Densitaxis: Active particle motion in density gradients.

Organisms often swim through density-stratified fluids. Here, we investigate the dynamics of active particles swimming in fluid density gradients and report theoretical evidence of taxis as a result of these gradients (densitaxis). Specifically, we calculate the effect of density stratification on the dynamics of a force- and torque-free spherical squirmer and show that density gradients induce reorientation that tends to align swimming either parallel or normal to the gradient depending on the swimming gait. In particular, swimmers that propel by generating thrust in the front (pullers) rotate to swim parallel to gradients and hence display (positive or negative) densitaxis, while swimmers that propel by generating thrust in the back (pushers) rotate to swim normal to the gradients. This work could be useful to understand the motion of marine organisms in ocean or be leveraged to sort or organize a suspension of active particles by modulating density gradients.

Capillary Imbibition in a Diverging Flexible Channel.

We study the imbibition of a wetting liquid between flexible sheets that are fixed at both ends. Assuming a narrow gap between the sheets, we solve the lubrication equation coupled with a slender body deformation. When the sheets are parallel, we find that the deformation initially speeds up the flow, as shown in previous studies, but only up to the middle of the channel. As the channel contracts, the hydrodynamic resistance increases and ultimately slows down the filling process. Below a threshold stiffness, the channel collapses and imbibition stops. We propose a scaling of the filling duration near this threshold. Next, we show that if the sheets are initially tilted with a minimal angle, the channel avoids collapse. The liquid front pulls the diverging sheets and spreads in a nearly parallel portion, which maintains the capillary propulsion and enhances the wicking. Therefore, while it is established that diverging rigid plates imbibe liquids slower than parallel ones do, we show that elasticity reverses this principle: diverging flexible sheets imbibe liquids faster than parallel ones. We find an optimal tilt angle that gives the shortest filling time.

Energetics of cytoskeletal gel contraction.

Cytoskeletal gels are prototyped to reproduce the mechanical contraction of the cytoskeleton in vitro. They are composed of a polymer network (backbone), swollen by the presence of a liquid solvent, and active molecules (molecular motors, MMs) that transduce chemical energy into the mechanical work of contraction. These motors attach to the polymer chains to shorten them and/or act as dynamic crosslinks, thereby constraining the thermal fluctuations of the chains. We describe both mechanisms thermodynamically as a microstructural reconfiguration, where the backbone stiffens to motivate solvent (out)flow and accommodate contraction. Via simple steady-state energetic analysis, under the simplest case of isotropic deformation, we quantify the mechanical energy required to achieve contraction as a function of polymer chain density and molecular motor density. We identify two limit regimes, namely, fast MM activation (FM), and slow MM activation (SM). FM assumes that MMs provide all the available mechanical energy 'instantaneously' and leave the polymer in a stiffened state, i.e. the MM activity occurs at a time scale that is much smaller than that of solvent diffusion. SM assumes that the timescale for MM activation is much longer than that of solvent diffusion. To achieve the same final contracted state, FM requires the largest amount of work per unit reference volume, while SM requires the least. For all intermediate cases where the timescale of MM activation is comparable with that of solvent diffusion, the required work ranges between these two limits. We provide all these quantities as a function of chain density and MM density. Finally, we compare our results on contraction energetics with experiments and observe good agreement.

Confined active matter in external fields.

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

Active particles crossing sharp viscosity gradients.

Active particles (living or synthetic) often move through inhomogeneous environments, such as gradients in light, heat or nutrient concentration, that can lead to directed motion (or taxis). Recent research has explored inhomogeneity in the rheological properties of a suspending fluid, in particular viscosity, as a mechanical (rather than biological) mechanism for taxis. Theoretical and experimental studies have shown that gradients in viscosity can lead to reorientation due to asymmetric viscous forces. In particular, recent experiments with Chlamydomonas Reinhardtii algae swimming across sharp viscosity gradients have observed that the microorganisms are redirected and scattered due to the viscosity change. Here we develop a simple theoretical model to explain these experiments. We model the swimmers as spherical squirmers and focus on small, but sharp, viscosity changes. We derive a law, analogous to Snell's law of refraction, that governs the orientation of active particles in the presence of a viscosity interface. Theoretical predictions show good agreement with experiments and provide a mechanistic understanding of the observed reorientation process.

Rheology of periodically sheared suspensions undergoing reversible-irreversible transition.

The rheology of noncolloidal suspensions under cyclic shear is studied numerically. The main findings are a strain amplitude (γ_{0}) dependent response in the shear stress and second normal stress difference (N_{2}). Specifically, we find a reduced viscosity, an enhanced intracycle shear thinning, the onset of a finite N_{2}, and its frequency doubling, all near a critical strain amplitude γ_{c} that scales with the volume fraction ϕ as γ_{c}∼ϕ^{-2}. These rheological changes also signify a reversible-irreversible transition (RIT), dividing stroboscopic particle dynamics into a reversible absorbing phase (for γ_{0}<γ_{c}) and a persistently diffusing phase (for γ_{0}>γ_{c}). We explain the results based on two flow-induced mechanisms and elucidate their connection in the context of RIT through the underlying microstructure, which tends toward hyperuniformity near γ_{0}=γ_{c}. Overall, we expect this correspondence between rheology and emergent dynamics to hold in a wide range of settings where structural organizations are dominated by volume exclusions.

