Study of a variant of Stokes’ first and second problems for fluids with pressure dependent viscosities

In this paper we extend the seminal work of Stokes concerning the flow due to a suddenly accelerated plate and an oscillating plate for the Navier–Stokes fluid, to a fluid with pressure dependent viscosity. The viscosity of many fluids varies significantly with pressure, a fact recognized by Stokes, and Barus in fact conducted experiments that showed that the variation of the viscosity with pressure was exponential. Given such a tremendous variation, it would be interesting to see how this change in viscosity affects the nature of the solution to these problems. We find that the velocity field, and hence the structure of the vorticity and the shear stress at the walls for fluids with pressure dependent viscosity are markedly different from those for the classical Navier–Stokes fluid.