2023/04/24 by Rodolfo Brandão, Brandão, Rodolfo
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Micro and Nano Robotics #Pickering emulsions and particle stabilization
paper · pdf · doi:10.48550/arxiv.2304.12497
openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spontaneous motion due to symmetry breaking has been theoretically predicted for both active droplets and isotropically active particles in an unbounded fluid domain, provided their intrinsic Péclet number Pe exceeds a critical value. However, due to their inherently small Pe, this phenomenon has yet to be experimentally observed for active particles. In this paper, we theoretically demonstrate that spontaneous motion for an active spherical particle closely fitting in a cylindrical channel is possible at arbitrarily small Pe. Scaling arguments in the limit where the dimensionless clearance ε≪1 reveal that when Pe=O(ε1/2), the confined particle reaches speeds comparable to those achieved in an unbounded fluid at moderate (supercritical) Pe values. We use matched asymptotic expansions in that distinguished limit, where the fluid domain decomposes into several asymptotic regions: a gap region, where the lubrication approximation applies; particle-scale regions, where the concentration is uniform; and far-field regions, where solute transport is one-dimensional. We derive an asymptotic formula for the particle speed, which is a monotonically decreasing function of Pe=Pe/ε1/2 and approaches a finite limit as Pe\searrow0. Our results could pave the way for experimental realisations of symmetry-breaking spontaneous motion in active particles.