Violation of the incompressibility of liquid by simple shear flow

Fluid dynamics, which describes the flow of gas and liquid, has contributed tremendously to science and technology. If we can safely ignore the density change associated with flow, then we can regard fluid to be incompressible. For simple shear flow, for example, it has been established that there is no pressure change associated with flow and thus no violation of the incompressibility. This is because the flow does not accompany any volume deformation (no pressure change due to viscous stress) and inertia effects can be neglected (no inertial pressure drop). According to this conventional wisdom, any flow-induced instability such as cavitation are unexpected for simple shear flow. However, if we take into account the fact that the viscosity is a function of the density, this scenario is drastically changed. Contrary to the above common belief, here we demonstrate that the incompressibility condition can be violated by a coupling between flow and density fluctuations via the density dependence of viscosity eta even for simple shear flow and a liquid can become mechanically unstable above the critical shear rate, gamma(c) = (partial derivative eta/partial derivative(p))(T)(-1), where p is the pressure and T is the temperature. Our model predicts that for very viscous liquids this shear-induced instability should occur at a moderate shear rate, which we can easily access experimentally.