Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method

TL;DR

This paper introduces an advanced force-coupling method for simulating large-scale active suspensions of micro-swimmers, capturing complex interactions and time-dependent behaviors with high accuracy and efficiency.

Contribution

The authors develop a novel FCM-based approach for simulating semi-dilute squirmer suspensions, including effects like steric interactions and spheroidal shapes, enabling large-scale and dynamic studies.

Findings

Validated the method against exact solutions and other numerical methods.

Demonstrated the emergence of polar order and size-independent instability growth.

Achieved near continuum-level simulation results for tens of thousands of swimmers.

Abstract

We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection ($10^4-10 ^5$) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.