Hydrodynamic simulations of self-phoretic microswimmers

Minimal numerical ingredients describe chemical microswimmers' 3-D motion

The underlying mechanisms and physics of catalytic Janus microswimmers is highly complex, requiring details of the associated phoretic fields and the physiochemical properties of catalyst, particle, boundaries, and the fuel used. Therefore, developing a minimal (and more general) model capable of capturing the overall dynamics of these autonomous particles is highly desirable. In the presented work, we demonstrate that a coarse-grained dissipative particle-hydrodynamics model is capable of describing the behaviour of various chemical microswimmer systems. Specifically, we show how a competing balance between hydrodynamic interactions experienced by a squirmer in the presence of a substrate, gravity, and mass and shape asymmetries can reproduce a range of dynamics seen in different experimental systems. We hope that our general model will inspire further synthetic work where various modes of swimmer motion can be encoded via shape and mass during fabrication, helping to realise the still outstanding goal of microswimmers capable of complex 3-D behaviour.

Active self-assembly of colloidal machines with passive rotational parts via coordination of phoresis and osmosis

The organization of microscopic objects into specific structures with movable parts is a prerequisite for building sophisticated micromachines with complex functions, as exemplified by their macroscopic counterparts. Here we report the self-assembly of active and passive colloids into micromachinery with passive rotational parts. Depending on the attachment of the active colloid to a substrate, which varies the degrees of free freedom of the assembly, colloidal machines with rich internal rotational dynamics are realized. Energetic analysis reveals that the energy efficiency increases with the degrees of freedom of the machine. The experimental results can be rationalized by the cooperation of phoretic interaction and osmotic flow encoded in the shape of the active colloid, which site-specifically binds and exerts a torque to passive colloids, supported by finite element calculations and mesoscale simulations. Our work offers a new design principle that utilizes nonequilibrium interfacial phenomena for spontaneous construction of multiple-component reconfigurable micromachinery.

Isotropic active colloids: explicit vs. implicit descriptions of propulsion mechanisms

Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of activity. Here, we take advantage of a recent two-dimensional model of isotropic active particles whose propulsion originates from the interactions between solute particles in the bath. The colloid catalyzes a chemical reaction in its vicinity, which results in a local phase separation of solute particles, and the density fluctuations of solute particles cause the enhanced diffusion of the colloid. In this paper, we investigate an assembly of such active particles, using (i) an explicit model, where the microscopic dynamics of the solute particles is accounted for; and (ii) an implicit model, whose parameters are inferred from the explicit model at infinite dilution. In the explicit solute model, the long-time diffusion coefficient of the active colloids strongly decreases with density, an effect which is not captured by the derived implicit model. This suggests that classical models, which usually decouple pair interactions from activity, fail to describe collective dynamics in active colloidal systems driven by solute-solute interactions.

Designing Covalent Organic Framework-Based Light-Driven Microswimmers toward Therapeutic Applications

While micromachines with tailored functionalities enable therapeutic applications in biological environments, their controlled motion and targeted drug delivery in biological media require sophisticated designs for practical applications. Covalent organic frameworks (COFs), a new generation of crystalline and nanoporous polymers, offer new perspectives for light-driven microswimmers in heterogeneous biological environments including intraocular fluids, thus setting the stage for biomedical applications such as retinal drug delivery. Two different types of COFs, uniformly spherical TABP-PDA-COF sub-micrometer particles and texturally nanoporous, micrometer-sized TpAzo-COF particles are described and compared as light-driven microrobots. They can be used as highly efficient visible-light-driven drug carriers in aqueous ionic and cellular media. Their absorption ranging down to red light enables phototaxis even in deeper and viscous biological media, while the organic nature of COFs ensures their biocompatibility. Their inherently porous structures with ≈2.6  and ≈3.4 nm pores, and large surface areas allow for targeted and efficient drug loading even for insoluble drugs, which can be released on demand. Additionally, indocyanine green (ICG) dye loading in the pores enables photoacoustic imaging, optical coherence tomography, and hyperthermia in operando conditions. This real-time visualization of the drug-loaded COF microswimmers enables unique insights into the action of photoactive porous drug carriers for therapeutic applications.

