The Boundary Element Method for Fluctuating Active Colloids

The boundary element method (BEM) is a computational method particularly suited to solution of linear partial differential equations (PDEs), including the Laplace and Stokes equations, in complex geometries. The PDEs are formulated as boundary integral equations over bounding surfaces, which can be discretized for numerical solution. This manuscript reviews application of the BEM for simulation of the dynamics of “active” colloids that can self-propel through liquid solution. We introduce basic concepts and model equations for both catalytically active colloids and the “squirmer” model of a ciliated biological microswimmer. We review the foundations of the BEM for both the Laplace and Stokes equations, including the application to confined geometries, and the extension of the method to include thermal fluctuations of the colloid. Finally, we discuss recent and potential applications to research problems concerning active colloids. The aim of this review is to facilitate development and adoption of boundary element models that capture the interplay of deterministic and stochastic effects in the dynamics of active colloids

Shape-induced pairing of spheroidal squirmers

The "squirmer model" is a classical hydrodynamic model for the motion of interfacially-driven microswimmers, such as self-phoretic colloids or volvocine green algae. To date, most studies using the squirmer model have considered spherical particles with axisymmetric distribution of surface slip. Here, we develop a general approach to the pairing and scattering dynamics of two spheroidal squirmers. We assume that the direction of motion of the squirmers is restricted to a plane, which is approximately realized in many experimental systems. In the framework of an analytically tractable kinetic model, we predict that, for identical squirmers, an immotile "head-to-head" configuration is stable only when the particles have oblate shape and a non-axisymmetric distribution of surface slip. We also obtain conditions for stability of a motile "head-to-tail" configuration: for instance, the two particles must have unequal self-propulsion velocities. Our analytical predictions are compared against detailed numerical calculations obtained using the boundary element method.Comment: Main text: 6 pages, 4 figures. SI: 9 pages, 5 figure

Bacterial Biohybrid Microswimmers

Over millions of years, Nature has optimized the motion of biological systems at the micro and nanoscales. Motor proteins to motile single cells have managed to overcome Brownian motion and solve several challenges that arise at low Reynolds numbers. In this review, we will briefly describe naturally motile systems and their strategies to move, starting with a general introduction that surveys a broad range of developments, followed by an overview about the physical laws and parameters that govern and limit motion at the microscale. We characterize some of the classes of biological microswimmers that have arisen in the course of evolution, as well as the hybrid structures that have been constructed based on these, ranging from Montemagno's ATPase motor to the SpermBot. Thereafter, we maintain our focus on bacteria and their biohybrids. We introduce the inherent properties of bacteria as a natural microswimmer and explain the different principles bacteria use for their motion. We then elucidate different strategies that have been employed for the coupling of a variety of artificial microobjects to the bacterial surface, and evaluate the different effects the coupled objects have on the motion of the 'biohybrid.' Concluding, we give a short overview and a realistic evaluation of proposed applications in the field

Universal motion of mirror-symmetric microparticles in confined Stokes flow

Comprehensive understanding of particle motion in microfluidic devices is essential to unlock novel technologies for shape-based separation and sorting of microparticles like microplastics, cells and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape-dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.Comment: 10 pages, 4 figures, 1 table, 1 PDF file containing Supplementary Text, Figures and Tabl

Floor- or ceiling-sliding for chemically active, gyrotactic, sedimenting Janus particles

Surface bound catalytic chemical reactions self-propel chemically active Janus particles. In the vicinity of boundaries, these particles exhibit rich behavior, such as the occurrence of wall-bound steady states of "sliding". Most active particles tend to sediment as they are density mismatched with the solution. Moreover Janus spheres, which consist of an inert core material decorated with a cap-like, thin layer of a catalyst, are gyrotactic ("bottom-heavy"). Occurrence of sliding states near the horizontal walls depends on the interplay between the active motion and the gravity-driven sedimentation and alignment. It is thus important to understand and quantify the influence of these gravity-induced effects on the behavior of model chemically active particles moving near walls. For model gyrotactic, self-phoretic Janus particles, here we study theoretically the occurrence of sliding states at horizontal planar walls that are either below ("floor") or above ("ceiling") the particle. We construct "state diagrams" characterizing the occurrence of such states as a function of the sedimentation velocity and of the gyrotactic response of the particle, as well as of the phoretic mobility of the particle. We show that in certain cases sliding states may emerge simultaneously at both the ceiling and the floor, while the larger part of the experimentally relevant parameter space corresponds to particles that would exhibit sliding states only either at the floor or at the ceiling or there are no sliding states at all. These predictions are critically compared with the results of previous experimental studies and our experiments conducted on Pt-coated polystyrene and silica-core particles suspended in aqueous hydrogen peroxide solutions.Comment: Total number of pages: 33, Number of figures: 18. The video files, as mentioned in the supplementary material will be provided by the corresponding author upon reques

