Entrainment and scattering in microswimmer--colloid interactions

We use boundary element simulations to study the interaction of model microswimmers with a neutrally buoyant spherical particle. The ratio of the size of the particle to that of the swimmer is varied from $R^\mathrm{P} / R^\mathrm{S} \ll 1$, corresponding to swimmer--tracer scattering, to $R^\mathrm{P} / R^\mathrm{S} \gg 1$, approximately equivalent to the swimmer interacting with a fixed, flat surface. We find that details of the swimmer and particle trajectories vary for different swimmers. However, the overall characteristics of the scattering event fall into two regimes, depending on the relative magnitudes of the impact parameter, $\rho$, and the collision radius, $R^\mathrm{coll}=R^\mathrm{P} + R^\mathrm{S}$. The range of particle motion, defined as the maximum distance between two points on the trajectory, has only a weak dependence on the impact parameter when $\rho < R^\mathrm{coll}$ and decreases with the radius of the particle. In contrast, when $\rho>R^\mathrm{coll}$ the range decreases as a power law in $\rho$ and is insensitive to the size of the particle. We also demonstrate that large particles can cause swimmers to be deflected through large angles. In some instances, this swimmer deflection can lead to larger net displacements of the particle. Based on these results, we estimate the effective diffusivity of a particle in a dilute bath of swimmers and show that there is a non-monotonic dependence on particle radius. Similarly, we show that the effective diffusivity of a swimmer scattering in a suspension of particles varies non-monotonically with particle radius.Comment: 19 pages, 11 figures. Accepted in Physical Review Fluid

Microswimmer Propulsion by Two Steadily Rotating Helical Flagella

Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by experimental observations of a group of magnetotactic bacterial strains, we extended the model by considering two flagella attached to the cell body and rotating about their respective axes. Using numerical simulations, we analyzed the motion of such a microswimmer in bulk fluid and close to a solid surface. We show that positioning the two flagella far apart on the cell body reduces the rate of rotation of the body and increases the swimming speed. Near surfaces, we found that swimmers with two flagella can swim in relatively straight trajectories or circular orbits in either direction. It is also possible for the swimmer to escape from surfaces, unlike a model swimmer of similar shape but with only a single flagellum. Thus, we conclude that there are important implications of swimming with two flagella or flagellar bundles rather than one. These considerations are relevant not only for understanding differences in bacterial morphology but also for designing microrobotic swimmers.Natural Sciences and Engineering Research Council [RGPIN-2018-04418

Cardinality-restricted chains and antichains in partially ordered sets

AbstractFor a given poset and positive integer κ, four problems are considered. Covering: Determine a minimum cardinality cover of the poset elements by chains (antichains), each of length (width) at most κ. Optimization: Given also weights on the poset elements, find a chain (antichain) of maximum total weight among those of length (width) at most κ. It is shown that the chain covering problem is NP-complete, while chain optimization is polynomial-time solvable. Several classes of facets are derived for the polytope generated by incidence vectors of antichains of width at most κ. Certain of these facets are then used to develop a polyhedral combinatorial algorithm for the antichain optimization problem. Computational results are given for the algorithm on randomly generated posets with up to 1005 elements and 4 ⩽ κ ⩽ 30

Synthetic quorum sensing in model microcapsule colonies

Biological quorum sensing refers to the ability of cells to gauge their population density and collectively initiate a new behavior once a critical density is reached. Designing synthetic materials systems that exhibit quorum sensing-like behavior could enable the fabrication of devices with both self-recognition and self-regulating functionality. Herein, we develop models for a colony of synthetic microcapsules that communicate by producing and releasing signaling molecules. Production of the chemicals is regulated by a biomimetic negative feedback loop, the "repressilator" network. Through theory and simulation, we show that the chemical behavior of such capsules is sensitive to both the density and number of capsules in the colony. For example, decreasing the spacing between a fixed number of capsules can trigger a transition in chemical activity from the steady, repressed state to large-amplitude oscillations in chemical production. Alternatively, for a fixed density, an increase in the number of capsules in the colony can also promote a transition into the oscillatory state. This configuration-dependent behavior of the capsule colony exemplifies quorum-sensing behavior. Using our theoretical model, we predict the transitions from the steady state to oscillatory behavior as a function of the colony size and capsule density.U.S. Department of Energy: DE-SC000098

