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

## TL;DR

This paper introduces an analytical method based on intermediate asymptotics to predict the microstructure, specifically the radial distribution function, of Lennard-Jones fluids under shear flow, extending previous hard-sphere models.

## Contribution

The paper presents a novel analytical scheme that accurately predicts the RDF of Lennard-Jones fluids under shear, including attractive interactions and new depletion effects.

## Key findings

- Recovered previous results for hard-sphere fluids
- Predicted RDF for Lennard-Jones fluids under shear
- Discovered a new depletion effect in the RDF

## 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.