We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a 'swimmer efficiency' functional $η$ is introduced. It is proven, that in order to obtain maximum swimmer efficiency the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.
Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro-scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present manuscript, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circul…
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 theoretically study the self-propulsion of a thin (slender) colloid driven by asymmetric chemical reactions on its surface at vanishing Reynolds number. Using the method of matched asymptotic expansions, we obtain the colloid self-propulsion velocity as a function of its shape and surface physico-chemical properties. The mechanics of self-phoresis for rod-like swimmers has a richer spectrum of behaviours than spherical swimmers due to the presence of two small length scales, the slenderness of the rod and the width of the slip layer. This leads to subtleties in taking the limit of vanishing…
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…
We present a detailed theoretical study which demonstrates that electrokinetic effects can also play a role in the motion of metallic-insulator spherical Janus particles. Essential to our analysis is the identification of the fact that the reaction rates depend on Pt- coating thickness and that the thickness of coating varies from pole to equator of the coated hemisphere. We find that their motion is due to a combination of neutral and ionic diffusiophoretic as well as electrophoretic effects whose interplay can be changed by varying the ionic properties of the fluid. This has great potential …
Micro/Nano motors are micro to nano-sized particles and systems that are capable of motion in fluidic systems. Their motion can be a result of many mechanisms, one of the most well-known of which is electrolyte diffusiophoresis, in which asymmetric production of charged ions across the surface of the particle leads to phoresis. The focus of this work is to construct Urease motors with careful control of their Janus balance, i.e., to control the percentage of surface covered with the enzyme and study the effect of this asymmetry on the propulsion velocity of the particles. In that regard, we we…
We study the effect of a nearby planar wall on the propulsion of a phoretic Janus micro-swimmer driven by asymmetric reactions on its surface which absorb reactants and generate products. We show that the behaviour of these swimmers near a wall can be classified ${\bf based \ on \ whether}$ the swimmers are ${\bf mainly}$ absorbing or producing reaction solutes ${\bf and \ whether}$ their swimming directions are such that the inert or active face is at the front. We find that the wall-induced solute gradients always promote swimmer propulsion along the wall while the effect of hydrodynamics le…
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 Bénard-Marangoni convection, phoretic phenomena can create spontaneous and self-sustained wall-driven mixing flows within a straight, chemically-uniform acti…
Designing microscopic and nanoscopic self-propelled particles and characterising their motion has become a major scientific challenge over the past decades. To this purpose, phoretic effects, namely propulsion mechanisms relying on local field gradients, have been the focus of many theoretical and experimental studies. In this review, we adopt a tutorial approach to present the basic physical mechanisms at stake in phoretic motion, and describe the different experimental works that lead to the fabrication of active particles based on this principle. We also present the collective effects obser…
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…
We analyse the self-diffusiophoresis of a spherical particle animated by a nonuniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux, and one where this flux is governed by first-order kinetics with a specified distribution of rate constant. We employ a macroscale model where the short-range interaction of the solute with the particle boundary is represented by an effective slip condition. The solute transport is governed by an advection-diffusion equation. We focus upon the singular limit of large Pé…
We introduce a representative minimal model for phoretically interacting active colloids. Combining kinetic theory, linear stability analyses, and a general relation between self-propulsion and phoretic interactions in auto-diffusiophoretic and auto-thermophoretic Janus colloids collapses the parameter space to two dimensions: area fraction and Péclet number. This collapse arises when the lifetime of the self-generated phoretic fields is not too short, and leads to a universal phase diagram showing that phoretic interactions {\it generically} induce pattern formation in typical Janus colloids,…
We study the effect of a nearby planar wall on the propulsion of a spherical phoretic micro-swimmer driven by reactions on its surface. An asymmetric coverage of catalysts on its surface which absorb reactants and generate products gives rise to an anisotropic interfacial flow that propels the swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a function of the asymmetric catalytic coverage of the surface. By an analysis of the fundamental singularities of the flow and concentration or electrostatic potential gradients generated we are able to obtain and rationalise …
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 report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system's short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.
