David Saintillan

Suspensions of motile microswimmers such as bacteria and other active colloids frequently encounter porous environments where obstacles and complex shear flows strongly influence their dynamics. Here, we study the distribution and transport of a dilute suspension of active particles in a square lattice of pillars, which serves as a model porous medium. The microswimmers are modeled as slender point particles, and Brownian Dynamics simulations are performed to determine how their number density and polarization fields change with systematic variations in the medium porosity, polydispersity, flow strength, and self-propulsion strength. We find that in the absence of flow, self-propulsion drives particle accumulation and radial polarization at the pillar surfaces. In the presence of a background flow, particles preferentially accumulate in the wake of pillars and exhibit upstream polarization near their surface, consistent with experimental observations. At moderate flow strengths, topological defects nucleate in the polarization field. These defects are of purely kinematic origin and mark the transition from global upstream swimming at low flow strengths to the coexistence of upstream and downstream swimming regions in the lattice at high flow strengths. The structured lattice studied here provides a controlled framework for isolating the physical mechanisms governing active transport in complex geometries, with direct relevance to transport in structured microfluidic settings.

Suspensions of motile microswimmers such as bacteria and other active colloids frequently encounter porous environments where obstacles and complex shear flows strongly influence their dynamics. Here, we study the distribution and transport of a dilute suspension of active particles in a square lattice of pillars, which serves as a model porous medium. The microswimmers are modeled as slender point particles, and Brownian Dynamics simulations are performed to determine how their number density and polarization fields change with systematic variations in the medium porosity, polydispersity, flow strength, and self-propulsion strength. We find that in the absence of flow, self-propulsion drives particle accumulation and radial polarization at the pillar surfaces. In the presence of a background flow, particles preferentially accumulate in the wake of pillars and exhibit upstream polarization near their surface, consistent with experimental observations. At moderate flow strengths, topological defects nucleate in the polarization field. These defects are of purely kinematic origin and mark the transition from global upstream swimming at low flow strengths to the coexistence of upstream and downstream swimming regions in the lattice at high flow strengths. The structured lattice studied here provides a controlled framework for isolating the physical mechanisms governing active transport in complex geometries, with direct relevance to transport in structured microfluidic settings.

Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved viscous interface. The evolution of the particle configurations is modeled using the Fokker-Planck equation on the curved surface, formulated using Cartan's moving frame method, and coupled to the bulk and surface Stokes equations with flows driven by an interfacial nematic active stress. Specifically, for a spherical vesicle, the flow field and the distribution of the particles are analyzed theoretically and numerically within the framework of spin-weighted functions and spin-weighted spherical harmonics, which provide a natural geometric description of the probability distribution function on the sphere. A linear stability analysis about the uniform, isotropic state is performed and predicts a finite-wavelength instability, with mode selection arising from the competition between the vesicle radius and the Saffman-Delbrück length. This instability and the associated mode-selection mechanism are also confirmed in nonlinear numerical simulations using a pseudo-spectral method based on spin-weighted spherical harmonics.

Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved viscous interface. The evolution of the particle configurations is modeled using the Fokker-Planck equation on the curved surface, formulated using Cartan's moving frame method, and coupled to the bulk and surface Stokes equations with flows driven by an interfacial nematic active stress. Specifically, for a spherical vesicle, the flow field and the distribution of the particles are analyzed theoretically and numerically within the framework of spin-weighted functions and spin-weighted spherical harmonics, which provide a natural geometric description of the probability distribution function on the sphere. A linear stability analysis about the uniform, isotropic state is performed and predicts a finite-wavelength instability, with mode selection arising from the competition between the vesicle radius and the Saffman-Delbrück length. This instability and the associated mode-selection mechanism are also confirmed in nonlinear numerical simulations using a pseudo-spectral method based on spin-weighted spherical harmonics.

