Stokes’ hypothesis is invalid: A flow-dependent criterion for neglecting bulk viscosity

In modeling flows of compressible fluids, it is common practice to set the bulk viscosity equal to zero. This assumption, known as Stokes’ hypothesis, has been the subject of debate since its introduction by Stokes in 1845. In this work, we present continuum-mechanical, experimental, and atomistic arguments showing that Stokes’ hypothesis is not valid for any real fluid. Nevertheless, it is well known that modeling approaches based on this assumption often yield results of acceptable accuracy in practical applications. We show that this apparent success is not primarily due to the bulk viscosity being zero or negligibly small. Rather, whether bulk-viscous effects may be neglected depends on a careful analysis of the flow under consideration. We present a novel kinematic criterion that replaces Stokes’ constitutive hypothesis and determines in which flows bulk-viscous effects may be neglected.