Self-Similar Solution of the First Stokes Problem for Non-Newtonian Fluids with Power-Law Viscosity

The first Stokes problem is considered for flows of non-Newtonian fluids with effective viscosity varying in accordance with the power law. Self-similar solutions are constructed for the fluids, whose mechanical behavior is described by the Ostwald–de Waele and Herschel–Bulkley rheological models with the corresponding restrictions on the nonlinearity degree exponent n. It is shown that for the Ostwald–de Waele fluid self-similar solutions exist only for 0 < n < 1, which corresponds to the pseudoplastic behavior. At the same time, self-similar solutions for the Herschel–Bulkley fluid can be obtained only at n > 1, when this fluid exhibits the properties of dilatancy.