Clustering of self-thermophilic asymmetric dimers: the relevance of hydrodynamics

Self-thermophilic dimers are characterized by a net phoretic attraction which, in combination with hydrodynamic interactions, results in the formation of crystalline-like aggregates. To distinguish the effect of the different contributions is frequently an important challenge. We present a simulation investigation done in parallel in the presence and the absence of hydrodynamic interactions for the case of asymmetric self-thermophoretic dimers. In the absence of hydrodynamics, the clusters have the standard heads-in configurations. In contrast, in the presence of hydrodynamics, clusters with heads-in conformation are being formed, in which dimers with their propulsion velocity pointing out of the cluster are assembled and stabilized by strong hydrodynamic osmotic flows. Significant variation in the material properties is to be expected from such differences in the collective behavior, whose understanding and control is of great relevance for the development of new synthetic active materials.

Beyond Janus Geometry: Characterization of Flow Fields around Nonspherical Photocatalytic Microswimmers

Catalytic microswimmers that move by a phoretic mechanism in response to a self-induced chemical gradient are often obtained by the design of spherical janus microparticles, which suffer from multi-step fabrication and low yields. Approaches that circumvent laborious multi-step fabrication include the exploitation of the possibility of nonuniform catalytic activity along the surface of irregular particle shapes, local excitation or intrinsic asymmetry. Unfortunately, the effects on the generation of motion remain poorly understood. In this work, single crystalline BiVO₄ microswimmers are presented that rely on a strict inherent asymmetry of charge-carrier distribution under illumination. The origin of the asymmetrical flow pattern is elucidated because of the high spatial resolution of measured flow fields around pinned BiVO₄ colloids. As a result the flow from oxidative to reductive particle sides is confirmed. Distribution of oxidation and reduction reactions suggests a dominant self-electrophoretic motion mechanism with a source quadrupole as the origin of the induced flows. It is shown that the symmetry of the flow fields is broken by self-shadowing of the particles and synthetic surface defects that impact the photocatalytic activity of the microswimmers. The results demonstrate the complexity of symmetry breaking in nonspherical microswimmers and emphasize the role of self-shadowing for photocatalytic microswimmers. The findings are leading the way toward understanding of propulsion mechanisms of phoretic colloids of various shapes.

A lattice Boltzmann model for self-diffusiophoretic particles near and at liquid-liquid interfaces

We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved solvent hydrodynamics, and, thanks to its versatility, it can handle important aspects of the multiphysics of the problem, including particle wettability and differential solubility of the product in the two liquid phases. The method is extensively validated in simple numerical experiments, whose outcome is theoretically predictable, and then applied to the study of the behavior of active particles next to and trapped at interfaces. We show that their motion can be variously steered by tuning relevant control parameters, such as the phoretic mobilities, the contact angle, and the product solubility.

Doxorubicin-Loaded Walnut-Shaped Polydopamine Nanomotor for Photothermal-Chemotherapy of Cancer

The combination of photothermal therapy and chemical drug therapy shows good prospects in cancer treatment, but there are also some limitations such as low permeability of therapeutic agents and uneven photothermal therapy. Here, we synthesized a walnut-shaped polydopamine (PDA) nanomotor driven by near infrared (NIR) light. The nanomotor was modified by methoxy polyethylene glycol amine (mPEG-NH₂) for improving water solubility. PDA-PEG loaded adriamycin through π-π accumulation and hydrogen bonding. The experimental results showed that the PDA nanomotors had good biocompatibility and photothermal effect. Further, the NIR light irradiation and tumor cell microenvironment are conducive to drug release. In addition, under the irradiation of an NIR laser, the asymmetry of walnut-shaped nanoparticles makes the particles obtain the ability of autonomous movement, which can improve the permeability of particles in 3D tumor balls, which can provide support for drug penetration and heat dispersion. This strategy offers potential innovative materials for photothermal/chemotherapy synergistic therapy of tumors.

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model

We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Regimes of motion of magnetocapillary swimmers

The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer's maximum velocity centred around the particle's inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations.

