Dynamics of a chiral swimmer sedimenting on a flat plate

Research on sedimentation characteristics of squirmer in a power-law fluid

Sedimentation characteristics of a squirmer in a power-law fluid within a vertical channel are studied numerically using the two-dimensional lattice Boltzmann method. The effects of swimming type (- 5 ≤ β ≤ 5), self-propelling strength (0.5 ≤ α ≤ 1.1), power-law indexes (0.5 ≤ n ≤ 1.5), and the density ratio of the squirmer to the fluid (γ = 1.01, 1.5 and 2.3) on the sedimentation of the squirmer are analyzed. Four settlement patterns are identified: steady falling in the center, downward along the wall, oscillating with large amplitude and oscillating around the centerline. The squirmer in the channel exhibits more fluctuations in shear-thinning (n < 1) and Newtonian (n = 1) fluids compared to shear-thickening fluids (n > 1). Additionally, a puller (β > 0) settles faster than a pusher (β < 0) in shear-thinning and Newtonian fluids. Puller generates flow towards their head and away from their tail, exhibiting small amplitude oscillations. Pushers exhibit higher amplitude oscillations throughout the channel, creating flow towards their tail and away from their head. At lower γ, the fluctuation of the squirmer is less pronounced compared to higher γ.

The motion of micro-swimmers over a cavity in a micro-channel

This article combines the lattice Boltzmann method (LBM) with the squirmer model to investigate the motion of micro-swimmers in a channel-cavity system. The study analyses various influential factors, including the value of the squirmer-type factor (β), the swimming Reynolds number (Rep), the size of the cavity, initial position and particle size on the movement of micro-swimmers within the channel-cavity system. We simultaneously studied three types of squirmer models, Puller (β > 0), Pusher (β < 0), and Neutral (β = 0) swimmers. The findings reveal that the motion of micro-swimmers is determined by the value of β and Rep, which can be classified into six distinct motion modes. For Puller and Pusher, when the β value is constant, an increase in Rep will lead to transition in the motion mode. Moreover, the appropriate depth of cavity within the channel-cavity system plays a crucial role in capturing and separating Neutral swimmers. This study, for the first time, explores the effect of complex channel-cavity systems on the behaviour of micro-swimmers and highlights their separation and capture ability. These findings offer novel insights for the design and enhancement of micro-channel structures in achieving efficient separation and capture of micro-swimmers.

Direct numerical simulations of a microswimmer in a viscoelastic fluid

This study presents the application of the smoothed profile (SP) method to perform direct numerical simulations for the motion of both passive and active "squirming" particles in Newtonian and viscoelastic fluids. We found that fluid elasticity has a significant impact on both the transient behavior and the steady-state velocity of the particles. Specifically, we observe that the swirling flow generated by the squirmer's surface velocity significantly enhances their swimming speed as the Weissenberg number increases, regardless of the swimming type. Furthermore, we find that pushers outperform pullers in Oldroyd-B fluids, suggesting that the speed of a squirmer depends on the swimmer type. To understand the physical origin of the phenomenon of swirling flow enhancing the swimming speed, we investigate the velocity field and polymer conformation around non-swirling and swirling neutral squirmers in viscoelastic fluids. Our investigation reveals that the velocity field around the neutral swirling squirmers exhibits pusher-like extensional flow characteristics, as well as an asymmetric polymer conformation distribution, which gives rise to this increased propulsion. This is confirmed by the investigation of the force on a fixed squirmer, which revealed that the polymer stress, particularly its diagonal components, plays a critical role in enhancing the swimming speed of swirling squirmers in viscoelastic fluids. Additionally, our results demonstrate that the maximum swimming speeds of swirling squirmers occur at an intermediate value of the fluid viscosity ratio for all swimmer types. These findings have important implications for understanding the behavior of particles and micro-organisms in complex fluids.

Swimming of Buoyant Bacteria in Quiescent Medium and Shear Flows

Gravity has an unavoidable effect on all living organisms inhabiting fluidic surroundings. To investigate the spatial distribution of bacteria in quiescent fluids and their rheotactic behavior in shear flows under buoyancy, we adjust the buoyant force to regulate bacterial swimming in a microfluidic channel. It is found that swimming bacteria of Escherichia coli exhibit an obvious vertical separation when exposed to a medium with high density and gradually gather close to the up wall within minutes. The bacterial population presents a net upward number flux, which enhances the trapping of motile bacteria onto the up surface as a result of buoyancy force apart from the hydrodynamic and kinematic interactions in quiescent fluids. When flow is imposed into the channel, the buoyancy effect is however significantly suppressed. Additionally, the drift velocity perpendicular to the buoyancy vector as a result of chirality-induced transverse swimming decreases with buoyancy force. However, this transverse drift capability is recovered after excluding the intrinsic swimming motility in a quiescent medium. Failing to escape from the trapping as a result of buoyant force allows for a facile separation of bacteria along the vertical direction. The findings also offer a controllable way to redisperse and homogenize the bacteria distribution close to walls by imposing a weak shear flow.

