Modeling chemo-hydrodynamic interactions of phoretic particles: a unified framework

Abstract

Phoretic particles exploit local self-generated physico-chemical gradients to achieve self-propulsion at the micron scale. The collective dynamics of a large number of such particles is currently the focus of intense research efforts, both from a physical perspective to understand the precise mechanisms of the interactions and their respective roles, as well as from an experimental point of view to explain the observations of complex dynamics as well as formation of coherent large-scale structures. However, an exact modelling of such multi-particle problems is difficult and most efforts so far rely on the superposition of far-field approximations for each particle's signature, which are only valid asymptotically in the dilute suspension limit. A systematic and unified analytical framework based on the classical Method of Reflections (MoR) is developed here for both Laplace and Stokes' problems to obtain the higher-order interactions and the resulting velocities of multiple phoretic particles, up to any order of accuracy in the radius-to-distance ratio $\epsilon$ of the particles. Beyond simple pairwise chemical or hydrodynamic interactions, this model allows us to account for the generic chemo-hydrodynamic couplings as well as $N$-particle interactions ($N\ge 3$). The ${\epsilon }^5$-accurate interaction velocities are then explicitly obtained and the resulting implementation of this MoR model is discussed and validated quantitatively against exact solutions of a few canonical problems.

31 pages, 13 figures, to appear in Physical Review Fluids

References in corpus (40)

• Novel type of phase transition in a system of self-driven particles
• Active Particles in Complex and Crowded Environments
• Self-motile colloidal particles: from directed propulsion to random walk
• The Mechanics and Statistics of Active Matter
• Motility-Induced Phase Separation
• Spontaneous motion in hierarchically assembled active matter
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Patterns and Collective Behavior in Granular Media: Theoretical Concepts
• Dynamic clustering in active colloidal suspensions with chemical signaling
• Designing phoretic micro- and nano-swimmers
• Collective Motion of Vibrated Polar Disks
• Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations
• Emergent behavior in active colloids
• Living Liquid Crystals
• Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion
• Clusters, asters and collective oscillations in chemotactic colloids
• Self-assembly of catalytically active colloidal molecules: Tailoring activity through surface chemistry
• Emergent vortices in populations of colloidal rollers
• Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Unstable fronts and stable "critters" formed by microrollers
• 'Fuelled' motion: phoretic motility and collective behaviour of active colloids
• Velocity Correlations in an Active Nematic
• Phoretic self-propulsion at finite Péclet numbers
• Curling Liquid Crystal Microswimmers: a cascade of spontaneous symmetry breaking
• Flow-induced phase separation of active particles is controlled by boundary conditions
• Phoretic Interactions Generically Induce Dynamic Clusters and Wave Patterns in Active Colloids
• Spontaneous aggregation and global polar ordering in squirmer suspensions
• Autophoretic locomotion from geometric asymmetry
• Which Interactions Dominate in Active Colloids?
• Autophoretic motion in three dimensions
• Many-body dynamics of chemically propelled nanomotors
• Pair Interaction of Catalytically Active Colloids: From Assembly to Escape
• Phoretic and hydrodynamic interactions of weakly-confined autophoretic particles
• A regularised singularity approach to phoretic problems
• Competing chemical and hydrodynamic interactions in autophoretic colloidal suspensions
• Artificial chemotaxis of phoretic swimmers: Instantaneous and long-time behaviour
• Generalized Stokes laws for active colloids and their applications
• Higher-order force moments of active particles

Cited by in corpus (11)

• Exact phoretic interaction of two chemically-active particles
• Interactions in Active Colloids
• Collisions and rebounds of chemically-active droplets
• Instability and self-propulsion of active droplets along a wall
• Exact axisymmetric interaction of phoretically active Janus particles
• Alignment and scattering of colliding active droplets
• Hydrochemical interactions of phoretic particles: a regularized multipole framework
• Hydro-chemical interactions in dilute phoretic suspensions: from individual particle properties to collective organization
• Self-propulsion in 2D Confinement: Phoretic and Hydrodynamic Interactions
• Self-organization of active colloids mediated by chemical interactions
• Asymptotic theory of hydrodynamic interactions between slender filaments