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 velocity on the details of the molecule-surface interaction. We find a strong asymmetry in the dependence of the colloid's velocity as a function of the level of catalytic coating, when there is a different interaction between the solute and solvent molecules and the inert and catalytic part of the colloid, respectively. The direction of motion can even be reversed by varying the level of the catalytic coating. Finally, we investigate the robustness of these results with respect to variations in the reaction rate near the edge between the catalytic and inert parts of the particle. Our results are of significant interest to the interpretation of experimental results on the motion of self-propelled particles.
We study the diffusiophoretic self-propulsion of a colloidal catalytic particle due to a surface chemical reaction in a vicinity of a solid wall. Diffusiophoresis is a chemico-mechanical transduction mechanism in which a concentration gradient of an interacting solute produces an unbalanced force on a colloidal particle and drives it along the gradient. We consider a spherical particle with an axisymmetric reacting cap covering the polar angle range $0\le θ\le θ_{cap}$ in the presence of a repulsive solute, near an infinite planar wall, and solve the coupled solute concentration and Stokes equ…
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）
Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. We here report experimental measurements of significantly different velocities of such microswimmers in the vicinity of substrates made from different materials. We find that velocities scale with the solution contact angle $θ$ on the substrate, which in turn relates to the associated hydrodynamic substrate slip length, as $V\propto(\cosθ+1)^{-3/2}$. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynam…
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…
The dynamics of a spherical chemically-powered synthetic colloidal motor that operates by a self-diffusiophoretic mechanism and has a catalytic domain of arbitrary shape is studied using both continuum theory and particle-based simulations. The motor executes active rotational motion when self-generated concentration gradients and interactions between the chemical species and colloidal motor surface break spherical symmetry. Local variations of chemical reaction rates on the motor catalytic surface with catalytic domain sizes and shapes provide such broken symmetry conditions. A continuum theo…
The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions …
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 …
Self-propelling particles or microswimmers have opened a new field of investigation with both fundamental and practical perspectives. They represent very convenient model objects for experimental studies of active matter, and have implications in nano-robotics, drug delivery, and more. Here, we summarize recent advances in theoretical description of the self-propulsion of catalytic microswimmers that non-uniformly release ions, including its physical origins and the current switch in focus to non-linear effects, geometric tuning and more. In particular, we show that the ionic self-propulsion a…
Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a `chemical' coupling parameter $Γ_c$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic One Component Plasma (OCP) system. When confined to a constant-volume domain, Body-Centered Cubic crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian m…
Catalytic swimmers have attracted much attention as alternatives to biological systems for examining collective microscopic dynamics and the response to physico-chemical signals. Yet, understanding and predicting even the most fundamental characteristics of their individual propulsion still raises important challenges. While chemical asymmetry is widely recognized as the cornerstone of catalytic propulsion, different experimental studies have reported that particles with identical chemical properties may propel in opposite directions. Here, we show that, beyond its chemical properties, the det…
Typically, in the description of active Brownian particles, a constant effective propulsion force is assumed, which is then subjected to fluctuations in orientation and translation leading to a persistent random walk with an enlarged long-time diffusion coefficient. Here, we generalize previous results for the swimming path statistics to a time-dependent and thus in many situations more realistic propulsion which is a prescribed input. We analytically calculate both the noise-free and the noise-averaged trajectories for time-periodic propulsion under the action of an additional torque. In the …
The self-propulsion of artificial and biological microswimmers (i.e., active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e., that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand re…
Self-propulsion of a Janus droplet in a solution of surfactant, which reacts on a half of a drop surface, is studied theoretically. The droplet acts as a catalytic motor creating a concentration gradient, which generates its surface-tension-driven motion; the self-propulsion speed is rather high, $60\; {\rm μm/s}$ and more. This catalytic motor has several advantages over other micromotors: simple manufacturing, easily attained neutral buoyancy. In contrast to a single-fluid droplet, which demonstrates a self-propulsion as a result of symmetry breaking instability, for Janus one no stability t…