Toward a theoretical framework for self-diffusiophoretic propulsion near a wedge
School of Mathematics and Statistics, The Open University（开放大学数学与统计学院）；Max Planck Institute for Dynamics and Self-Organization (MPI-DS)（马克斯·普朗克动力学与自组织研究所）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）
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…
We report an experimental study on ion-exchange based modular micro-swimmers in low-salt water. Cationic ion-exchange particles and passive cargo particles assemble into self-propelling complexes, showing self-propulsion at speeds of several microns per second over extended distances and times. We quantify the assembly and speed of the complexes for different combinations of ion exchange particles and cargo particles, substrate types, salt types and concentrations, and cell geometries. Irrespective of experimental boundary conditions, we observe a regular development of the assembly shape with…
Active droplets can swim spontaneously in viscous flows as a result of the non-linear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by this solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Péclet number $\mbox{Pe}$ is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance $d$ from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrisical…
Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here we uncover a regime in which solute-gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, whic…
Active agents - like phoretic particles, bacteria, sperm, and cytoskeletal filaments in motility assays - show a large variety of motility-induced collective behaviors, such as aggregation, clustering and phase separation. The behavior of dense suspensions of phoretic particles and of bacteria during biofilm formation is determined by two principle physical mechanisms: (i) volume exclusion (short-range steric repulsion) and (ii) quorum sensing (longer-range reduced propulsion due to alteration of the local chemical environment). To systematically characterize such systems, we study semi-penetr…
Among the few methods which have been proposed to create small-scale swimmers, those relying on self-phoretic mechanisms present an interesting design challenge in that chemical gradients are required to generate net propulsion. Building on recent work, we propose that asymmetries in geometry are sufficient to induce chemical gradients and swimming. We illustrate this idea using two different calculations. We first calculate exactly the self-propulsion speed of a system composed of two spheres of unequal sizes but identically chemically homogeneous. We then consider arbitrary, small-amplitude,…
We investigate coarse-grained models of suspended self-thermophoretic microswimmers. Upon heating, the Janus spheres, with hemispheres made of different materials, induce a heterogeneous local solvent temperature that causes the self-phoretic particle propulsion. Starting from atomistic molecular dynamics simulations, we verify the coarse-grained description of the fluid in terms of a local molecular temperature field, and its role for the particle's thermophoretic self-propulsion and hot Brownian motion. The latter is governed by effective nonequilibrium temperatures, which are measured from …
Colloidal spheres with a partial platinum surface coating perform auto-phoretic motion when suspended in hydrogen peroxide solution. We present a theoretical analysis of the self-propulsion velocity of these particles using a continuum multi-component, self-diffusiophoretic model. With this model as a basis, we show how the slip-layer approximation can be derived and in which limits it holds. First, we consider the differences between the full multi-component model and the slip-layer approximation. Then the slip model is used to demonstrate and explore the sensitive nature of the particle's ve…
The structure of a finite particle cluster is typically determined by total energy minimization. Here we consider the case where a cluster of soft sphere dipoles becomes active, i.e. when the individual particles exhibit an additional self-propulsion along their dipole moments. We numerically solve the overdamped equations of motion for soft-sphere dipoles in a solvent. Starting from an initial metastable dipolar cluster, the self-propulsion generates a complex cluster dynamics. The final cluster state has in general a structure widely different to the initial one, the details depend on the mo…
Using large scale molecular dynamics simulations we study the orientational dynamics of a heated Janus particle which exhibits self-propulsion. The asymmetry in the microscopic interaction of the colloid with the solvent is implemented by choosing different wetting parameters for the two halves of the sphere. Consequently a gradient in temperature is created across the poles of the sphere due to different interfacial resistance across the solid-fluid boundary in the two hemispheres. It is this self-created temperature gradient which leads to a self-propulsion along the direction of the symmetr…
We study the dynamical steady-states of a monolayer of chemically active self-phoretic colloids as a function of packing fraction and self-propulsion speed by means of Brownian dynamics simulations. We focus on the case that a chemical field induces competing attractive positional and repulsive orientational interactions. Analyzing the distribution of cluster size and local density as well as the hexatic order parameter, we distinguish four distinct dynamical states which include collapsed, active gas, dynamical clustering, and motility-induced phase-separated states. The long-range chemical f…
Recent findings of possible applications of bio-friendly synthetic self-phoretic swimmers, have motivated the researchers in investigating the various motion-generating mechanisms to optimize the operating characteristics of the same. In this paper we model the auto-electrophoretic motion of a bimetallic (Au-Pt) spherical swimmer in a non-Newtonian medium. In view of the fact that many bio-fluids closely follow the generalized Newtonian rheology, the rheology of the surrounding swimming medium is considered to follow the Carreau-Yasuda viscosity model. Further to capture the experimentally obs…
