ON THE STABILITY OF THE SIMPLE SHEAR-FLOW OF A JOHNSON-SEGALMAN FLUID

We solve the time-dependent simple shear flow of a Johnson-Segalman fl uid with added Newtonian viscosity. We focus on the case where the ste ady-state shear stress/shear rate curve is not monotonic. We show that , in addition to the standard smooth linear solution for the velocity, there exists, in a certain range of the velocity of the moving plate, an uncountable infinity of steady-state solutions in which the veloci ty is piecewise linear, the shear stress is constant and the other str ess components are characterized by jump discontinuities. The stabilit y of the steady-state solutions is investigated numerically. In agreem ent with linear stability analysis, it is shown that steady-state solu tions are unstable only if the slope of a linear velocity segment is i n the negative-slope regime of the shear stress/shear rate curve. The time-dependent solutions are always bounded and converge to a stable s teady state. The number of the discontinuity points and the final valu e of the shear stress depend on the initial perturbation. No regimes o f self-sustained oscillations have been found. (C) 1998 Elsevier Scien ce B.V.