Lattice-Boltzmann hydrodynamics of anisotropic active matter

Sedimentation and structure of squirmer suspensions under gravity

The effect of gravity on the collective motion of living microswimmers, such as bacteria and micro-algae, is pivotal to unravel not only bio-convection patterns but also the settling of bacterial biofilms on solid surfaces. In this work, we investigate suspensions of microswimmers under the influence of a gravitational field and hydrodynamics, simulated via the dissipative particle dynamics (DPD) coarse-grained model. We first study the collective sedimentation of passive colloids and microswimmers of the puller and pusher types upon increasing the imposed gravitational field and compare them with previous results. Once sedimentation occurs, we observe that, as the gravitational field increases, the bottom layer undergoes a transition to an ordered state compatible with a hexagonal crystal. In comparison with passive colloids, both pullers and pushers easily rearrange at the bottom layer to anneal defects. Specifically, pullers are better than pushers in preserving the hexagonal order of the bottom mono-layer at high gravitational fields.

Geometrical impacts of platonic particles on nematic liquid crystal dynamics

Platonic-solid-like particles in liquid crystals offer intriguing opportunities for engineering complex materials with tailored properties. Inspired by platonic solids' geometric simplicity and symmetry, these particles possess well-defined shapes such as cubes, tetrahedra, octahedra, dodecahedra, and icosahedra. When dispersed within nematic liquid-crystalline media, these particles interact with the surrounding medium in intricate ways, influencing the local orientational order of liquid crystal molecules. In this work, we implement continuum simulations to study how the combination of particle shape and surface anchoring gives rise to line defects that follow the edges of the particles and how they are affected by the presence of a Poiseuille flow. Platonic-solid-like particles in liquid crystals have shown promise in diverse applications ranging from photonics and metamaterials to colloidal self-assembly and responsive soft materials.

Influence of bacterial swimming and hydrodynamics on attachment of phages

Bacteriophages ("phages") are viruses that infect bacteria. Since they do not actively self-propel, phages rely on thermal diffusion to find target cells-but can also be advected by fluid flows, such as those generated by motile bacteria themselves in bulk fluids. How does the flow field generated by a swimming bacterium influence how it encounters phages? Here, we address this question using coupled molecular dynamics and lattice Boltzmann simulations of flagellated bacteria swimming through a bulk fluid containing uniformly-dispersed phages. We find that while swimming increases the rate at which phages attach to both the cell body and flagellar propeller, hydrodynamic interactions strongly suppress this increase at the cell body, but conversely enhance this increase at the flagellar bundle. Our results highlight the pivotal influence of hydrodynamics on the interactions between bacteria and phages, as well as other diffusible species, in microbial environments.

Minimal numerical ingredients describe chemical microswimmers' 3-D motion

The underlying mechanisms and physics of catalytic Janus microswimmers is highly complex, requiring details of the associated phoretic fields and the physiochemical properties of catalyst, particle, boundaries, and the fuel used. Therefore, developing a minimal (and more general) model capable of capturing the overall dynamics of these autonomous particles is highly desirable. In the presented work, we demonstrate that a coarse-grained dissipative particle-hydrodynamics model is capable of describing the behaviour of various chemical microswimmer systems. Specifically, we show how a competing balance between hydrodynamic interactions experienced by a squirmer in the presence of a substrate, gravity, and mass and shape asymmetries can reproduce a range of dynamics seen in different experimental systems. We hope that our general model will inspire further synthetic work where various modes of swimmer motion can be encoded via shape and mass during fabrication, helping to realise the still outstanding goal of microswimmers capable of complex 3-D behaviour.

A novel model for biofilm initiation in porous media flow

Bacteria often form biofilms in porous environments where an external flow is present, such as soil or filtration systems. To understand the initial stages of biofilm formation, one needs to study the interactions between cells, the fluid and the confining geometries. Here, we present an agent based numerical model for bacteria that takes into account the planktonic stage of motile cells as well as surface attachment and biofilm growth in a lattice Boltzmann fluid. In the planktonic stage we show the importance of the interplay between complex flow and cell motility when determining positions of surface attachment. In the growth stage we show the applicability of our model by investigating how external flow and biofilm stiffness determine qualitative colony morphologies as well as quantitative measurements of, e.g., permeability.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement

We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in the absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean settling velocity is quantitatively assessed, especially in comparison with unconfined situations. Results show that the expected effects of confinement are very well captured by the numerical simulations, wherein the confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the proposed methodology in highlighting the effects of confinement on the motion of particles in the presence of thermal fluctuations.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

The influence of motility on bacterial accumulation in a microporous channel

We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this model is capable of reproducing the bacterial accumulation on the rear side of an obstacle, as has recently been experimentally observed by [G. L. Miño, et al., Adv. Microbiol., 2018, 8, 451] using E. coli bacteria. By systematically varying the external flow strength and the motility of the bacteria, we resolve the interplay between the local flow strength and the swimming characteristics that lead to the accumulation. Moreover, by changing the geometry of the channel, we also reveal the important role of the interactions between the bacteria and the confining walls for the accumulation process.

