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

Self-organizing microfluidic crystals

We consider how to design a microfluidic system in which suspended particles spontaneously order into flowing crystals when driven by external pressure. Via theory and numerics, we find that particle–particle hydrodynamic interactions drive self-organization under suitable conditions of particle morphology and geometric confinement. Small clusters of asymmetric “tadpole” particles, strongly confined in one direction and weakly confined in another, spontaneously order in a direction perpendicular to the external flow, forming one dimensional lattices. Large suspensions of tadpoles exhibit strong density heterogeneities and form aggregates. By rationally tailoring particle shape, we tame this aggregation and achieve formation of large two-dimensional crystals.United States. Army Research Office (Institute for Collaborative Biotechnologies (ICB), contract no. W911NF-09-D-0001

Control of Budded Domains in Amphiphilic Bilayer Membranes

Phase separated domains in multicomponent vesicles form spherical buds to reduce interfacial energy. We study the response of a multicomponent budded vesicle to an imposed shear flow with dissipative particle dynamics. We find that shear can either act to stretch the bud open or separate the bud from the vesicle, depending on bud orientation. We examine the interplay of interfacial tension, bending energy, and shear in determining the behavior of the vesicle, and provide criteria for the design of vesicles for controlled bud release.The neck connecting the budded domain with the bulk vesicle assumes a catenoid shape to minimize bending energy. We model the mechanism for pinch-off of catenoid necks with continuum elastic theory and dissipative particle dynamics. We examine pore nucleation and growth driven by Gaussian energy, by the adhesion energy of an encapsulated particle, and by the line energy of an interface between two amphiphile species, aiming to provide principles for the design of vesicles for biomimetic phagocytosis

Calculating the motion of highly confined, arbitrary-shaped particles in Hele-Shaw channels

We combine theory, numerical calculations, and experiments to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To test our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using `continuous flow lithography'. Contrary to what was reported in earlier work (Uspal et al., Nature communications 4 (2013)), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme.Comment: 18 pages, 5 figures, 4 supplemental movie

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

Collective hydrodynamics of soft microparticles in quasi-two-dimensional confinement

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2014.120Cataloged from PDF version of thesis.Includes bibliographical references (pages [151]-156).Flow of microparticles through geometrically confined spaces is a core element of most microfluidic technologies. Flowing particles are typically ordered and manipulated with external forces or coflowing streams, but these methods can be limited in generality and scalability. New techniques to control particle trajectories would enable new applications in such areas as materials assembly, optofluidics, and miniaturized "on-chip" bioassays and cytometry. Recently, researchers have sought to understand the conditions under which particles can organize themselves through interactions generic to the flow of suspensions through microchannels. In particular, a particle moving through a viscous fluid will create a disturbance flow, affecting the motion of distant particles. These hydrodynamic interactions (HI) are sensitive to particle shape and the presence of confining boundaries. This sensitivity presents a powerful opportunity: particle trajectories could be "programmed" into particle morphology and channel design. These could chosen so that many-body hydrodynamic interactions drive self-organization of the desired particle motions. Even a single particle could be designed to "self-steer" to a desired position in the channel cross-section through its hydrodynamic self-interaction. In this thesis, we present a series of studies exploring new possibilities for achieving selforganization, self-steering, and other flow-driven collective phenomena via design of particle shape and channel geometry. We focus on a particular setting: quasi-two-dimensional (q2D) confinement, in which particles are tightly "sandwiched" between parallel plates, free to move in only two dimensions. In this confinement regime, hydrodynamic interactions take a unique dipolar form. This form had been shown to sustain novel collective phenomena with much greater spatiotemporal coherence than can be achieved in unconfined or weakly confined suspensions. However, self-organization of q2D suspensions had not been demonstrated prior to our studies. Starting from a two-body problem, we progressively consider larger numbers of particles and more complex particle shapes. In our first study, we develop model equations for the coupled motion of two discs in a quasi-two-dimensional channel. Numerically, we find that a pair can form a hydrodynamic bound state with complex oscillatory motion. We demonstrate that this "quasiparticle" can be manipulated via patterning of confining boundaries. In the following study, we consider larger clusters of discs. We provide symmetry principles for the a priori construction of "flowing crystals": configurations of particles that maintain their relative positions as they are carried by the flow. The crystalline states generalize the two-body bound state to more complex configurations and collective modes. We also consider the wider dynamical landscape, finding metastable states with new, exquisitely coordinated particle motions. However, neither flowing crystals nor metastable states spontaneously form from a disordered configuration of discs. In pursuit of self-steering and self-organization, we turn to particle shape, and study the dynamics of a single "dumbbell" comprising two connected discs. We find that a fore-aft asymmetric dumbbell will reliably align with the flow and focus to the channel centerline. In contrast, a symmetric particle will oscillate between the channel side walls indefinitely. Through theoretical arguments, we isolate three viscous hydrodynamic mechanisms that together produce self-steering, and which generically occur for asymmetric particles in q2D. We carry out experiments with Continuous Flow Lithography (CFL), finding qualitative and semi-quantitative agreement with our theoretical predictions. Obtaining statistics from hundreds of particle trajectories, we provide a convincing experimental demonstration of self-steering for device applications. To our knowledge, this study provides the first demonstration that rigid particles can focus to the centerline in a channel flow. This progression culminates in our final study. Inspired by the mobility formalism of polymer dynamics, we develop a theoretical and numerical framework that can recover the collective dynamics of many particles with complex shape. We find that small clusters of dumbbells can self-organize from disorder into one-dimensional flowing crystals. However, dumbbells can also pair as undesirable "defects." This two-body effect frustrates self-organization in large suspensions of dumbbells, driving formation of particle aggregates. To tame this aggregation, we rationally redesign particle shape, tailoring hydrodynamic interactions to promote chaining of particles in the flow direction. The redesigned "trumbbell" particles self-organize into large, two-dimensional flowing crystals. We reveal how crystal self-organization occurs through a multistage process. One, two, several, and finally many-body interactions become implicated in successive stages. This study is the first to demonstrate that flowing lattices can be stabilized purely by viscous hydrodynamic interactions.by William Eric Uspal.Ph. D