Self-propulsion Strength Research Articles

Study on the interaction and motion patterns of squirmers swimming in a shear flow

In order to study the dynamic characteristics of micro-organisms or engineered swimmers, the simulations of the motion and interaction of a pair of squirmers in a shear flow are conducted using the lattice Boltzmann method (LBM) in the range of squirmer-type factor −5 ≤ β ≤ 5, self-propulsion strength 0.1 ≤ α ≤ 0.8, initial spacing between two squirmers 0.5d ≤ d′ ≤ 3d (d is the diameter of the squirmers). The interactions and motion mechanisms of squirmers in puller–puller, pusher–pusher, puller–pusher, and pusher–puller configurations are analyzed. The results show that there are three typical motion patterns in the puller–puller configuration, i.e., steady tilting motion (STM), large-amplitude oscillation motion (LAO), and small-amplitude oscillation motion (SAO). The motion of pullers has a large vertical range, and the swimming angle continues to increase in the LAO, while the pullers oscillate near the plate and have a small range of changes in swimming angles in the SAO. The situation is more complex in the pusher–pusher configuration, and there are five motion patterns, i.e., STM, LAO, SAO, limit cycle motion (LCM), and open limit cycle motion (OLCM). Three different STMs are found according to the pressure distribution around the pushers. d′ is an important parameter affecting the interaction of squirmers. In the puller–puller configuration, the backflow area on the right side of puller 1 is completely suppressed when d′ = 0.5d, but this suppression gradually weakens as d′ increases. Changes in d′ result in the differences in the final motion patterns of pullers on the upper and low plates. In the pusher–pusher configuration, changes in d′ result in transitions between different motion patterns. There exist a critical swimming angle θc when d′ changes, and the pattern changes from the STM to the LCM when θ > θc. At d′ = 0.5d, in the puller–pusher configuration, there exists a stable structure formed by the mutual repulsion caused by the high pressure area between the puller and pusher. In the pusher–puller configuration, there is a low-pressure area on one side of the pusher, which attracts the low-pressure area on the head of the puller and affects their subsequent motion patterns.

Controlling the transport of the mixture involving active and passive rods in confined channel.

The transport of the binary mixture of self-propelled rods (SPRs) and passive rods in the asymmetric conjugate periodic channel is studied by dissipative particle dynamics (DPD) simulations. It is found that the autonomous pumping of the binary mixture of active and passive rods can be achieved by either the individual or collective behaviour of SPRs. More specifically, the transport of passive rods can be driven through the individual, collective jostlement of the active rods, and crowding out effect. The strength of self-propulsion, rod length, rod concentration, and geometric feature of the channel determines the mechanism of pumping. In addition, the drift of the binary mixture can be in the positive and negative directions of the channel or the currents of SPRs and passive rods in opposite directions and relies on the geometric feature of the channel and concentration of the two species. Overall, our simulation study offers an efficient approach of flow control for both species.

Collective behavior of soft self-propelled disks with rotational inertia

We investigate collective properties of a large system of soft self-propelled inertial disks with active Langevin dynamics simulation in two dimensions. Rotational inertia of the disks is found to favor motility induced phase separation (MIPS), due to increased effective persistence of the disks. The MIPS phase diagram in the parameter space of rotational inertia and disk softness is reported over a range of values of translation inertia and self-propulsion strength of the disks. Our analytical prediction of the phase boundary between the homogeneous (no-MIPS) and MIPS state in the limit of small and large rotational inertia is found to agree with the numerical data over a large range of translational inertia. Shape of the high density MIPS phase is found to change from circular to rectangular one as the system moves away from the phase boundary. Structural and dynamical properties of the system, measured by several physical quantities, are found to be invariant in the central region of the high density MIPS phase, whereas they are found to vary gradually near the peripheral region of the high density phase. Importantly, the width of the peripheral region near the phase boundary is much larger compared to the narrow peripheral region far away from the phase boundary. Rich dynamics of the disks inside the high density MIPS phase is addressed. Spatial correlation of velocity of the disks is found to increase with rotational inertia and disk hardness. However, temporal correlation of the disks’ velocity is found to be a function of rotational inertia, while it is independent of disk softness.

Deformable active nematic particles and emerging edge currents in circular confinements

We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such systems can lead to different collective behaviour, e.g. synchronized self-spinning and collective translation. The different behaviour results from the delicate interplay between internal nematic structure, particle shape deformation and particle–particle interaction. For intermediate active strength an asymmetric particle shape emerges and leads to chirality and self-spinning crystals. For larger active strength the shape is symmetric and translational collective motion emerges. Within circular confinements, depending on the packing fraction, the self-spinning regime either stabilizes positional and orientational order or can lead to edge currents and global rotation which destroys the synchronized self-spinning crystalline structure.Graphical abstract

The collective motion of thermophoretic-type active particle suspension under spatial–temporal modulation

The mesoscopic collective behavior of a thermophoretic-type active particle suspension under a spatial–temporal modulated excitation field is experimentally studied. By using a digital light processing chip, a sinusoidal-like spatial–temporal varying laser pattern (intensity wave) is projected on the particle suspension to modulate the particle propulsion strength through the thermophoretic effect and to exert spatial confinement through the optical trapping effect. For static and slow (wave speed ≪ particle propulsion speed) modulations, in contrast to the passive particles trapped around the wave crest, the self-propulsion strength splits the particle distribution into two branches adjacent to the edges of confinement similar to the bacteria system, and the profile of particle distribution moves coherently with the modulation wave. Once the wave speed increases to the order of the particle propulsion speed, the splitting of particle distribution disappears. Furthermore, it is remarkable that the forward propagating modulation-induced certain fraction of backward streaming particles are observed. This is a generic behavior of a self-propelling active particle suspension, which is not found in the bacteria system. This finding should be useful for particle manipulation at the mesoscopic scale.