Squirmer rods as elongated microswimmers: flow fields and confinement

Microswimmers or active elements, such as bacteria and active filaments, have an elongated shape, which determines their individual and collective dynamics. There is still a need to identify what role long-range hydrodynamic interactions play in their fascinating dynamic structure formation. We construct rods of different aspect ratios using several spherical squirmer model swimmers. With the help of the mesoscale simulation method of multi-particle collision dynamics we analyze the flow fields of these squirmer rods both in a bulk fluid and in Hele-Shaw geometries of different slab widths. Based on the hydrodynamic multipole expansion either for bulk or confinement between two parallel plates, we categorize the different multipole contributions of neutral as well as pusher-type squirmer rods. We demonstrate how confinement alters the radial decay of the flow fields for a given force or source multipole moment compared to the bulk fluid.

Magnetic Actuation of Surface Walkers: The Effects of Confinement and Inertia

Driven by a magnetic field, the rotation of a particle near a wall can be rectified into a net translation. The particles thus actuated, or surface walkers, are a kind of active colloid that finds application in biology and microfluidics. Here, we investigate the motion of spherical surface walkers confined between two walls using simulations based on the immersed-boundary lattice Boltzmann method. The degree of confinement and the nature of the confining walls (slip vs no-slip) significantly affect a particle's translational speed and can even reverse its translational direction. When the rotational Reynolds number Re_ω is larger than 1, inertia effects reduce the critical frequency of the magnetic field, beyond which the sphere can no longer follow the external rotating field. The reduction of the critical frequency is especially pronounced when the sphere is confined near a no-slip wall. As Re_ω increases beyond 1, even when the sphere can still rotate in the synchronous regime, its translational Reynolds number Re_T no longer increases linearly with Re_ω and even decreases when Re_ω exceeds ∼10.

Mesoscopic simulations of anisotropic chemically powered nanomotors

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Lattice Boltzmann methods and active fluids

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.

A computational model for bacterial run-and-tumble motion

In this article we present a computational model for the simulation of self-propelled anisotropic bacteria. To this end we use a self-propelled particle model and augment it with a statistical algorithm for the run-and-tumble motion. We derive an equation for the distribution of reorientations of the bacteria that we use to analyze the statistics of the random walk and that allows us to tune the behavior of our model to the characteristics of an E. coli bacterium. We validate our implementation in terms of a single swimmer and demonstrate that our model is capable of reproducing E. coli's run-and-tumble motion with excellent accuracy.

Morphology of depletant-induced erythrocyte aggregates

Red blood cells suspended in quiescent plasma tend to aggregate into multicellular assemblages, including linearly stacked columnar rouleaux, which can reversibly form more complex clusters or branching networks. While these aggregates play an essential role in establishing hemorheological and pathological properties, the biophysics behind their self-assembly into dynamic mesoscopic structures remains under-explored. We employ coarse-grained molecular simulations to model low-hematocrit erythrocytes subject to short-range implicit depletion forces, and demonstrate not only that depletion interactions are sufficient to account for a sudden dispersion-aggregate transition, but also that the volume fraction of depletant macromolecules controls small aggregate morphology. We observe a sudden transition from a dispersion to a linear column rouleau, followed by a slow emergence of disorderly amorphous clusters of many short rouleaux at larger volume fractions. This work demonstrates how discocyte topology and short-range, non-specific, physical interactions are sufficient to self-assemble erythrocytes into various aggregate structures, with markedly different morphologies and biomedical consequences.

State diagram of a three-sphere microswimmer in a channel

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

Maximum in density heterogeneities of active swimmers

Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.

Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions

Field-induced isotropic-to-nematic phase transition of colloidal rods studied with Dynamic Monte Carlo simulations.

Flow properties and hydrodynamic interactions of rigid spherical microswimmers

We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals that hydrodynamic interactions among rigid-bodied microswimmers differ considerably from those among the corresponding point-force dipoles. Our results are relevant for the study of collective behavior of hydrodynamically interacting microswimmers by means of Stokesian dynamics simulations at moderate concentrations.

Electrokinetic Lattice Boltzmann Solver Coupled to Molecular Dynamics: Application to Polymer Translocation

We have developed a theoretical and computational approach to deal with systems that involve a disparate range of spatiotemporal scales, such as those composed of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multicomponent Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multicomponent description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. Lastly, we discuss the advantages and complexities of the approach.

Lattice-Boltzmann simulations of microswimmer-tracer interactions

Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016)JCPSA60021-960610.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

Understanding the onset of oscillatory swimming in microchannels

Self-propelled colloids (swimmers) in confining geometries follow trajectories determined by hydrodynamic interactions with the bounding surfaces. However, typically these interactions are ignored or truncated to the lowest order. We demonstrate that higher-order hydrodynamic moments cause rod-like swimmers to follow oscillatory trajectories in quiescent fluid between two parallel plates, using a combination of lattice-Boltzmann simulations and far-field calculations. This behavior occurs even far from the confining walls and does not require lubrication results. We show that a swimmer's hydrodynamic quadrupole moment is crucial to the onset of the oscillatory trajectories. This insight allows us to develop a simple model for the dynamics near the channel center based on these higher hydrodynamic moments, and suggests opportunities for trajectory-based experimental characterization of swimmers' hydrodynamic properties.