A variant of Stokes’ second problem for a new shear thinning model for paint

A variant of Stokes’ second problem, namely the flow of a pool of liquid between two plates with the bottom plate oscillating, is studied for a novel shear thinning fluid model for paint. The governing equations are obtained using the semi-inverse approach. The governing equation is solved numerically, subject to the appropriate initial and boundary conditions. The cases of bottom plate subject to oscillatory velocity and oscillatory shear stress are studied. The results are qualitatively similar: the fluid damps the oscillations and introduces a phase shift, the extent of each depending on the distance from the plate. A parameter study is conducted for the case of the bottom plate being subject to oscillatory velocity. Increasing the amplitude of oscillations increases the maximum velocity close to the plate, but the effect diminishes with increasing amplitude. On the other hand, increasing the frequency decreases the maximum velocity close to the plate. The effect of the material parameters of paint on the maximum velocity close to the plate, although counterintuitive, matches what is expected for shear thinning fluids. • Studied variant of Stokes’ second problem for paint between two parallel plates. • Governing equation derived using semi-inverse approach and solved numerically. • Parameter study of effect of amplitude and frequency of plate and material parameters. • Increasing oscillation frequency leads to damping of velocity close to the plate. • Increasing α 1 (viscosity) leads to increase in velocity close to the oscillating plate.