Collective behavior of thermophoretic dimeric active colloids in three-dimensional bulk

Colloids driven by phoresis constitute one of the main avenues for the design of synthetic microswimmers. For these swimmers, the specific form of the phoretic and hydrodynamic interactions dramatically influences their dynamics. Explicit solvent simulations allow the investigation of the different behaviors of dimeric Janus active colloids. The phoretic character is modified from thermophilic to thermophobic, and this, together with the relative size of the beads, strongly influences the resulting solvent velocity fields. Hydrodynamic flows can change from puller-type to pusher-type, although the actual flows significantly differ from these standard flows. Such hydrodynamic interactions combined with phoretic interactions between dimers result in several interesting phenomena in three-dimensional bulk conditions. Thermophilic dimeric swimmers are attracted to each other and form large and stable aggregates. Repulsive phoretic interactions among thermophobic dimeric swimmers hinder such clustering and lead, together with long- and short-ranged attractive hydrodynamic interactions, to short-lived, aligned swarming structures.

Bio-inspired Acousto-magnetic Microswarm Robots with Upstream Motility

The ability to propel against flows, i.e., to perform positive rheotaxis, can provide exciting opportunities for applications in targeted therapeutics and non-invasive surgery. To date, no biocompatible technologies exist for navigating microparticles upstream when they are in a background fluid flow. Inspired by many naturally- occurring microswimmers such as bacteria, spermatozoa, and plankton that utilize the non-slip boundary conditions of the wall to exhibit upstream propulsion, here, we report on the design and characterization of self-assembled microswarms that can execute upstream motility in a combination of external acoustic and magnetic fields. Both acoustic and magnetic fields are safe to humans, non-invasive, can penetrate deeply into the human body, and are well-developed in clinical settings. The combination of both fields can overcome the limitations encountered by single actuation methods. The design criteria of the acoustically-induced reaction force of the microswarms, which is needed to perform rolling-type motion, are discussed. We show quantitative agreement between experimental data and our model that captures the rolling behaviour. The upstream capability provides a design strategy for delivering small drug molecules to hard-to-reach sites and represents a fundamental step toward the realization of micro- and nanosystem-navigation against the blood flow.

Active motion of passive asymmetric dumbbells in a non-equilibrium bath

Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein-Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v_∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v_∥l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.

Multi-particle collision dynamics with a non-ideal equation of state. I

The method of multi-particle collision dynamics (MPCD) and its different implementations are commonly used in the field of soft matter physics to simulate fluid flow at the micron scale. Typically, the coarse-grained fluid particles are described by the equation of state of an ideal gas, and the fluid is rather compressible. This is in contrast to conventional fluids, which are incompressible for velocities much below the speed of sound, and can cause inhomogeneities in density. We propose an algorithm for MPCD with a modified collision rule that results in a non-ideal equation of state and a significantly decreased compressibility. It allows simulations at less computational costs compared to conventional MPCD algorithms. We derive analytic expressions for the equation of state and the corresponding compressibility as well as shear viscosity. They show overall very good agreement with simulations, where we determine the pressure by simulating a quiet bulk fluid and the shear viscosity by simulating a linear shear flow and a Poiseuille flow.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Effect of the interaction strength and anisotropy on the diffusio-phoresis of spherical colloids

Gradients in temperature, concentration or electrostatic potential cannot exert forces on a bulk fluid; they can, however, exert forces on a fluid in a microscopic boundary layer surrounding a (nano)colloidal solute, resulting in so-called phoretic flow. Here we present a simulation study of phoretic flow around a spherical colloid held fixed in a concentration gradient. We show that the resulting flow velocity depends non-monotonically on the strength of the colloid-fluid interaction. The reason for this non-monotonic dependence is that solute particles are effectively trapped in a shell around the colloid and cannot contribute to diffusio-phoresis. We also observe that the flow depends sensitively on the anisotropy of solute-colloid interaction.