Abstract Swimming bacteria move through a fluid by actuating their moving body parts. They are force-free and can be described as hydrodynamic force dipoles: pushers or pullers. This modelling description is broadly used in biological physics and active matter research, and it has successfully predicted, for example, the superfluid behaviour of suspensions of pushers or the bend instability and emergence of turbulent flows in active nematics. However, this description accounts only for the translational motion of the swimming body and neglects the effects of hydrodynamic torque dipoles, which are relevant to bacteria with rotary motor-driven flagella, such as swimming Escherichia coli . Here we show that the torque dipole of confined swimming E. coli can power the persistent rotation of symmetric discs. The torque dipole leads to a traction force on the discs, an additive mechanism that is both contactless and independent of the orientation of the bacteria. Our results indicate that the torque dipole of swimming E. coli is notable in confined geometries, which is relevant to bacterial transport through porous materials, biofilms and the development of chiral fluids.

The genome contains genetic information essential for a cell’s life. The genome’s spatial organization inside the cell nucleus is critical for its proper function including gene regulation. The two major genomic compartments, euchromatin and heterochromatin, contain largely transcriptionally active and silenced genes, respectively, and exhibit distinct dynamics. In this work, we present a hydrodynamic framework that describes the large-scale behavior of euchromatin and heterochromatin and accounts for the interplay of mechanical forces, active processes, and nuclear confinement. Our model shows contractile stresses from cross-linking proteins lead to the formation of heterochromatin droplets via mechanically driven phase separation. These droplets grow, coalesce, and, in nuclear confinement, wet the boundary. Active processes, such as gene transcription in euchromatin, introduce nonequilibrium fluctuations that drive long-range, coherent motions of chromatin as well as the nucleoplasm and, thus, alter the genome’s spatial organization. These fluctuations also indirectly deform heterochromatin droplets, by continuously changing their shape. Taken together, our findings reveal how active forces, mechanical stresses, and hydrodynamic flows contribute to the genome’s organization at large scales and provide a physical framework for understanding chromatin organization and dynamics in live cells.

The dynamics of filaments in flow are central to understanding a wide range of biological and soft-matter systems, yet their behavior under time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of Brownian inextensible elastic filaments subjected to strong uniform oscillatory shear by combining microfluidic experiments on actin filaments with numerical simulations based on a fluctuating Euler-Bernoulli elastica model in a viscous fluid. As the oscillation period increases, irreversibility emerges from the interplay of flow-induced deformations and thermal noise. This leads to a departure from reversible, deterministic rigid-body dynamics: in this regime, the filaments cycle between nearly straight, flow-aligned conformations at full periods and buckled shapes at half periods. Owing to the time-glide symmetry of the system, two such attracting states in fact coexist with a phase shift of half a period. The system spontaneously selects one, but occasionally switches between them as a result of noise, producing intermittent transitions between apparent order and disorder. This system constitutes an experimentally accessible realization of stochastic symmetry breaking, attractor hopping, and intermittency in a minimal nonequilibrium soft-matter system, with novel implications for the design and control of soft matter systems under time-dependent flows.

The dynamics of filaments in flow are central to understanding a wide range of biological and soft-matter systems, yet their behavior under time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of Brownian inextensible elastic filaments subjected to strong uniform oscillatory shear by combining microfluidic experiments on actin filaments with numerical simulations based on a fluctuating Euler-Bernoulli elastica model in a viscous fluid. As the oscillation period increases, irreversibility emerges from the interplay of flow-induced deformations and thermal noise. This leads to a departure from reversible, deterministic rigid-body dynamics: in this regime, the filaments cycle between nearly straight, flow-aligned conformations at full periods and buckled shapes at half periods. Owing to the time-glide symmetry of the system, two such attracting states in fact coexist with a phase shift of half a period. The system spontaneously selects one, but occasionally switches between them as a result of noise, producing intermittent transitions between apparent order and disorder. This system constitutes an experimentally accessible realization of stochastic symmetry breaking, attractor hopping, and intermittency in a minimal nonequilibrium soft-matter system, with novel implications for the design and control of soft matter systems under time-dependent flows.

We investigate the stability of two configurations: a passive viscous Newtonian droplet immersed in an active nematic liquid crystal, and an active nematic droplet surrounded by a passive layer, both under circular confinement. Our results reveal how capillary, active, elastic, and viscous stresses interact to govern droplet dynamics. These findings may inform our understanding of diverse biological systems featuring interfaces between active and passive fluids, from droplets in bacterial suspensions to subcellular compartments within the cytoplasm and cell nucleus.

