Generalized Boltzmann equation: Slip-no-slip dynamic transition in flows of strongly non-linear fluids

A “hydro-kinetic” equation with the relaxation time involving both molecular and hydrodynamic components proposed in this paper, defines an infinite hierarchy of relaxation times. It is shown that, applied to wall flows, this equation leads to qualitatively correct results in an extremely wide range of parameter η-variation. Among other features, it predicts the onset of slip velocity at the wall as an instability of the corresponding hydrodynamic approximation.