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 $\varepsilon$ 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 ($N\geq 3$). The $\varepsilon^5$-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.
Phoretic swimmers are a class of artificial active particles that has received significant attention in recent years. By making use of self-generated gradients (e.g. in temperature, electric potential or some chemical product) phoretic swimmers are capable of self-propulsion without the complications of mobile body parts or a controlled external field. Focusing on diffusiophoresis, we quantify in this paper the mechanisms through which phoretic particles may achieve chemotaxis, both at the individual and the non-interacting population level. We first derive a fully analytical law for the insta…
Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only t…
Janus phoretic colloids (JPs) self-propel as a result of self-generated chemical gradients and exhibit spontaneous nontrivial dynamics within phoretic suspensions, on length scales much larger than the microscopic swimmer size. Such collective dynamics arise from the competition of (i) the self-propulsion velocity of the particles, (ii) the attractive/repulsive chemically-mediated interactions between particles and (iii) the flow disturbance they introduce in the surrounding medium. These three ingredients are directly determined by the shape and physico-chemical properties of the colloids' su…
Similarly to their biological counterparts, suspensions of chemically-active autophoretic swimmers exhibit nontrivial dynamics involving self-organization processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a differ…
Chemically active Janus particles generate tangential concentration gradients along their surface for self-propulsion. Although this is well studied in unbounded domains, the analysis in biologically relevant environments such as confinements is scarce. In this work, we study the motion of a Janus sphere in weak confinement. The particle is placed at an arbitrary location, with an arbitrary orientation between the two walls. Using the method of reflections, we study the effect of confining planar boundaries on the phoretic and hydrodynamic interactions, and their consequence on the Janus parti…
We demonstrate that diffusiophoretic, thermophoretic and chemotactic phenomena in turbulence lead to clustering of particles on multi-fractal sets that can be described using one single framework, valid when the particle size is much smaller than the smallest length scale of turbulence $l_0$. To quantify the clustering, we derive positive pair correlations and fractal dimensions that hold for scales smaller than $l_0$. Statistics of the number of particles in a small volume are non-Poissonian manifesting deviations from the case of uncorrelated particles. For scales larger than $l_0$ we predic…
We study the nonequilibrium interaction of two isotropic chemically-active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed-point---a phenomenon that cannot be captured under the far-field approximation. We find that due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size, or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that …
Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) -- as employed in many experimental studies -- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747}, 572 (2014)]. Accordingly, intuitively appealing analogies …
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 i…
We study the detention statistics of self-propelling droplet microswimmers attaching to microfluidic pillars. These droplets show negative autochemotaxis: they shed a persistent repulsive trail of spent fuel that biases them to detach from pillars of a certain size after orbiting them just once. We have designed a microfluidic assay recording swimmers in pillar arrays of varying diameter, derived detention statistics via digital image analysis and interpreted these statistics via the Langevin dynamics of an active Brownian particle (ABP) model. By comparing data from orbits with and without re…
We study the axisymmetric interaction of two chemically active Janus particles. By relying on the linearity of the field equations and symmetry arguments, we derive a generic solution for the relative velocity of the particles. We show that regardless of the chemical properties of the system, the relative velocity can be written as a linear summation of geometrical functions which only depend on the gap size between the particles. We evaluate these functions via an exact approach which accounts for the full chemical and hydrodynamic interactions. Using the obtained solution, we expose the role…
Decapod crustaceans have appendages with an array of rigid hairs covered in chemo-receptors, used to sense and track food. Crustaceans directly influence the flow behavior by changing the speed of flow past the hairy surface, thereby manipulating the Reynolds number (Re). Hairs act either as a rake - diverting flow around the hair array, or as a sieve - filtering flow through the hairs. In our experiments, we uncover a third transitional phase: deflection - where the flow partially penetrates the hair array and is deflected laterally. We develop a reduced order model that predicts the flow pha…
We present a modular Python library for computing many-body hydrodynamic and phoretic interactions between spherical active particles in suspension, when these are given by solutions of the Stokes and Laplace equations. Underpinning the library is a grid-free methodology that combines dimensionality reduction, spectral expansion, and Ritz-Galerkin discretization, thereby reducing the computation to the solution of a linear system. The system can be solved analytically as a series expansion or numerically at a cost quadratic in the number of particles. Suspension-scale quantities like fluid flo…
Self-diffusiophoretic particles exploit local concentration gradients of a solute species in order to self-propel at the micron scale. While an isolated chemically- and geometrically-isotropic particle cannot swim, we show that it can achieve self-propulsion through interactions with other individually-non-motile particles by forming geometrically-anisotropic clusters via phoretic and hydrodynamic interactions. This result identifies a new route to symmetry-breaking for the concentration field and to self-propulsion, that is not based on an anisotropic design, but on the collective dynamics of…
We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer --- for which, e.g., the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip ("squirming") modes --- for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results a…
We consider analytically and numerically head-on collision between two self-propelled drops. Each drop is driven by chemical reactions that produce or consume the concentration isotropically. The isotropic distribution of the concentration field is destabilized by motion of the drop which is itself made by Marangoni flow from concentration-dependent surface tension. This symmetry-breaking self-propulsion is distinct from other self-propulsion mechanisms due to the intrinsic polarity such as squirmers and self-phoretic motion; there is a bifurcation point below which the drop is stationary and …
Active colloids are microscopic particles, which self-propel through viscous fluids by converting energy extracted from their environment into directed motion. We first explain how articial microswimmers move forward by generating near-surface flow fields via self-phoresis or the self-induced Marangoni effect. We then discuss generic features of the dynamics of single active colloids in bulk and in confinement, as well as in the presence of gravity, field gradients, and fluid flow. In the third part, we review the emergent collective behavior of active colloidal suspensions focussing on their …
Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface; hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly effects the global dynamics, due to variations in…