Phase separation of self-propelled disks with ferromagnetic and nematic alignment.

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

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.Graphic abstract

Phase-field-crystal description of active crystallites: Elastic and inelastic collisions

The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid and crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with a homogeneous background. At sufficiently strong activity (related to self-propulsion strength), they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states in one spatial dimension. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean density. Then we focus on the interaction of traveling localized states, studying their collision behavior. As a result, we distinguish "elastic" and "inelastic" collisions. In the former, localized states recover their properties after a collision, while in the latter, they may completely or partially annihilate, forming resting bound states or various traveling states.

Light-driven motion of self-propelled porous Janus particles

We introduce a versatile mechanism of light-driven self-propelled motion applied to porous Janus-type particles. The mechanism is based on the generation of local light-driven diffusio-osmotic (l-LDDO) flow around each single porous particle subjected to suitable irradiation conditions. The photosensitivity is introduced by a cationic azobenzene containing surfactant, which undergoes a photoisomerization reaction from a more hydrophobic trans-state to a rather hydrophilic cis-state under illumination with light. The negatively charged porous silica particles are dispersed in a corresponding aqueous solution and absorb molecules in their trans-state but expel them in their cis-state. During illumination with blue light triggering both trans-cis and cis-trans isomerization at the same time, the colloids start to move due to the generation of a steady-state diffusive flow of cis-isomers out of and trans-isomers into the particle. This is because a hemi-spherical metal cap partially sealing the colloid breaks the symmetry of the otherwise radially directed local flow around the particle, leading to self-propelled motion. Janus particles exhibit superdiffusive motion with a velocity of ∼0.5 μm/s and a persistence length of ca. 50 μm, confined to microchannels the direction can be maintained up to 300 μm before rotational diffusion reverts it. Particles forming dimers of different shapes can be made to travel along circular trajectories. The unique feature of this mechanism is that the strength of self-propulsion can be tuned by convenient external optical stimuli (intensity and irradiation wavelength) such that a broad variety of experimental situations can be realized in a spatiotemporal way and in situ.

Linear viscoelasticity of a dilute active suspension

The linear viscoelasticity of a dilute suspension of active (self-propelled) rigid spheroidal particles is calculated under a small-amplitude oscillatory shear (SAOS) deformation. The imposed shear acts to drive the microstructure of the suspension, as parameterized by the orientational probability distribution function, out of equilibrium. The microstructure relaxes via two independent mechanisms: rotational Brownian motion and correlated tumbling; the combination of which results in an increased rate of stress relaxation, relative to a suspension that relaxes solely by either mechanism. We explicitly calculate the non-equilibrium orientational microstructure due to the SAOS deformation, rotational diffusion, and tumbling. From this, we determine the linear viscoelasticity of the suspension from the orientationally averaged stresslet, which arises from the imposed flow, rotational diffusion, and particle activity (self-propulsion). Next, we demonstrate that a modified Cox-Merz rule is applicable to a dilute, active suspension via a comparison of our linear viscoelasticity results to a theoretical prediction of the steady shear viscosity of active, slender rods (Saintillan, Exp Mech 50(9) 1275–1281, 2010). Finally, through a comparison of our results to experiments on Escherichia coli (Lopez et al., Phys Rev Lett 115(2) 028, 301, 2015), we show that the linear viscoelasticity of an active suspension can be utilized to determine the mechanism of self-propulsion (i.e., pusher or puller), and estimate the strength of self-propulsion and correlation between tumbling events.

Anomalous dynamics of an elastic membrane in an active fluid.

Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multifolded states, whereas stiff membranes fluctuate between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the microscale.

How does a flexible chain of active particles swell?

We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

Communication: Escape kinetics of self-propelled Janus particles from a cavity: numerical simulations.

We numerically investigate the escape kinetics of elliptic Janus particles from narrow two-dimensional cavities with reflecting walls. The self-propulsion velocity of the Janus particle is directed along either their major (prolate) or minor (oblate) axis. We show that the mean exit time is very sensitive to the cavity geometry, particle shape, and self-propulsion strength. The mean exit time is found to be a minimum when the self-propulsion length is equal to the cavity size. We also find the optimum mean escape time as a function of the self-propulsion velocity, translational diffusion, and particle shape. Thus, effective transport control mechanisms for Janus particles in a channel can be implemented.

Cooperative motion of active Brownian spheres in three-dimensional dense suspensions

The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a certain density and strength of self-propulsion. The packing fraction of the dense phase approaches random close packing at high activity, yet the system remains fluid. Although no alignment mechanism exists in this model, we find long-lived cooperative motion of particles in the dense regime. This behavior is probably due to an interface-induced sorting process. Spatial displacement correlation functions are nearly scale free for systems with densities close to or above the glass transition density of passive systems.

Traveling and Resting Crystals in Active Systems

A microscopic field theory for crystallization in active systems is proposed which unifies the phase-field-crystal model of freezing with the Toner-Tu theory for self-propelled particles. A wealth of different active crystalline states are predicted and characterized. In particular, for increasing strength of self-propulsion, a transition from a resting crystal to a traveling crystalline state is found where the particles migrate collectively while keeping their crystalline order. Our predictions, which are verifiable in experiments and in particle-resolved computer simulations, provide a starting point for the design of new active materials.