An isolated charge-neutral drop suspended in an unbounded medium does not migrate in a uniform DC electric field. A nearby wall breaks the symmetry and causes the drop to drift towards or away from the boundary, depending on the electric properties of the fluids and the wall. In the case of an electrically insulating wall and an electric field applied tangentially to the wall, the interaction of the drop with its electrostatic image gives rise to repulsion by the wall. However, the electrohydrodynamic flow causes either repulsion for a drop with $\mathrm{R/P}<1$, where $\mathrm{R}$ and $\mathrm{P}$ are the drop-to-medium ratios of conductivity and permittivity, respectively, or attraction for $\mathrm{R/P}>1$. We experimentally measure droplet trajectories and quantify the wall-induced electrohydrodynamic lift in the case $\mathrm{R/P}<1$. Numerical simulations using the boundary integral method agree well with the experiment and also explore the $\mathrm{R/P}>1$ case. The results show that the lateral migration of a drop in a uniform electric field applied parallel to an insulating wall is dominated by the long-range flow due to the image stresslet.

Motile bacteria are a wonder of nature's engineering: microscopic engines that transduce biochemical energy into the work they require to explore their environment. This added energy turns the surrounding fluid into a bath that departs from an equilibrium one. Bacterial baths agitate suspended spheres more vividly than thermal fluctuations and can power microscopic ratchets. A salient requirement to extract work from bacterial baths was the asymmetric shape of the ratchets, designed to rectify the interactions with bacteria. In contrast with past results, here we show that swimming E. coli power the persistent rotation of discs, in absence of asymmetry. Combining state-of-the art nanoprinting, quantitative measurements of the dynamics of individual bacteria, and hydrodynamic modeling, we elucidate the mechanism and show that the counter-rotation of the flagella and the bacterium body lead to a torque dipole and traction onto the disc, and subsequent rotation. Remarkably, the mechanism is independent of the direction or orientation of navigation of bacteria under the disc, hence additive and contactless. Resulting from the interplay of the torque dipole of flagellated bacteria with simple geometric confinement, this hydrodynamic mechanism bridges scales, leveraging the chirality of bacteria nanomotors towards the manipulation of objects at least ten thousand times larger. The study lays the groundwork for novel bio-hybrid micromachines that harness living microorganisms for controlled motion at the microscale. Our findings provide further fundamental insights into bacterial hydrodynamics and open avenues for the development of autonomous, self-powered microdiscs for the study of chiral fluids.

An isolated charge-neutral drop suspended in an unbounded medium does not migrate in a uniform DC electric field. A nearby wall breaks the symmetry and causes the drop to drift towards or away from the boundary, depending on the electric properties of the fluids and the wall. In the case of an electrically insulating wall and an electric field applied tangentially to the wall, the interaction of the drop with its electrostatic image gives rise to repulsion by the wall. However, the electrohydrodynamic flow causes either repulsion for a drop with $\mathrm{R/P}&lt;1$, where $\mathrm{R}$ and $\mathrm{P}$ are the drop-to-medium ratios of conductivity and permittivity, respectively, or attraction for $\mathrm{R/P}&gt;1$. We experimentally measure droplet trajectories and quantify the wall-induced electrohydrodynamic lift in the case $\mathrm{R/P}&lt;1$. Numerical simulations using the boundary integral method agree well with the experiment and also explore the $\mathrm{R/P}&gt;1$ case. The results show that the lateral migration of a drop in a uniform electric field applied parallel to an insulating wall is dominated by the long-range flow due to the image stresslet.

Abstract Recent advances in cell biology and experimental techniques using reconstituted cell extracts have generated significant interest in understanding how geometry and topology influence active fluid dynamics. In this work, we present a comprehensive continuum theory and computational method to explore the dynamics of active nematic fluids on arbitrary surfaces without topological constraints. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a two-manifold. We introduce the Levi–Civita connection and surface curvature form within the framework of complex line bundles. By adopting this geometric approach, we introduce a gauge-invariant discretization method that preserves the continuous local-to-global theorems in differential geometry. We establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. We formulate advection of the nematic field based on a unifying definition of the Lie derivative, resulting in a stable geometric semi-Lagrangian (sL) discretization scheme for transport by the flow. In general, the proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and global topology on the two-dimensional hydrodynamics of active nematic systems.

