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.