The N -Link Swimmer in Three Dimensions: Controllability and Optimality Results

The controllability of a fully three-dimensional N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the N -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided

Harnessing surface-bound enzymatic reactions to organize microcapsules in solution

By developing new computational models, we examine how enzymatic reactions on an underlying surface can be harnessed to direct the motion and organization of reagent-laden microcapsules in a fluid-filled microchannel. In the presence of appropriate reagents, surface-bound enzymes can act as pumps, which drive large-scale fluid flows. When the reagents diffuse through the capsules' porous shells, they can react with enzymatic sites on the bottom surface. The ensuing reaction generates fluid density variations, which result in fluid flows. These flows carry the suspended microcapsules and drive them to aggregate into "colonies" on and near the enzyme-covered sites. This aggregation continues until the reagent has been depleted and the convection stops. We show that the shape of the assembled colonies can be tailored by patterning the distribution of enzymes on the surface. This fundamental physicochemical mechanism could have played a role in the self-organization of early biological cells (protocells) and can be used to regulate the autonomous motion and targeted delivery of microcarriers in microfluidic devices.Charles E. Kaufman Foundation: ID0EWGBG5633Center for Bio-Inspired Energy Science: ID0EYLBG5634, DE-SC000098

Convective flow reversal in self-powered enzyme micropumps

Surface-bound enzymes can act as pumps that drive large-scale fluid flows in the presence of their substrates or promoters. Thus, enzymatic catalysis can be harnessed for "on demand" pumping in nano-and microfluidic devices powered by an intrinsic energy source. The mechanisms controlling the pumping have not, however, been completely elucidated. Herein, we combine theory and experiments to demonstrate a previously unreported spatiotemporal variation in pumping behavior in urease-based pumps and uncover the mechanisms behind these dynamics. We developed a theoretical model for the transduction of chemical energy into mechanical fluid flow in these systems, capturing buoyancy effects due to the solution containing nonuniform concentrations of substrate and product. We find that the qualitative features of the flow depend on the ratios of diffusivities delta = D-P / D-S and expansion coefficients beta = beta(P) / beta(S) of the reaction substrate (S) and product (P). If delta > 1 and delta > beta (or if delta < 1 and delta < beta), an unexpected phenomenon arises: the flow direction reverses with time and distance from the pump. Our experimental results are in qualitative agreement with the model and show that both the speed and direction of fluid pumping (i) depend on the enzyme activity and coverage, (ii) vary with the distance from the pump, and (iii) evolve with time. These findings permit the rational design of enzymatic pumps that accurately control the direction and speed of fluid flow without external power sources, enabling effective, self-powered fluidic devices.National Science Foundation: DGE-1255832, DMR-1420620Defense Threat Reduction Agency: HDTRA1-13-1-003

Simulating collective transport of virtual ants

This paper simulates the behaviour of collective transport where a group of ants transports an object in a cooperative fashion. Different from humans, the task coordination of collective transport, with ants, is not achieved by direct communication between group individuals, but through indirect information transmission via mechanical movements of the object. This paper proposes a stochastic probability model to model the decision-making procedure of group individuals and trains a neural network via reinforcement learning to represent the force policy. Our method is scalable to different numbers of individuals and is adaptable to users' input, including transport trajectory, object shape, external intervention, etc. Our method can reproduce the characteristic strategies of ants, such as realign and reposition. The simulations show that with the strategy of reposition, the ants can avoid deadlock scenarios during the task of collective transport