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

Abstract

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

Pair correlation function of charge-stabilized colloidal systems under sheared conditions

“…where Y = − ∇ · v i / ṽ i . Following again the same steps reported in [16] for the zero-th and first order terms in the inner layer, we find the following expressions:…”

“…Recently, a theory based on intermediate asymptotics expansions has been developed, which analytically describes the micro-structure of a dilute suspension of particles. The work has been validated by comparison with numerical simulation data of hard spheres from Stokesian dynamics [13] and it has been found out that the predictions are valid for semi-dilute conditions (φ up to 0.2) under strongly simple sheared conditions [16]. The reason for this is a cancellation of errors between the neglect of the tangential contribution to the lubrication forces acting on Brownian motion and the absence of many-body interactions.…”

“…where D 0 is the diffusion coefficient of an isolated particle and G(r) a parametrized function which approximates the rigorous solution for the lubrication force component of the hydrodynamic interactions [18,16] along the line of centres, meanwhile H(r) is its equivalent relative to the tangential directions with respect to the motion of the colloids; in the calculations we will consider only the contribution of the lubrication forces along the radial directions, which means H(r) = 0. Finally, the conservative interaction force K int is given by K int = (−∇U (r), 0, 0), where U (r) is the interaction potential between two particles.…”

“…The approximation consists in applying an angular average, denoted as · · · , over a certain portion of solid angle to Eq. (16).…”

“…In this work we presented an analytical theory of the pair correlation function of charge-stabilized colloids in shear flow, using the intermediate-aymptotics solution method to the Smoluchowski equation that was recently developed in [16]. The theory has been built on a series of hypothesis:…”