Microscale locomotion in a nematic liquid crystal

Inertial swimming in an Oldroyd-B fluid

The effects of fluid inertia on a self-propelling inextensible waving sheet in an Oldroyd-B fluid are examined. The swimming velocity of the sheet is calculated in the limit in which the amplitude of the waves propagating along the sheet is small relative to the wavelength of the waves. The rate of work done by the sheet is also calculated. It is found that the swimming speed decreases monotonically approaching a limiting value with increasing Reynolds number (R) for a Newtonian fluid. For an Oldroyd-B fluid, the swimming speed increases to a maximum and then decreases asymptotically to a limiting value with increasing R. In contrast, it increases monotonically to a limiting value with increasing R for a Maxwell fluid. The limiting value is highest for the Maxwell fluid and lowest for the Oldroyd-B fluid. The corresponding value for the Newtonian fluid lies in between. The rate of work done by the sheet increases with increasing Reynolds number for all Deborah numbers. However, the energy consumed at a fixed swimming speed is lesser for an Oldroyd-B fluid than that of a Newtonian fluid. These results suggest that contrary to the Newtonian case, the fluid inertia supports the swimming sheet motion in a complex fluid. At a particular Deborah number, the oscillation frequency of the sheet could be adjusted to achieve the maximum speed. Similarly, at a particular frequency of oscillation, the Deborah numbers could be adjusted to achieve the maximum speed. These observations are in sharp contrast with the previous results reported for Newtonian and second-order fluids.

Taylor's swimming sheet near a soft boundary

In 1951, G. I. Taylor modeled swimming microorganisms by hypothesizing an infinite sheet in 2D moving in a viscous medium due to a wave passing through it. This simple model not only captured the ability of microorganisms to swim due to the wavy motion of a flagella, but further development into the model captured the optimal nature of metachronal waves observed in ciliates. While the additional effects of nearby rigid boundaries and complex environments have been addressed, herein we explore the correction induced by a nearby soft boundary. Our simple model allows us to show that the magnitude of the swimming velocity gets modified near soft boundaries, and reduces for transverse waves while it increases for longitudinal waves. We further delve into the energetics of the process and the deformation of the corresponding soft boundary, highlighting the synchronization of the oscillations induced on the soft boundary with the waves passing through the sheet and the corresponding changes to the power exerted on the fluid. The simplicity of the model allows to analytically sketch the key generic behaviours and mechanisms that should be relevant for microswimming in soft environnements.

Taylor's swimming sheet in a smectic-A liquid crystal

We calculate the swimming speed of a Taylor sheet in a smectic-A liquid crystal. Assuming that the amplitude of the wave propagating on the sheet is much smaller than the wave number, we solve the governing equations using the method of series expansion up to the second order in amplitude. We find that the sheet can swim much faster in smectic-A liquid crystals than in Newtonian fluids. The elasticity associated with the layer compressibility is responsible for the enhanced speed. We also calculate the power dissipated in the fluid and the flux of the fluid. The fluid is pumped opposite to the direction of the wave propagation.

Frustrated 'run and tumble' of swimming Escherichia coli bacteria in nematic liquid crystals

In many situations, bacteria move in complex environments, as soils, oceans or the human gut-track, where carrier fluids show complex structures associated with non-Newtonian rheology. Many fundamental questions concerning the ability to navigate in such environments remain unsolved. Recently, it has been shown that the kinetics of bacterial motion in structured fluids as liquid crystals (LCs) is constrained by the orientational molecular order (or director field) and that novel spatio-temporal patterns arise. A question unaddressed so far is how bacteria change swimming direction in such an environment. In this work, we study the swimming mechanism of a single bacterium, Esherichia coli, constrained to move along the director field of a lyotropic chromonic liquid crystal confined to a planar cell. Here, the spontaneous 'run and tumble' motion of the bacterium gets frustrated: the elasticity of the LC prevents flagella from unbundling. Interestingly, to change direction, bacteria execute a reversal motion along the director field, driven by the relocation of a single flagellum, a 'frustrated tumble'. We characterize this phenomenon in detail experimentally, exploiting exceptional spatial and temporal resolution of bacterial and flagellar dynamics, using a two colour Lagrangian tracking technique. We suggest a possible mechanism accounting for these observations.

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Active Brownian motion with memory delay induced by a viscoelastic medium

By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement, and mean-square displacement which we evaluate in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. Further, we identify a memory-induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle, our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.

Anchoring-induced nonmonotonic velocity versus temperature dependence of motile bacteria in a lyotropic nematic liquid crystal

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

Multiparticle collision dynamics simulations of a squirmer in a nematic fluid

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer's speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.

Locomotion of Miniature Soft Robots

Miniature soft robots are mobile devices, which are made of smart materials that can be actuated by external stimuli to realize their desired functionalities. Here, the key advancements and challenges of the locomotion producible by miniature soft robots in micro- to centimeter length scales are highlighted. It is highly desirable to endow these small machines with dexterous locomotive gaits as it enables them to easily access highly confined and enclosed spaces via a noninvasive manner. If miniature soft robots are able to capitalize this unique ability, they will have the potential to transform a vast range of applications, including but not limited to, minimally invasive medical treatments, lab-on-chip applications, and search-and-rescue missions. The gaits of miniature soft robots are categorized into terrestrial, aquatic, and aerial locomotion. Except for the centimeter-scale robots that can perform aerial locomotion, the discussions in this report are centered around soft robots that are in the micro- to millimeter length scales. Under each category of locomotion, prospective methods and strategies that can improve their gait performances are also discussed. This report provides critical analyses and discussions that can inspire future strategies to make miniature soft robots significantly more agile.

Anomalous Diffusion of Motile Colloids Dispersed in Liquid Crystals

We study the superdiffusion of driven colloidal particles dispersed in a nematic liquid crystal. While motion is ballistic in the driving direction, our experiments show that transversal fluctuations become superdiffusive depending on the topological defect pattern around the inclusions. The phenomenon can be reproduced with different driving methods and propulsion speeds, while it is strongly dependent on particle size and temperature. We propose a mechanism based on the geometry of the liquid crystal backflow around the inclusions to justify the persistence of thermal fluctuations and to explain the observed temperature and particle size dependence of the superdiffusive behavior based on material and geometrical parameters.

Long-time anomalous swimmer diffusion in smectic liquid crystals

The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.

Hydrodynamics Defines the Stable Swimming Direction of Spherical Squirmers in a Nematic Liquid Crystal

We present a study of the hydrodynamics of an active particle-a model squirmer-in an environment with a broken rotational symmetry: a nematic liquid crystal. By combining simulations with analytic calculations, we show that the hydrodynamic coupling between the squirmer flow field and liquid crystalline director can lead to reorientation of the swimmers. The preferred orientation depends on the exact details of the squirmer flow field. In a steady state, pushers are shown to swim parallel with the nematic director while pullers swim perpendicular to the nematic director. This behavior arises solely from hydrodynamic coupling between the squirmer flow field and anisotropic viscosities of the host fluid. Our results suggest that an anisotropic swimming medium can be used to characterize and guide spherical microswimmers in the bulk.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to tlnt of the mean-square displacement with time t. This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.