Active rotational dynamics of a self-diffusiophoretic colloidal motor

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 theoretical description of the active rotational motion is given, along with the results of particle-based simulations of the active dynamics. From these results a detailed description of the factors responsible for the active rotational dynamics can be given. Since active rotational motion often plays a significant part in the nature of the collective dynamics of many-motor systems and can be used to control motor motion in targeted cargo transport, our results should find applications beyond those considered here.

Surface Wettability-Directed Propulsion of Glucose-Powered Nanoflask Motors

Chemically driven colloidal motors capable of implementing different movements under a common environment are of great importance for various complex tasks. However, the key parameters underlying different motion behaviors are incompletely understood. Here, we demonstrate that carbonaceous nanoflask (CNF) motors move spontaneously in glucose powered by the cascade reaction of glucose oxidase and catalase, and their directional propulsion can be premeditated by controlling the surface wettability of nanomotors. The hydrophilic CNF motors move from the round-bottom to the opening neck (backward), whereas the hydrophobic CNF motors swim from the opening neck to the round-bottom (forward). We demonstrate that the backward motion of the hydrophilic CNF motors is driven by the local glucose gradient due to self-diffusiophoresis, and the forward movement of the hydrophobic CNF motors is caused by the locally produced glucose acid gradient. The fluid simulation reveals that the hydrophilic and hydrophobic CNF motors correspond to the puller and pusher models, respectively. Our study offers a minimal strategy to manipulate the direction of motion of motors for specific applications and to change the hydrodynamic behaviors of glucose-powered motors.

Mesoscopic simulations of anisotropic chemically powered nanomotors

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Linear and angular motion of self-diffusiophoretic Janus particles

We theoretically study the active motion of self-diffusiophoretic Janus particles (JPs) using the Onsager-Casimir reciprocal relations. The linear and angular velocity of a single JP are shown to respectively result from a coupling of electrochemical forces to the fluid flow fields induced by a force and torque on the JP. A model calculation is provided for half-capped JPs catalyzing a chemical reaction of solutes at their surface by reducing the continuity equations of the reacting solutes to Poisson equations for the corresponding electrochemical fields. We find that an anisotropic surface reactivity alone is enough to give rise to active linear motion of a JP, whereas active rotation only occurs if the JP is not axisymmetric. In the absence of specific interactions with the solutes, the active linear velocity of the JP is shown to be related to the stoichiometrically weighted sum of the friction coefficients (or hydrodynamic radii) of the reacting solutes. Our reciprocal treatment further suggests that a specific interaction with the solutes is required to observe far-field diffusiophoretic interactions between JPs, which rely on an interfacial solute excess at the JP surface. Most notably, our approach applies beyond the boundary-layer approximation and accounts for both the diffusio- and electrophoretic nature of active motion.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Experimental observation of flow fields around active Janus spheres

The phoretic mechanisms at stake in the propulsion of asymmetric colloids have been the subject of debates during the past years. In particular, the importance of electrokinetic effects on the motility of Pt-PS Janus sphere was recently discussed. Here, we probe the hydrodynamic flow field around a catalytically active colloid 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 understanding their collective dynamics.

Thrust and Hydrodynamic Efficiency of the Bundled Flagella

The motility mechanism of prokaryotic organisms has inspired many untethered microswimmers that could potentially perform minimally invasive medical procedures in stagnant fluid regions inside the human body. Some of these microswimmers are inspired by bacteria with single or multiple helical flagella to propel efficiently and fast. For multiple flagella configurations, the direct measurement of thrust and hydrodynamic propulsion efficiency has been challenging due to the ambiguous mechanical coupling between the flow field and mechanical power input. To address this challenge and to compare alternative micropropulsion designs, a methodology based on volumetric velocity field acquisition is developed to acquire the key propulsive performance parameters from scaled-up swimmer prototypes. A digital particle image velocimetry (PIV) analysis protocol was implemented and experiments were conducted with the aid of computational fluid dynamics (CFD). First, this methodology was validated using a rotating single-flagellum similitude model. In addition to the standard PIV error assessment, validation studies included 2D vs. 3D PIV, axial vs. lateral PIV and simultaneously acquired direct thrust force measurement comparisons. Compatible with typical micropropulsion flow regimes, experiments were conducted both for very low and higher Reynolds (Re) number regimes (up to a Re number = 0.01) than that are reported in the literature. Finally, multiple flagella bundling configurations at 0°, 90° and 180° helical phase-shift angles were studied using scaled-up multiple concentric flagella thrust elements. Thrust generation was found to be maximal for the in-phase (0°) bundling configuration but with ~50% lower hydrodynamic efficiency than the single flagellum. The proposed measurement protocol and static thrust test-bench can be used for bio-inspired microscale propulsion methods, where direct thrust and efficiency measurement are required.

