Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics

Determining the microstructure of colloidal suspensions under shear flows has been a challenge for theoreticaland computational methods due to the singularly perturbed boundary-layer nature of the problem. Previousapproaches have been limited to the case of hard-sphere systems and suffer from various limitations in theirapplicability. We present an alternative analytic scheme based on intermediate asymptotics which solves theSmoluchowski diffusion-convection equation including both intermolecular and hydrodynamic interactions. Themethod is able to recover previous results for the hard-sphere fluid and to predict the radial distribution function(rdf) of attractive fluids such as the Lennard-Jones (LJ) fluid. In particular, a new depletion effect is predictedin the rdf of the LJ fluid under shear. This method can be used for the theoretical modeling and understandingof real fluids subjected to flow, with applications ranging from chemical systems to colloids, rheology, plasmas,and atmospherical science.