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Register a new userHydrochemical interactions of phoretic particles: a regularized multipole framework
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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 Greens functions of the Laplace and Stokes operators to approximate the particle signatures in the far-field, which is only valid in the very dilute limit in simple geometries. To overcome these limitations, we propose a regularized mutipole 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 CFD solvers, allowing for large scale simulations of semi-dilute diffusio-phoretic suspensions.
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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 particles 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 ($Ngeq 3$). 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 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 the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions can not be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behaviour of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.
Phoretic mechanisms, whereby gradients of chemical solutes induce surface-driven flows, have recently been used to generate directed propulsion of patterned colloidal particles. When the chemical solutes diffuse slowly, an instability further provides active but isotropic particles with a route to self-propulsion by spontaneously breaking the symmetry of the solute distribution. Here we show theoretically that, in a mechanism analogous to Benard-Marangoni convection, phoretic phenomena can create spontaneous and self-sustained wall-driven mixing flows within a straight, chemically-uniform active channel. Such spontaneous flows do not result in any net pumping for a uniform channel but greatly modify the distribution of transport of the chemical solute. The instability is predicted to occur for a solute Peclet number above a critical value and for a band of finite perturbation wavenumbers. We solve the perturbation problem analytically to characterize the instability, and use both steady and unsteady numerical computations of the full nonlinear transport problem to capture the long-time coupled dynamics of the solute and flow within the channel.
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 surface. Owing to such link, we adapt a recent and popular kinetic model for dilute suspensions of chemically-active JPs where the particles far-field hydrodynamic and chemical signatures are intrinsically linked and explicitly determined by the design properties. Using linear stability analysis, we show that self-propulsion can induce a wave-selective mechanism for certain particles configurations consistent with experimental observations. Numerical simulations of the complete kinetic model are further performed to analyze the relative importance of chemical and hydrodynamic interactions in the nonlinear dynamics. Our results show that regular patterns in the particle density are promoted by chemical signaling but prevented by the strong fluid flows generated collectively by the polarized particles, regardless of their chemotactic or antichemotactic nature (i.e. for both puller and pusher swimmers).
Unlike pressure-driven flows, surface-mediated phoretic flows provide efficient means to drive fluid motion on very small scales. Colloidal particles covered with chemically-active patches with nonzero phoretic mobility (e.g. Janus particles) swim using self-generated gradients, and similar physics can be exploited to create phoretic pumps. Here we analyse in detail the design principles of phoretic pumps and show that for a minimal phoretic pump, consisting of 3 distinct chemical patches, the optimal arrangement of the patches maximizing the flow rate is universal and independent of chemistry.
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