Micron-sized particles moving through solution in response to self-generated chemical gradients serve as model systems for studying active matter. Their far-reaching potential applications will require the particles to sense and respond to their local environment in a robust manner. The self-generated hydrodynamic and chemical fields, which induce particle motion, probe and are modified by that very environment, including confining boundaries. Focusing on a catalytically active Janus particle as a paradigmatic example, we predict that near a hard planar wall such a particle exhibits several sc…
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…
Active diffusiophoresis - swimming through interaction with a self-generated, neutral, solute gradient - is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. Firstly, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity…
In this Account, we describe how synthetic motors that operate by self-diffusiophoresis make use of a self-generated concentration gradient to drive motor motion. A description of propulsion by self-diffusiophoresis is presented for Janus particle motors comprising catalytic and noncatalytic faces. The properties of the dynamics of chemically powered motors are illustrated by presenting the results of particle-based simulations of sphere-dimer motors constructed from linked catalytic and noncatalytic spheres. The geometries of both Janus and sphere-dimer motors with asymmetric catalytic activi…
Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit se…
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…
The dynamics and pair trajectory of two self-propelled colloids are reported. The autonomous motions of the colloids are due to a catalytic chemical reaction taking place asymmetrically on their surfaces that generates a concentration gradient of interactive solutes around the particles and actuate particle propulsion. We consider two spherical particles with symmetric catalytic caps extending over the local polar angles $θ^1_{cap}$ and $θ^2_{cap}$ from the centers of active sectors in an otherwise quiescent fluid. A combined analytical-numerical technique was developed to solve the coupled ma…
We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations …
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,…
The effect of added salt on the propulsion of Janus platinum-polystyrene colloids in hydrogen peroxide solution is studied experimentally. It is found that micromolar quantities of potassium and silver nitrate salts reduce the swimming velocity by similar amounts, while leading to significantly different effects on the overall rate of catalytic breakdown of hydrogen peroxide. It is argued that the seemingly paradoxical experimental observations could be theoretically explained by using a generalised reaction scheme that involves charged intermediates and has the topology of two nested loops.
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…
Physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments focused on motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns origins of reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering the self-propulsion and demonstrate that MR can lead to increase of the partic…
We provide experimental results to show that self-propulsion of Janus particles made by coating platinum on the hemisphere of dielectric particles in hydrogen peroxide solution is similar to selfelectrophoresis. By different surface treatments and measuring the motion of particles and their ζ-potentials, we find that the speed and direction of motion are determined by the ζ-potential in a given concentration of hydrogen peroxide solution. When sign of ζ-potential is changed from negative to positive, the direction of motion reverses from toward non-catalytic side to catalytic side. We also fin…
The fabrication of synthetic self-propelled particles and the experimental investigations of their dynamics have stimulated interest in self-generated phoretic effects that propel nano- and micron-scale objects. Theoretical modeling of these phenomena is often based on a continuum description of the solvent for different phoretic propulsion mechanisms, including, self-electrophoresis, self-diffusiophoresis and self-thermophoresis. The work in this paper considers various types of catalytic chemical reaction at the motor surface and in the bulk fluid that come into play in mesoscopic descriptio…
Motion of active particles, such as catalytic micro- and nano-motors, is usually characterized via either dynamic light scattering or optical microscopy. In both cases, speed of particles is obtained from the calculus of the mean square displacement (MSD) and typically, the theoretical formula of the MSD is derived from the motion equations of an active Brownian particle. One of the most commonly reported parameters is the speed of the particle, usually attributed to its propulsion, and is widely used to compare the motion efficiency of catalytic motors. However, it is common to find different…
We present a simple chemical strategy for the formation of a self-propelling cluster via the process of capture and assembly of passive colloids on the surface of a chemically active colloid. The two species of colloids that are isotropic and Brownian otherwise interact to form propelling cluster. With the help of coarse-grained numerical simulations, we show that a chemically active colloid can induce diffusiophoretic motility to nearby chemically inert colloids towards itself. This propulsion and then self-assembly can then lead to the formation of active cluster. We observe the formation of…
