A regularised singularity approach to phoretic problems.

Area of Science:

• Computational physics and fluid dynamics.
• Microhydrodynamics and soft matter physics.

Background:

• Autophoretic particles exhibit self-propulsion driven by gradients in their chemical environment.
• Accurate simulation of microscale swimming is crucial for understanding complex fluid phenomena.
• Existing methods often struggle with efficiency, flexibility, or handling multiple interacting particles.

Purpose of the Study:

• To introduce an efficient, accurate, and flexible numerical method for autophoretic particle swimming.
• To address the challenges of simulating one or more particles in the purely diffusive limit.
• To provide a robust computational pipeline for complex microswimmer systems.

Main Methods:

• Utilizes successive boundary element solutions for Laplacian and Stokes flow equations.
• Employs regularized Green's functions, extending the 'regularized stokeslets' method.
• Incorporates the method of images for handling boundaries like plane walls without increasing system size.

Main Results:

• The boundary element method requires no bulk domain quantities for swimming velocity computation.
• The method demonstrates efficiency and accuracy, validated against known analytical solutions (two-sphere system, Janus particle).
• No re-meshing is needed for time-dependent problems, enhancing computational flexibility.

Conclusions:

• The proposed numerical method offers a powerful and versatile tool for studying autophoretic swimmers.
• It provides a rigorous computational framework for complex geometries and multi-body interactions.
• The approach facilitates advancements in understanding microscale transport and self-organization phenomena.