We study emergent dynamics in a viscous drop subject to interfacial nematic activity. Using hydrodynamic simulations, we show how the interplay of nematodynamics, activity-driven flows in the fluid bulk, and surface deformations gives rise to a sequence of self-organized behaviors of increasing complexity, from periodic braiding motions of topological defects to chaotic defect dynamics and active turbulence, along with spontaneous shape changes and translation. Our findings recapitulate qualitative features of experiments and shed light on the mechanisms underpinning morphological dynamics in active interfaces.

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

The dynamics of evolving fluid films in the viscous Stokes limit is relevant to various applications, such as the modelling of lipid bilayers in cells. While the governing equations were formulated by Scriven (1960), solving for the flow of a deformable viscous surface with arbitrary shape and topology has remained a challenge. In this study, we present a straightforward discrete model based on variational principles to address this long-standing problem. We replace the classical equations, which are expressed with tensor calculus in local coordinates, with a simple coordinate-free, differential-geometric formulation. The formulation provides a fundamental understanding of the underlying mechanics and translates directly to discretization. We construct a discrete analogue of the system using Onsager's variational principle, which, in a smooth context, governs the flow of a viscous medium. In the discrete setting, instead of term-wise discretizing the coordinate-based Stokes equations, we construct a discrete Rayleighian for the system and derive the discrete Stokes equations via the variational principle. This approach results in a stable, structure-preserving variational integrator that solves the system on general manifolds.

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and cell nucleus.

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. With many fundamental properties of motile active matter now reasonably well understood and under control, the ground is prepared for the study of physical aspects and mechanisms of motion in complex environments, of the behavior of systems with new physical features like chirality, of the development of novel micromachines and microbots, of the emergent collective behavior and swarming of intelligent self-propelled particles, and of particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics.

The dynamics of evolving fluid films in the viscous Stokes limit is relevant to various applications, such as the modeling of lipid bilayers in cells. While the governing equations were formulated by Scriven in 1960, solving for the flow of a deformable viscous surface with arbitrary shape and topology has remained a challenge. In this study, we present a straightforward discrete model based on variational principles to address this long-standing problem. We replace the classical equations, which are expressed with tensor calculus in local coordinates, with a simple coordinate-free, differential-geometric formulation. The formulation provides a fundamental understanding of the underlying mechanics and directly translates to discretization. We construct a discrete analogue of the system using the Onsager variational principle, which, in a smooth context, governs the flow of a viscous medium. In the discrete setting, instead of term-wise discretizing the coordinate-based Stokes equations, we construct a discrete Rayleighian for the system and derive the discrete Stokes equations via the variational principle. This approach results in a stable, structure-preserving variational integrator that solves the system on general manifolds.

Abstract The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity $${\mathscr {D}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi></mml:math> of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratio, and high activity.

Recent advances in cell biology and experimental techniques using reconstituted cell extracts have generated significant interest in understanding how geometry and topology influence active fluid dynamics. In this work, we present a comprehensive continuous theory and computational method to explore the dynamics of active nematic fluids on arbitrary surfaces without topological constraints. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a 2-manifold. We introduce the Levi-Civita connection and surface curvature form within the framework of complex line bundles. By adopting this geometric approach, we introduce a gauge-invariant discretization method that preserves the continuous local-to-global theorems in differential geometry. We establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. We formulate advection of the nematic field based on a unifying definition of the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. In general, the proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and global topology on the 2D hydrodynamics of active nematic systems. Moreover, the complex line representation of the nematic field and the unifying Lie advection present a systematic approach for generalizing our method to active $k$-atic systems.

