The Raspberry Model for Hydrodynamic Interactions Revisited. I. Periodic Arrays of Spheres and Dumbbells

TL;DR

This paper critically evaluates the raspberry model's ability to accurately simulate hydrodynamic interactions of colloidal particles, proposing improvements and extending analysis to non-convex shapes like dumbbells.

Contribution

It identifies discrepancies in the raspberry model's mobility predictions and introduces internal coupling points to improve accuracy, also applying the model to complex shapes.

Findings

Discrepancy between translational and rotational mobility in the raspberry model.

Adding internal coupling points improves the model's accuracy.

The filled raspberry model accurately reproduces hydrodynamics of colloidal dumbbells.

Abstract

The so-called 'raspberry' model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by [V. Lobaskin and B. D\"unweg, New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy the problem by adding internal coupling points. Finally, we examine a non-convex shape, namely a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in [J. de Graaf, et al., J. Chem. Phys. 143, 084107 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.