TY - JOUR
T1 - Hydrochemical interactions of phoretic particles:
T2 - A regularized multipole framework
AU - Rojas-Pérez, Francisco
AU - Delmotte, Blaise
AU - Michelin, Sébastien
N1 - Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.
PY - 2021
Y1 - 2021
N2 - Chemically active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and chemical gradients that modify the trajectories of other particles. As a result, the dynamics of reactive suspensions is fundamentally governed by hydro-chemical interactions. A full solution of the detailed hydro-chemical problem with many particles is challenging and computationally expensive. Most current methods rely on the Green's functions of the Laplace and Stokes operators to approximate the particle signatures in the far field, an approach which is only valid in the very dilute limit in simple geometries. To overcome these limitations, we propose a regularized multipole framework, directly inspired by the force coupling method (FCM), to model phoretic suspensions. Our approach, called diffusio-phoretic FCM (DFCM), relies on grid-based volume averages of the concentration field to compute the particle surface concentration moments. These moments define the chemical multipoles of the diffusion (Laplace) problem and provide the swimming forcing of the Stokes equations. Unlike far-field models based on singularity superposition, DFCM accounts for mutually induced dipoles. The accuracy of the method is evaluated against exact and accurate numerical solutions for a few canonical cases. We also quantify its improvements over far-field approximations for a wide range of inter-particle distances. The resulting framework can readily be implemented into efficient solvers, allowing for large scale simulations of semi-dilute diffusio-phoretic suspensions.
AB - Chemically active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and chemical gradients that modify the trajectories of other particles. As a result, the dynamics of reactive suspensions is fundamentally governed by hydro-chemical interactions. A full solution of the detailed hydro-chemical problem with many particles is challenging and computationally expensive. Most current methods rely on the Green's functions of the Laplace and Stokes operators to approximate the particle signatures in the far field, an approach which is only valid in the very dilute limit in simple geometries. To overcome these limitations, we propose a regularized multipole framework, directly inspired by the force coupling method (FCM), to model phoretic suspensions. Our approach, called diffusio-phoretic FCM (DFCM), relies on grid-based volume averages of the concentration field to compute the particle surface concentration moments. These moments define the chemical multipoles of the diffusion (Laplace) problem and provide the swimming forcing of the Stokes equations. Unlike far-field models based on singularity superposition, DFCM accounts for mutually induced dipoles. The accuracy of the method is evaluated against exact and accurate numerical solutions for a few canonical cases. We also quantify its improvements over far-field approximations for a wide range of inter-particle distances. The resulting framework can readily be implemented into efficient solvers, allowing for large scale simulations of semi-dilute diffusio-phoretic suspensions.
KW - active matter
KW - micro-organism dynamics
UR - http://www.scopus.com/inward/record.url?scp=85113210759&partnerID=8YFLogxK
U2 - 10.1017/jfm.2021.387
DO - 10.1017/jfm.2021.387
M3 - Artículo
AN - SCOPUS:85113210759
SN - 0022-1120
VL - 919
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A22
ER -