Which interactions dominate in active colloids?

Despite mounting evidence that the same gradients, which active colloids use for swimming, induce important cross-interactions (phoretic interactions), they are still ignored in most many-body descriptions, perhaps to avoid complexity and a zoo of unknown parameters. Here we derive a simple model, which reduces phoretic far-field interactions to a pair-interaction whose strength is mainly controlled by one genuine parameter (swimming speed). The model suggests that phoretic interactions are generically important for autophoretic colloids (unless effective screening of the phoretic fields is strong) and should dominate over hydrodynamic interactions for the typical case of half-coating and moderately nonuniform surface mobilities. Unlike standard minimal models, but in accordance with canonical experiments, our model generically predicts dynamic clustering in active colloids at a low density. This suggests that dynamic clustering can emerge from the interplay of screened phoretic attractions and active diffusion.

Phototaxis of active colloids by self-thermophoresis

Phototaxis usually refers to the ability of a motile micoorganism to move directionally within a light gradient, which is important for microorganisms to gain energy or avoid damage. Here, we show that an active Janus particle driven by self-thermophoresis from light heating is able to exhibit significant phototactic motion by means of mesoscale dynamics simulation. Depending on the particle-fluid interactions, the active particle can move along or against the light gradient, corresponding to positive or negative phototaxis, respectively. We find that the phototaxis of the active colloid is determined by various mechanisms, including alignment (polarization) of the particle to the light gradient, orientation-dependent motility and spatially inhomogeneous motility. Our results shed light on the phototactic behavior of artificial active colloids and open up a new possibility to design photo-responsive micromachines.

Orientational dynamics of a heated Janus particle

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. This choice leads to a different microscopic Kapitza resistance across the solid-fluid boundary of the two halves of the sphere, and consequently a gradient in temperature is created across the poles of the sphere. It is this self-created temperature gradient which leads to a self-propulsion along the direction of the symmetry axis. In this article, we look at the orientational dynamics of such a system, as well as the subsequent enhancement of the translational diffusivity of the heated Janus colloid at late times. The orientational correlation of the symmetry axis is measured from the simulation and provides a direct access to the rotational diffusion constant. The heating leads to an increase in the rotational diffusivity of the colloid. We quantify this increase in rotational diffusion D _r against the temperature difference δT ≡ T(R, 0) - T(R, π) across the poles of the Janus sphere as well as the average surface temperature difference ΔT ≡ T(R) - T(∞) from the ambient fluid. Since the rotational diffusion is determined by the complete flow field in the solvent, we illustrate that comparing D _r against δT is misleading and is better quantified when compared against ΔT. The later quantification results in a data collapse for different choices of the microscopic interaction. The average propulsion velocity is also measured for different choices of the wetting parameter. The directionality of self-propulsion changes depending on the microscopic interaction. We show that whenever the attractive interaction of the colloid with the solvent is switched off, the phoretic mobility changes sign. Furthermore, the propulsion velocity is zero for heating below a certain threshold value. This is also corroborated by the probability distribution of the angle between the displacement vector Δr(t) ≡ r(t) - r(0) and the symmetry axis. Finally, we combine the measured propulsion velocity and the rotational diffusion time τ _r = 1/2D _r to estimate the enhancement in the long time diffusion coefficient of the particle.