We study emergent dynamics in a viscous drop subject to interfacial nematic activity. Using hydrodynamic simulations, we show how the interplay of nematodynamics, activity-driven flows and surface deformations gives rise to a sequence of self-organized behaviors of increasing complexity, from periodic braiding motions of topological defects to chaotic defect dynamics and active turbulence, along with spontaneous shape changes and translation. Our findings recapitulate qualitative features of experiments and shed light on the mechanisms underpinning morphological dynamics in active interfaces.

The dispersion of a passive colloid immersed in a bath of non-interacting and non-Brownian run-and-tumble microswimmers in two dimensions is analyzed using stochastic simulations and an asymptotic theory, both based on a minimal model of swimmer-colloid collisions characterized solely by frictionless steric interactions. We estimate the effective long-time diffusivity $\mathcal{D}$ of the suspended colloid resulting from its interaction with the active bath, and elucidate its dependence on the level of activity (persistence length of swimmer trajectories), the mobility ratio of the colloid to a swimmer, and the number density of swimmers in the bath. We also propose a semi-analytical model for the colloid diffusivity in terms of the variance and correlation time of the net fluctuating active force on the colloid resulting from swimmer collisions. Quantitative agreement is found between numerical simulations and analytical results in the experimentally-relevant regime of low swimmer density, low mobility ratios, and high activity.

Catalytic motors, which self-propel in a liquid due to an inhomogeneous surface reaction, constitute an important illustration of active matter in a non-biological context. Prevailing models of the associated self-diffusiophoretic transport assume a chemical reaction at the boundary of the swimmer. We here address the more realistic scenario where that reaction is balanced by a homogeneous reaction in the bulk. The associated diffusive transport of solute, described by two Damk\"ohler numbers, exhibits a boundary-layer topology which is not encountered in the prevailing models.

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f(ϕ,Pe) of the obstacle area fraction ϕ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peϕ≪1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

This study presents a model of cell motility that explains the initiation of cell motion by a symmetry-breaking instability and reveals that complex cell behaviors - from motility to shape selection - are governed by dynamic activities at the cell edge.

We present a chemomechanical model to analyze the propulsion of mammalian spermatozoa. The model accounts for motor kinetics, flagellar deformations, and the hydrodynamics of the suspending fluid. Simulations demonstrate spontaneous oscillations leading to realistic swimming patterns. Notably, the swimming velocity exhibits two distinct peaks as a function of the activity of the molecular motors. These peaks are characterized by distinct waveforms and trajectories. Our findings contribute to a deeper understanding of the biophysical mechanisms involved in sperm locomotion.

We consider phoretic self-propulsion of a chemically active colloid where solute is consumed at both the colloid boundary and within the bulk solution. Assuming first-order kinetics, the dimensionless transport problem is governed by the surface Damköhler number ${\mathcal{S}}$ and the bulk Damköhler number ${\mathcal B}$. The dimensionless colloid velocity $U$, normalized by a self-phoretic scale, is a nonlinear function of these two parameters. We identify two scenarios where these numbers are linked. When the controlling physical parameter is colloid size, ${\mathcal{S}}$ is proportional to ${\mathcal B}^{1/2}$; when the controlling parameter is solute diffusivity, ${\mathcal{S}}$ is proportional to ${\mathcal B}$. In the limit of small Damköhler numbers, $U$ adopts the same asymptotic limit in both scenarios, proportional to ${\mathcal{S}}$. In the limit of large Damköhler numbers, the deviations of solute concentration from the equilibrium value are restricted to a narrow layer about the active portion of the colloid boundary. The asymptotic predictions of the associated boundary-layer problem are corroborated by an eigenfunction solution of the exact problem. The boundary-layer structure breaks down near the transition between the active and inactive portions of the boundary. The transport problem in that local region partially resembles the classical Sommerfeld problem of wave diffraction from an edge.

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of non-interacting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function $f(ϕ,\mathrm{Pe})$ of the obstacle area fraction $ϕ$ and Péclet number $\mathrm{Pe}$, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media ($\mathrm{Pe}\,ϕ\ll 1$), and its extension to denser media is obtained using stochastic simulations.

