# Hybrid molecular dynamics-Lattice Boltzmann simulations for complex liquids

## Contents

# Diploma/ Master thesis: Hybrid molecular dynamics-Lattice Boltzmann simulations for complex liquids

Status: Finished

## Introduction

In various chemical engineering problems, the interaction of phenomena acting on different time and spatial scales has to be accomplished in order to account for all relevant physical effects. The translocation of sub-micron particles through nanopores or studies on polymer displacements in different flows are examples of current research on that field, involving effects on the molecular and the mesoscopic/continuum scales.

In this context, a coupling between the molecular dynamics (MD) framework MarDyn and the Lattice Boltzmann (LB) component within the Peano framework has previously been established. The coupling allows for hybrid MD-LB simulations: A certain region is resolved by MD whereas the huge surrounding area is simulated by LB.

The focus of the present project lies on the extension of the current coupling to complex molecules. So far, the coupling allowed for the simulation of liquid argon, based on single-centered Lennard-Jones molecules. In order to be able to simulate molecules of arbitrary shape, several extensions are required:

- In typical channel flow scenarios, molecules that would enter the MD region need to be inserted. The USHER algorithm has been previously developed by Delgado-Buscalioni et al. for this purpose. A more general version of this algorithm will be required now in order to account for rotations of complex molecules.

- The correct hydrodynamic pressure needs to exerted onto the finite sized molecular domain. So far, an explicit formulation of a boundary force was given an applied to the molecules near the boundaries in order to push them back into the MD region. This formulation is based on the integration of the radial distribution function of the molecules (=probability for a molecule to find another molecule within a certain distance). Currently, this integral is given explicitly for a simple molecule model; a general version is required here for complex molecules.

## Summary of project steps

- Getting familiar with the basic concepts of the Peano framework and its lattice Boltzmann component
- Getting familiar with MarDyn with special regard to the coupling component
- Implementation of the general USHER scheme
- Implementation of approximated boundary forces for the molecules. As the complex molecules might imply several parameters (e.g. different Lennard-Jones parameters for the different centers), this corresponds to a high-dimensional problem to be solved. Different steps will be taken towards the correct formulation of the pressure boundary:
- Evaluation of the radial distribution function (one of the standard values sampled from MD simulations) and setup of a discrete integral expression of the boundary force. Here, a single MD simulation (without any coupling) needs to be run, the radial distribution function is evaluated and then included in the subsequent coupled MD-LB simulation.
- Test of interpolation techniques between different radial distribution functions to accelerate the boundary force setup process. When several radial distribution functions have already been evaluated and measured for different types of molecules, one might interpolate between the solutions to obtain a valid function for a new type of molecule.

Due to the size of the project *Peano*, software-engineering aspects such as modularity, encapsulation of functionality or good documentation of the code are very important. This does not represent any inconveniences for students who are not yet familiar with these topics but it is a chance to learn and directly apply them.

## Prerequisites

Good programming skills in C++, interest in (multiscale) physics and flow simulations.

If you already have some knowledge on MD or flow simulations, that's perfect! If not, it's definitely fine, too! :-)

## Start

Anytime

## Tutors

Philipp Neumann (Lattice Boltzmann methods, Peano)

Wolfgang Eckhardt (Molecular dynamics, MarDyn)