The morphological role of ligand inhibitors in blocking receptor- and clathrin-mediated endocytosis.

Cells often internalize particles through endocytic pathways that involve the binding between cell receptors and particle ligands, which drives the cell membrane to wrap the particle into a delivery vesicle. Previous findings showed that receptor-mediated endocytosis is impossible for spherical particles smaller than a minimum size because of the energy barrier created by membrane bending. In this study, we investigate the morphological role of ligand inhibitors in blocking endocytosis, inspired by antibodies that inhibit virus ligands to prevent infection. While ligand inhibitors have the obvious effect of reducing the driving force due to adhesion, they also have a nontrivial (morphological) impact on the entropic and elastic energy of the system. We determine the necessary conditions for endocytosis by considering the additional energy barrier due to the membrane bending to wrap the inhibiting protrusions. We find that inhibitors increase the minimum radius previously reported, depending on their density and size. In addition, we extend this result to the case of clathrin-mediated endocytosis, which is the most common pathway for virus entry. The assembly of a clathrin coat with a spontaneous curvature increases the energy barrier and sets a maximum particle size (in agreement with experimental observations on spherical particles). Our investigation suggests that morphological considerations can inform the optimal design of neutralizing viral antibodies and new strategies for targeted nanomedicine.

Active Particles in Viscosity Gradients.

Microswimmers in nature often experience spatial gradients of viscosity. In this Letter we develop theoretical results for the dynamics of active particles, biological or otherwise, swimming through viscosity gradients. We model the active particles using the squirmer model, and show how viscosity gradients lead to viscotaxis for squirmers, and how the effects of viscosity gradients depend on the swimming gait of the microswimmers. We also show how such gradients in viscosity can be used to control active particles and suggest a mechanism to sort them based on their swimming style.

Maximizing propulsive thrust of a driven filament at low Reynolds number via variable flexibility.

At low Reynolds numbers the locomotive capability of a body can be dramatically hindered by the absence of inertia. In this work, we show how propulsive performance in this regime can be significantly enhanced by employing spatially varying flexibility. As a prototypical example, we consider the propulsive thrust generated by a filament periodically driven at one end. The rigid case leads to zero propulsion, as so constrained by Purcell's scallop theorem, while for uniform filaments there exists a bending stiffness maximizing the propulsive force at a given frequency; here we demonstrate explicitly how considerable further improvement can be achieved by simply varying the stiffness along the filament. The optimal flexibility distribution is strongly configuration-dependent: while increasing the flexibility towards the tail-end enhances the propulsion of a clamped filament, for a hinged filament decreasing the flexibility towards the tail-end is instead favorable. The results reveal new design principles for maximizing propulsion at low Reynolds numbers, potentially useful for developing synthetic micro-swimmers requiring large propulsive force for various biomedical applications.

Propulsion via flexible flapping in granular media.

Biological locomotion in nature is often achieved by the interaction between a flexible body and its surrounding medium. The interaction of a flexible body with granular media is less understood compared with viscous fluids partially due to its complex rheological properties. In this work, we explore the effect of flexibility on granular propulsion by considering a simple mechanical model in which a rigid rod is connected to a torsional spring that is under a displacement actuation using a granular resistive force theory. Through a combined numerical and asymptotic investigation, we characterize the propulsive dynamics of such a flexible flapper in relation to the actuation amplitude and spring stiffness, and we compare these dynamics with those observed in a viscous fluid. In addition, we demonstrate that the maximum possible propulsive force can be obtained in the steady propulsion limit with a finite spring stiffness and large actuation amplitude. These results may apply to the development of synthetic locomotive systems that exploit flexibility to move through complex terrestrial media.

Hydrodynamic interactions of cilia on a spherical body.

Microorganisms develop coordinated beating patterns on surfaces lined with cilia known as metachronal waves. For a chain of cilia attached to a flat ciliate, it has been shown that hydrodynamic interactions alone can lead the system to synchronize. However, several microorganisms possess a curve-shaped ciliate body and so to understand the effect of this geometry on the formation of metachronal waves, we evaluate the hydrodynamic interactions of cilia near a large spherical body. Using a minimal model, we show that for a chain of cilia around the sphere, the natural periodicity in the geometry leads the system to synchronize. We also report an emergent wavelike behavior when an asymmetry is introduced to the system.

Hydrodynamic phase locking of swimming microorganisms.

Some microorganisms, such as spermatozoa, synchronize their flagella when swimming in close proximity. Using a simplified model (two infinite, parallel, two-dimensional waving sheets), we show that phase locking arises from hydrodynamics forces alone, and has its origin in the front-back asymmetry of the geometry of their flagellar waveform. The time evolution of the phase difference between coswimming cells depends only on the nature of this geometrical asymmetry, and microorganisms can phase lock into conformations which minimize or maximize energy dissipation.