Approximate kinetic theory of hard-sphere fluids near equilibrium. I. Formal theory

Beyond the Navier–Stokes equations: Burnett hydrodynamics

“…Molecular hydrodynamics then represents an alternative approach to study hydrodynamic phenomena in a region where the Navier-Stokes equations are expected to fail. Again the literature in this respect is vast so we will just provide a few references that focus the problem from different points of view [34,174,[266][267][268][269][270][271]. Moreover Bobylev's instability gave rise to a number of works focused to obtain a set of partial differential equations which are not unstable under temporal and longitudinal perturbations.…”

Microscopic Theories of the Rheology of Stable Colloidal Dispersions

“…The critical issue is how to apply these equilibrium closures to a nonequilibrium system. Our approach uses the framework of Szamel and Leegwater [65] and Resibois and Lebowitz [66] but replaces their final exact equation with the HNC or PY approximations of Scherwinski [62]. First, we replace the nonequilibrium system at a density n with an equilibrium system interacting through a fictitious potential created from the pair potential and a perturbing part,…”

Nonequilibrium structure and rheology of concentrated colloidal suspensions: Linear response

“…The closure approximation adopted in this work is similar to the one used before to describe self-diffusion and collective diffusion in colloidal suspensions. 21 That closure was inspired by the Resibois and Lebowitz approach to the linear kinetic theory of hard spheres 22 and other investigations 23,24 that followed their 1973 paper.…”