A multiblob approach to colloidal hydrodynamics with inherent lubrication

TL;DR

This paper introduces a multiblob colloidal hydrodynamics model that efficiently captures complex many-body interactions and lubrication effects, enabling faster simulations of dense colloidal suspensions with GPU acceleration.

Contribution

The study presents a novel multiblob model for colloidal hydrodynamics that naturally incorporates lubrication forces and achieves computational efficiency with GPU-based implementation.

Findings

Model accurately reproduces flow profiles and mobilities of spherical colloids.

It captures divergence of lubrication forces at finite inter-particle distances.

Significant speed-up in simulations of dense colloids using GPU and FFT techniques.

Abstract

This work presents an intermediate resolution model of the hydrodynamics of colloidal particles based on a mixed Eulerian-Lagrangian formulation. The particle is constructed with a small set of overlapping Peskin's Immersed Boundary kernels (blobs) which are held together by springs to build up a particle impenetrable core. Here, we used 12 blobs placed in the vertexes of an icosahedron with an extra one in its center. Although the particle surface is not explicitly resolved, we show that the short-distance hydrodynamic responses (flow profiles, translational and rotational mobilities, lubrication, etc) agree with spherical colloids and provide consistent effective radii. A remarkable property of the present multiblob model is that it naturally presents a "divergent" lubrication force at finite inter-particle distance. This permits to resolve the large viscosity increase at dense colloidal volume fractions. The intermediate resolution model is able to recover highly non-trivial (many-body) hydrodynamics using small particles whose radii are similar to the grid size $h$ (in the range $[1.6-3.2]\,h$). Considering that the cost of the embedding fluid phase scales like the cube of the particle radius, this result brings about a significant computational speed-up. Our code Fluam works in Graphics Processor Units (GPU's) and uses Fast Fourier Transform for the Poisson solver, which further improves its efficiency.