Abstract The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions to the extracellular substrate play a crucial role. In a recently proposed 1D model (Sens, PNAS 2020), a mechanical feedback loop between force-sensitive adhesions and cell tension was shown to be sufficient to explain spontaneous symmetry breaking and multiple motility patterns through stick-slip dynamics, without the need to account for signaling networks or active polar gels. We extended this model to 2D to study the interplay between cell shape and mechanics during crawling. Through a local force balance along a deformable boundary, we show that the membrane tension coupled with shape change can regulate the spatiotemporal evolution of the stochastic binding of mechanosensitive adhesions. Linear stability analysis identified the unstable parameter regimes where spontaneous symmetry breaking can take place. Using simulations to solve the fully coupled nonlinear system of equations, we show that starting from a randomly perturbed circular shape, this instability can lead to keratocyte-like shapes. Simulations predict that different adhesion kinetics and membrane tension can result in different cell motility modes including gliding, zigzag, rotating, and sometimes chaotic movements. Thus, using a minimal model of cell motility, we identify that the interplay between adhesions and tension can select emergent motility modes.

The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions to the extracellular substrate play a crucial role. In a recently proposed 1D model (Sens, PNAS 2020), a mechanical feedback loop between force-sensitive adhesions and cell tension was shown to be sufficient to explain spontaneous symmetry breaking and multiple motility patterns through stick-slip dynamics, without the need to account for signaling networks or active polar gels. We extended this model to 2D to study the interplay between cell shape and mechanics during crawling. Through a local force balance along a deformable boundary, we show that the membrane tension coupled with shape change can regulate the spatiotemporal evolution of the stochastic binding of mechanosensitive adhesions. Linear stability analysis identified the unstable parameter regimes where spontaneous symmetry breaking can take place. sing simulations to solve the fully coupled nonlinear system of equations, we show that starting from a randomly perturbed circular shape, this instability can lead to keratocyte-like shapes. Simulations predict that different adhesion kinetics and membrane tension can result in different cell motility modes including gliding, zigzag, rotating, and sometimes chaotic movements. Thus, using a minimal model of cell motility, we identify that the interplay between adhesions and tension can select emergent motility modes.

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling of interfacial charge transport and fluid flow can trigger electrohydrodynamic instabilities that lead to shape deformations and complex dynamics. We present a spectral boundary integral method to simulate droplet electrohydrodynamics in a uniform electric field. All physical variables, such as drop shape and interfacial charge density, are represented using spherical harmonic expansions. In addition to its exponential accuracy, the spectral representation affords a nondissipative dealiasing method required for numerical stability. A comprehensive charge transport model, valid under a wide range of electric field strengths, accounts for charge relaxation, Ohmic conduction, and surface charge convection by the flow. A shape reparametrization technique enables the exploration of significant droplet deformation regimes. For low-viscosity drops, the convection by the flow drives steep interfacial charge gradients near the drop equator. This introduces numerical ringing artifacts that we treat via a weighted spherical harmonic expansion, resulting in solution convergence. The method and simulations are validated against experimental data and analytical predictions in the axisymmetric Taylor and Quincke electrorotation regimes.

The fluid-structure interactions between flexible fibers and viscous flows play an essential role in various biological phenomena, medical problems, and industrial processes. Of particular interest is the case of particles freely transported in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations, and theoretical modeling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler-Bernoulli rods whose hydrodynamics are described by local slender-body theory.

, 95-98]. In this system, an electrohydrodynamic (EHD) instability called Quincke rotation was exploited to create self-propelling particles which aligned with each other due to EHD interactions, giving rise to collective motion on large length scales. It is natural to question whether a suspension of such particles in three dimensions will also display collective motion and spontaneously flow like bacterial suspensions do. Using molecular dynamics type simulations, we show that dielectrophoretic forces responsible for chaining in the direction of the applied electric field in conventional electrorheological fluids and the counter-rotation of neighboring particles in these chains prevent collective motion in suspensions undergoing spontaneous particle rotations. Our simulations discover that the fundamental microstructural unit of a suspension under Quincke rotation is a pair of counter-rotating spheres aligned in the direction of the electric field. We perform a linear stability analysis that explains this observation.