A popular method to induce synthetic propulsion at the microscale is to use the forces created by surface-produced gas bubbles inside the asymmetric body of a catalytic swimmer (referred to in the literature as microrocket). Gas bubbles nucleate and grow within the catalytic swimmer and migrate toward one of its opening under the effect of asymmetric geometric confinement, thus generating a net hydrodynamic force which propels the device. In this paper we use numerical simulations to develop a joint chemical (diffusive) and hydrodynamic (Stokes) analysis of the bubble growth within a conical c…
Micrometer scale colloidal particles that propel in a deterministic fashion in response to local environmental cues are useful analogs to self-propelling entities found in nature. Both natural and synthetic active colloidal systems are often near boundaries or are located in crowded environments. Herein, we describe experiments in which we measured the influence of hydrogen peroxide concentration and dispersed polyethylene glycol (PEG) on the clustering behavior of 5 micrometer catalytic active Janus particles at low concentration. We found the extent to which clustering occurred in ensembles …
Self-propelled particles and, in particular, those based on mesoporous silica, have raised considerable interest due to their potential applications in the environmental and biomedical fields thanks to their biocompatibility, tunable surface chemistry and large porosity. Although spherical particles have been widely used to fabricate nano- and micromotors, not much attention has been paid to other geometries, such as nanorods. Here, we report the fabrication of self-propelled mesoporous silica nanorods (MSNRs) that move by the catalytic decomposition of hydrogen peroxide by a sputtered Pt laye…
Herein, self-healing small-scale swimmers capable of autonomous propulsion and on-the-fly structural recovery are described. The new strategy instantaneously restores the functionality of the swimmer after it has suffered severe damage. Incorporation of magnetic microparticles in strips along with the printed functional body layers (consisting of conductive carbon, low-density hydrophobic polymer and catalytically active metal) results in rapid reorientation and reattachment of the moving damaged catalytic tail to its complimentary broken static body piece. Such magnetic alignment and attracti…
Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light gradients can also be achieved in a system of synthetic photo-activated microparticles being exposed to an inhomogeneous laser field. We observe a strong orientational response of the particles because of diffusiophoretic torques, which in combination with an intensity-dependent particle motility eventually leads to phototaxis. Since the aligning torques sat…
For natural microswimmers, the interplay of swimming activity and external flow can promote robust motion, e.g. propulsion against ("upstream rheotaxis") or perpendicular to the direction of flow. These effects are generally attributed to their complex body shapes and flagellar beat patterns. Here, using catalytic Janus particles as a model experimental system, we report on a strong directional response that occurs for spherical active particles in a channel flow. The particles align their propulsion axes to be nearly perpendicular to both the direction of flow and the normal vector of a nearb…
The hydrodynamic flow field around a catalytically active colloid is probed using particle tracking velocimetry both in the freely swimming state and when kept stationary with an external force. Our measurements provide information about the fluid velocity in the vicinity of the surface of the colloid, and confirm a mechanism for propulsion that was proposed recently. In addition to offering a unified understanding of the nonequilibrium interfacial transport processes at stake, our results open the way to a thorough description of the hydrodynamic interactions between such active particles and…
It has been shown that self-assembled chains of active colloidal particles can present sustained oscillations. These oscillations are possible because of the effective diffusiophoretic forces that mediate the interactions of colloids do not respect the action--reaction principle and hence, a Hopf bifurcation is possible even for overdamped dynamics. Anchoring the particles in one extreme breaks the head-tail symmetry and the oscillation is transformed into a traveling wave pattern and thus the chain behaves like a beating cilium. The net force on the anchor, estimated using the resistive force…
Suspended colloidal particles interacting chemically with a solute are able to self-propel by autophoretic motion when they are asymmetrically patterned (Janus colloids). Here we demonstrate that the chemical anisotropy is not a necessary condition to achieve locomotion. The non linear interplay between surface osmotic flows and solute advection can produce spontaneous, and self-sustained motion of isotropic particles. We solve, for a spherical particle, the classical nonlinear autophoretic theoretical framework at arbitrary Péclet number. For a given set of material parameters, there exists a…
Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused by a limited understanding of specifics of self-propulsion mechanisms at the nanoscale. Here, we study a generic model of a self-propelled nanoparticle that does not rely on a particular mechanism. Instead, its main assumption is the fundamental symmetry of microscopic dynamics of chemical reactions: the principle of microscopic reversibility. Significant co…
Recently, the Brownian dynamics of self-propelled (active) rod-like particles was explored to model the motion of colloidal microswimmers, catalytically-driven nanorods, and bacteria. Here, we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its sel…