Thermophoretic forces on a mesoscopic scale

We use a mesoscale-molecular simulation technique known as Multi-Particle Collision Dynamics (MPC) to study the forces acting on a stationary colloid inside a temperature gradient. We compare our measurements of the thermophoretic force to a theoretical prediction based on Onsager's reciprocal relations, assuming that the temperature gradient is constant across the colloid. We find a good agreement between our measurements and theoretical predictions over a wide range of system parameters, even when the condition of uniform gradients is not strictly fulfilled. Our measurements further suggest that the magnitude of the thermophoretic force depends on the hydrodynamic boundary condition at the colloidal surface, thus highlighting the hydrodynamic character of colloidal thermophoresis. We also investigate how fluid advection disturbs the interfacial layer around the colloid and introduce a dimensionless number to quantify the validity of local thermodynamic equilibrium.

Diffusiophoretically induced interactions between chemically active and inert particles

In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and a moving inert sphere, and second, freely moving reactive and inert spheres. The continuum reaction-diffusion and Stokes equations are solved analytically for these systems and microscopic simulations of the dynamics are carried out. Although the relative velocities of the spheres are very similar in the two systems, the local and global structures of streamlines and the flow velocity fields are found to be quite different. For freely moving spheres, when the two spheres approach each other the flow generated by the inert sphere through diffusiophoresis drags the reactive sphere towards it. This leads to a self-assembled dimer motor that is able to propel itself in solution. The fluid flow field at the moment of dimer formation changes direction. The ratio of sphere sizes in the dimer influences the characteristics of the flow fields, and this feature suggests that active self-assembly of spherical colloidal particles may be manipulated by sphere-size changes in such reactive systems.

Many-body dynamics of chemically propelled nanomotors

The collective behavior of chemically propelled sphere-dimer motors made from linked catalytic and noncatalytic spheres in a quasi-two-dimensional confined geometry is studied using a coarse-grained microscopic dynamical model. Chemical reactions at the catalytic spheres that convert fuel to product generate forces that couple to solvent degrees of freedom as a consequence of momentum conservation in the microscopic dynamics. The collective behavior of the many-body system is influenced by direct intermolecular interactions among the motors, chemotactic effects due to chemical gradients, hydrodynamic coupling, and thermal noise. Segregation into high and low density phases and globally homogeneous states with strong fluctuations are investigated as functions of the motor characteristics. Factors contributing to this behavior are discussed in the context of active Brownian models.

Simulating squirmers with multiparticle collision dynamics

Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.

Electrically Enhanced Self-Thermophoresis of Laser-Heated Janus Particles under a Rotating Electric Field

The motion of a laser-heated Janus particle is experimentally measured under a rotating electric field. Directionally circular motions of the Janus particle following or countering the direction of the rotating electric field are observed in the low-frequency region (from 1 to 6 kHz) depending on the direction of electrorotation. In the higher frequency region (>10 kHz), only pure electrorotation and electrothermal flow are observed. By measuring the dependence of the frequency, voltage, and laser heating power, we propose that the tangential component of circular motion is caused by electric field enhanced self-thermophoresis, which is proportional to the laser heating power and the electric field. This result indicates that thermophoresis could be modified by the induced zeta potential of the Janus particle tuned by the applied electric fields. By this mechanism, the intrinsic thermophoresis can be enhanced several times at a relatively low applied voltage (~3 Volt). Electrically tunable thermophoresis of a particle may bring new insights to thermophoresis phenomenon and also open a new direction for tunable active materials.

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.

Dynamics of a colloidal particle near a thermoosmotic wall under illumination

The effects of light on colloidal particles in solution are multiple, including transfer of photonic linear/angular momentum and heating of the particles or their surroundings. The temperature increase around colloidal particles due to light heating can drive a thermoosmotic flow along a nearby boundary wall, which significantly influences the motion of the particles. Here we perform mesoscopic dynamics simulations to study two typical scenarios, where thermoosmosis is critical. In the first scenario, we consider a light-absorbing colloidal particle heated by uniform illumination. Depending on the fluid-wall interactions, the thermoosmotic flow generated by the wall can exert a long-ranged hydrodynamic attraction or repulsion on the "hot" Brownian particle, which leads to a strong accumulation/depletion of the particle to/from the boundary. In the second scenario, we investigate the motion of a colloidal particle confined by an optical tweezer in a light-absorbing solution. In this case, thermoosmosis can induce a unidirectional rotation of the trapped particle, whose direction is determined by thermoosmotic properties of the wall. We show that colloidal particles near a thermoosmotic wall exhibit rich dynamics. Our results can be applied for the manipulation of colloidal particles in microfluidics.

