow velocity while the wave speed for a slab with zero to moderate viscosity is in the range of 50–60 percent of the flow velocity, which confirms previous experimental results. The predicted onset velocities of slow propagating waves for turbulent flow over plastisol gel are within 10 percent of those observed experimentally.