Simple flows of fluids with pressure-dependent viscosities

In his seminal paper on fluid motion, Stokes developed a general constituti ve relation which admitted the possibility that the viscosity could depend on the pressure. Such an assumption is particularly well suited to modellin g flows of many fluids at high pressures and is relevant to several flow si tuations involving lubricants. Fluid models in which the viscosity depends on the pressure have not received the attention that is due to them, and we consider unidirectional and two-dimensional flows of such fluids here. We note that solutions can have markedly different characteristics than the co rresponding solutions for the classical Navier-Stokes fluid. It is shown th at unidirectional flows corresponding to Couette or Poiseuille flow are pos sible only for special forms of the viscosity. Furthermore, we show that in teresting non-unique solutions are possible for flow between moving plates, which has no counterpart in the classical Navier-Stokes theory. We also st udy, numerically, two two-dimensional flows that are technologically signif icant: that between rotating, coaxial, eccentric cylinders and a flow acros s a slot. The solutions are found to provide Interesting departures from th ose for the classical Navier-Stokes fluid.