Mesoscopic modelling and simulation of soft matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Anisotropic thermophoresis

Colloidal migration in a temperature gradient is referred to as thermophoresis. In contrast to particles with a spherical shape, we show that elongated colloids may have a thermophoretic response that varies with the colloid orientation. Remarkably, this can translate into a non-vanishing thermophoretic force in the direction perpendicular to the temperature gradient. Opposite to the friction force, the thermophoretic force of a rod oriented with the temperature gradient can be larger or smaller than when oriented perpendicular to it. The precise anisotropic thermophoretic behavior clearly depends on the colloidal rod aspect ratio, and also on its surface details, which provides an interesting tunability to the devices constructed based on this principle. By means of mesoscale hydrodynamic simulations, we characterize this effect for different types of rod-like colloids.

Mesoscale simulation of phoretically osmotic boundary conditions

Boundary walls can drive the tangential flow of fluids by phoretic osmosis when exposed to a gradient field, including chemical, thermal or electric potential gradient. At the microscale, such boundary driving mechanisms become quite pronounced. Here, we propose a mesoscale strategy to simulate the phoretically osmotic boundaries, in which the microscopic fluid-wall interactions are coarse-grained into the bounce-back or specular reflection, and the phoretically osmotic force is generated by selectively reversing the tangential velocity of specific fluid particles near the boundary wall. With this scheme, the phoretically osmotic boundary can be realized with a minimal modification to the widely used mesoscopic no-slip/slip hydrodynamic boundary condition. Its implementation is quite efficient and the resulting phoretically osmotic flow is flexibly tunable. Its validity is verified by performing extensive mesoscale simulations for both the diffusioosmotic and thermoosmotic boundaries. In particular, we use the proposed scheme to investigate fluid transport driven by the phoretic osmosis in microfluidic systems and the effects of the diffusioosmosis on the dynamics of active catalytic colloidal particles. Our work thus offers new possibilities to study the phoretically osmotic effect in active complex fluids and microfluidic systems by simulation, where the gradient fields are ubiquitous.

Microscopic and continuum descriptions of Janus motor fluid flow fields

Active media, whose constituents are able to move autonomously, display novel features that differ from those of equilibrium systems. In addition to naturally occurring active systems such as populations of swimming bacteria, active systems of synthetic self-propelled nanomotors have been developed. These synthetic systems are interesting because of their potential applications in a variety of fields. Janus particles, synthetic motors of spherical geometry with one hemisphere that catalyses the conversion of fuel to product and one non-catalytic hemisphere, can propel themselves in solution by self-diffusiophoresis. In this mechanism, the concentration gradient generated by the asymmetric catalytic activity leads to a force on the motor that induces fluid flows in the surrounding medium. These fluid flows are studied in detail through microscopic simulations of Janus motor motion and continuum theory. It is shown that continuum theory is able to capture many, but not all, features of the dynamics of the Janus motor and the velocity fields of the fluid.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Thermoosmotic microfluidics

Microchannels with asymmetrically ratcheted walls are here shown to behave as effective and versatile microfluidic pumps if locally heated. When the boundary walls have different temperatures, the confined liquid experiences a temperature gradient along the sawtooth edges, which can induce a thermoosmotic flow. A mesoscale molecular simulation approach is here employed to investigate the flows which are contrasted using an analytical approach. Microchannels can be composed by one or two ratcheted walls which can be straight or cylindrical. Varying the channel geometry can not only change the overall fluid flux, but also vary the flow patters from shear to capillary type, or even to extensional type flows. This scheme does not require multiphase fluids or any movable channel parts, although they are possible to be implemented. The proposed principle is then very versatile to locally manipulate complex fluids, and a promising tool to recover waste heat, to facilitate cooling of microchips, and to manufacture portable lab-on-a-chip devices.