Settling mode of a bottom-heavy squirmer in a narrow vessel

The lattice Boltzmann-immersed boundary (IB-LB) method is used to numerically simulate the sedimentation motion of a single two-dimensional, bottom-heavy squirmer in a narrow vessel. The effects of the swimming Reynolds number Re_s = 0.1-3, eccentricity distance l = 0.15d-0.75d, and density ratio of squirmer to fluid γ = 1.1-2.0 on the settlement motion characteristics are investigated and analyzed. The results showed that four settling modes exist: vertical motion, unilateral oscillation, oscillation, and tilt. The bottom-heavy neutral squirmer and puller settle in the vessel during vertical motion when Re_s is 0.1-1.5. By increasing Re_s and swimming strength |β|, the bottom-heavy squirmer becomes more self-driven, shifting its settling mode from vertical motion to unilateral oscillation or oscillation. Increasing l or |β| does not affect the bottom-heavy neutral squirmer and puller's vertical settling mode but shifts the bottom-heavy pusher's settling mode from unilateral oscillation to oscillation or oscillation to unilateral oscillation. Similarly, altering γ or |β| has no impact on the eccentric neutral squirmer and puller's settling mode; however, pushers will switch from oscillation mode to attraction mode or from oscillation mode to tilt mode. Additionally, it was found that after the squirmer collided with the bottom wall, the bottom-heavy squirmer settled at the bottom of the vessel in a different state of motion.

Hydrodynamic Synchronization of Chiral Microswimmers

We study synchronization in bulk suspensions of spherical microswimmers with chiral trajectories using large scale numerics. The model is generic. It corresponds to the lowest order solution of a general model for self-propulsion at low Reynolds numbers, consisting of a nonaxisymmetric rotating source dipole. We show that both purely circular and helical swimmers can spontaneously synchronize their rotation. The synchronized state corresponds to velocity alignment with high orientational order in both the polar and azimuthal directions. Finally, we consider a racemic mixture of helical swimmers where intraspecies synchronization is observed while the system remains as a spatially uniform fluid. Our results demonstrate hydrodynamic synchronization as a natural collective phenomenon for microswimmers with chiral trajectories.

Resonant Diffusion of a Gravitactic Circle Swimmer

We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.

Swimming Mode of Two Interacting Squirmers under Gravity in a Narrow Vertical Channel

The swimming mode of two interacting squirmers under gravity in a narrow vertical channel is simulated numerically using the lattice Boltzmann method (LBM) in the range of self-propelling strength 0.1 ≤ α ≤ 1.1 and swimming type −5 ≤ β ≤ 5. The results showed that there exist five typical swimming patterns for individual squirmers, i.e., steady upward rising (SUR), oscillation across the channel (OAC), oscillation near the wall (ONW), steady upward rising with small-amplitude oscillation (SURO), and vertical motion along the sidewall (VMS). The parametric space (α, β) illustrated the interactions on each pattern. In particular, the range of oscillation angle for ONW is from 19.8° to 32.4° as α varies from 0.3 to 0.7. Moreover, the swimming modes of two interacting squirmers combine the two squirmers’ independent swimming patterns. On the other hand, the pullers (β < 0) attract with each other at the initial stage, resulting in a low-pressure region between them and making the two pullers gradually move closer and finally make contact, while the result for the pushers (β > 0) is the opposite. After the squirmers’ interaction, the squirmer orientation and pressure distribution determine subsequent squirmer swimming patterns. Two pushers separate quickly, while there will be a more extended interaction period before the two pullers are entirely separated.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Hydrodynamics of chiral squirmers

Many microorganisms take a chiral path while swimming in an ambient fluid. In this paper we study the combined behavior of two chiral swimmers using the well-known squirmer model taking into account chiral asymmetries. In contrast to the simple squirmer model, which has an axisymmetric distribution of slip velocity, the chiral squirmer has additional asymmetries in the surface slip, which contribute to both translations and rotations of the motion. As a result, swimming trajectories can become helical and chiral asymmetries arise in the flow patterns. We study the swimming trajectories of a pair of chiral squirmers that interact hydrodynamically. This interaction can lead to attraction and repulsion, and in some cases even to bounded states where the swimmers continue to periodically orbit around a common average trajectory. Such bound states are a signature of the chiral nature of the swimmers. Our study could be relevant to the collective movements of ciliated microorganisms.

A Review on the Some Issues of Multiphase Flow with Self-Driven Particles

Multiphase flow with self-driven particles is ubiquitous and complex. Exploring the flow properties has both important academic meaning and engineering value. This review emphasizes some recent studies on multiphase flow with self-driven particles: the hydrodynamic interactions between self-propelled/self-rotary particles and passive particles; the aggregation, phase separation and sedimentation of squirmers; the influence of rheological properties on its motion; and the kinematic characteristics of axisymmetric squirmers. Finally, some open problems, challenges, and future directions are highlighted.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.