Bacterial Biohybrid Microswimmers

Over millions of years, Nature has optimized the motion of biological systems at the micro and nanoscales. Motor proteins to motile single cells have managed to overcome Brownian motion and solve several challenges that arise at low Reynolds numbers. In this review, we will briefly describe naturally motile systems and their strategies to move, starting with a general introduction that surveys a broad range of developments, followed by an overview about the physical laws and parameters that govern and limit motion at the microscale. We characterize some of the classes of biological microswimmers that have arisen in the course of evolution, as well as the hybrid structures that have been constructed based on these, ranging from Montemagno's ATPase motor to the SpermBot. Thereafter, we maintain our focus on bacteria and their biohybrids. We introduce the inherent properties of bacteria as a natural microswimmer and explain the different principles bacteria use for their motion. We then elucidate different strategies that have been employed for the coupling of a variety of artificial microobjects to the bacterial surface, and evaluate the different effects the coupled objects have on the motion of the “biohybrid.” Concluding, we give a short overview and a realistic evaluation of proposed applications in the field

Engineering particle trajectories in microfluidic flows using particle shape

Recent advances in microfluidic technologies have created a demand for techniques to control the motion of flowing microparticles. Here we consider how the shape and geometric confinement of a rigid microparticle can be tailored for ‘self-steering’ under external flow. We find that an asymmetric particle, weakly confined in one direction and strongly confined in another, will align with the flow and focus to the channel centreline. Experimentally and theoretically, we isolate three viscous hydrodynamic mechanisms that contribute to particle dynamics. Through their combined effects, a particle is stably attracted to the channel centreline, effectively behaving as a damped oscillator. We demonstrate the use of self-steering particles for microfluidic device applications, eliminating the need for external forces or sheath flows.National Science Foundation (U.S.) (Grant CMMI-1120724)Novartis (Firm)United States. Army Research Office (Institute for Collaborative Biotechnologies Contract W911NF-09-D-0001

Inferring non-equilibrium interactions from tracer response near confined active Janus particles

Chemically active Janus particles sustain non-equilibrium spatial variations in the chemical composition of the suspending solution; these induce hydrodynamic flow and (self-)motility of the particles. Direct mapping of these fields has so far proven to be too challenging. Therefore, indirect methods are needed, e.g., deconvolving the response of “tracer” particles to the activity-induced fields. Here, we study experimentally the response of silica particles, sedimented at a wall, to active Pt/silica Janus particles. The latter are either immobilized at the wall, with the symmetry axis perpendicular or parallel to the wall, or motile. The experiments reveal complex effective interactions that are dependent on the configuration and on the state of motion of the active particle. Within the framework of a coarse-grained model, the behavior of tracers near an immobilized Janus particle can be captured qualitatively once activity-induced osmotic flows on the wall are considered

Upstream rheotaxis of catalytic Janus spheres

Fluid flow is ubiquitous in many environments that form habitats for microorganisms. Therefore, it is not surprising that both biological and artificial microswimmers show responses to flows that are determined by the interplay of chemical and physical factors. In particular, to deepen the understanding of how different systems respond to flows, it is crucial to comprehend the influence played by swimming pattern. The tendency of organisms to navigate up or down the flow is termed rheotaxis. Early theoretical studies predicted a positive rheotactic response for puller-type spherical Janus micromotors. However, recent experimental studies have focused on pusher-type Janus particles, finding that they exhibit cross-stream migration in externally applied flows. To study the response to the flow of swimmers with a qualitatively different flow pattern, we introduce Cu@SiO2micromotors that swim toward their catalytic cap. On the basis of experimental observations, and supported by flow field calculations using a model for self-electrophoresis, we hypothesize that they behave effectively as a puller-type system. We investigate the effect of externally imposed flow on these spherically symmetrical Cu@SiO2active Janus colloids, and we indeed observe a steady upstream directional response. Through a simple squirmer model for a puller, we recover the major experimental observations. Additionally, the model predicts a "jumping" behavior for puller-type micromotors at high flow speeds. Performing additional experiments at high flow speeds, we capture this phenomenon, in which the particles "roll" with their swimming axes aligned to the shear plane, in addition to being dragged downstream by the fluid flow