A microscopic model for chemically-powered Janus motors

Very small synthetic motors that make use of chemical reactions to propel themselves in solution hold promise for new applications in the development of new materials, science and medicine. The prospect of such potential applications, along with the fact that systems with many motors or active elements display interesting cooperative phenomena of fundamental interest, has made the study of synthetic motors an active research area. Janus motors, comprising catalytic and noncatalytic hemispheres, figure prominently in experimental and theoretical studies of these systems. While continuum models of Janus motor systems are often used to describe motor dynamics, microscopic models that are able to account for intermolecular interactions, many-body concentration gradients, fluid flows and thermal fluctuations provide a way to explore the dynamical behavior of these complex out-of-equilibrium systems that does not rely on approximations that are often made in continuum theories. The analysis of microscopic models from first principles provides a foundation from which the range of validity and limitations of approximate theories of the dynamics may be assessed. In this paper, a microscopic model for the diffusiophoretic propulsion of Janus motors, where motor interactions with the environment occur only through hard collisions, is constructed, analyzed and compared to theoretical predictions. Microscopic simulations of both single-motor and many-motor systems are carried out to illustrate the results.

Self-Diffusiophoresis of Janus Catalytic Micromotors in Confined Geometries

The self-diffusiophoresis of Janus catalytic micromotors (JCMs) in confined environment is studied using direct numerical simulations. The simulations revealed that, on average, the translocation of a JCM through a short pore is moderately slowed down by the confinement. This slowdown is far weaker compared to the transport of particles through similar pores driven by forces induced by external means or passive diffusiophoresis. Pairing of two JCMs facilitates the translocation of the one JCM entering the pore first but slows down the second JCM. Depending on its initial orientation, a JCM near the entrance of a pore can exhibit different rotational motion, which determines whether it can enter the pore. Once a JCM enters a narrow pore, it can execute a self-alignment process after which it becomes fully aligned with the pore axis and moves to the center line of the pore. Analysis of these results showed that, in addition to hydrodynamic effect, the translation and rotation of JCM is also affected by the "chemical effects", i.e., the modification of the chemical species concentration around a JCM by confining walls and neighboring JCMs. These chemical effects are unique to the self-diffusiophoresis of JCMs and should be considered in design and operations of JCMs in confined environment.

Catalytic microrotor driven by geometrical asymmetry

An asymmetric gear with homogeneous surface properties is, here, presented as a prototype to fabricate catalytic microrotors. The driving torque arises from the diffusiophoretic effect induced by the concentration gradients generated by catalytic chemical reactions at the gear surface. This torque produces a spontaneous and unidirectional rotation of the asymmetric gear. By means of mesoscopic simulations, we prove and characterize this scenario. The gear rotational velocity is determined by the gear-solvent interactions, the gear geometry, the solvent viscosity, and the catalytic reaction ratio. Our work presents a simple way to design self-propelled microrotors, alternative to existing catalytic bi-component, or thermophoretic ones.

Clustering and phase behaviour of attractive active particles with hydrodynamics

We simulate clustering, phase separation and hexatic ordering in a monolayered suspension of active squirming disks subject to an attractive Lennard-Jones-like pairwise interaction potential, taking hydrodynamic interactions between the particles fully into account. By comparing the hydrodynamic case with counterpart simulations for passive and active Brownian particles, we elucidate the relative roles of self-propulsion, interparticle attraction, and hydrodynamic interactions in determining clustering and phase behaviour. Even in the presence of an attractive potential, we find that hydrodynamic interactions strongly suppress the motility induced phase separation that might a priori have been expected in a highly active suspension. Instead, we find only a weak tendency for the particles to form stringlike clusters in this regime. At lower activities we demonstrate phase behaviour that is broadly equivalent to that of the counterpart passive system at low temperatures, characterized by regimes of gas-liquid, gas-solid and liquid-solid phase coexistence. In this way, we suggest that a dimensionless quantity representing the level of activity relative to the strength of attraction plays the role of something like an effective non-equilibrium temperature, counterpart to the (dimensionless) true thermodynamic temperature in the passive system. However there are also some important differences from the equilibrium case, most notably with regards the degree of hexatic ordering, which we discuss carefully.