David Saintillan

Instabilities, pattern formation, and mixing in active suspensions

Suspensions of self-propelled particles, such as swimming micro-organisms, are known to undergo complex dynamics as a result of hydrodynamic interactions. To elucidate these dynamics, a kinetic theory is developed and applied to study the linear stability and the nonlinear pattern formation in these systems. The evolution of a suspension of self-propelled particles is modeled using a conservation equation for the particle configurations, coupled to a mean-field description of the flow arising from the stress exerted by the particles on the fluid. Based on this model, we first investigate the stability of both aligned and isotropic suspensions. In aligned suspensions, an instability is shown to always occur at finite wavelengths, a result that extends previous predictions by Simha and Ramaswamy [“Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles,” Phys. Rev. Lett. 89, 058101 (2002)]. In isotropic suspensions, we demonstrate the existence of an instability for th...

A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers

Large-scale simulations of non-Brownian rigid fibers sedimenting under gravity at zero Reynolds number have been performed using a fast algorithm. The mathematical formulation follows the previous simulations by Butler and Shaqfeh [“Dynamic simulations of the inhomogeneous sedimentation of rigid fibres,” J. Fluid Mech. 468, 205 (2002)]. The motion of the fibers is described using slender-body theory, and the line distribution of point forces along their lengths is approximated by a Legendre polynomial in which only the total force, torque, and particle stresslet are retained. Periodic boundary conditions are used to simulate an infinite suspension, and both far-field hydrodynamic interactions and short-range lubrication forces are considered in all simulations. The calculation of the hydrodynamic interactions, which is typically the bottleneck for large systems with periodic boundary conditions, is accelerated using a smooth particle-mesh Ewald (SPME) algorithm previously used in molecular dynamics simula...

Emergence of coherent structures and large-scale flows in motile suspensions

The emergence of coherent structures, large-scale flows and correlated dynamics in suspensions of motile particles such as swimming micro-organisms or artificial microswimmers is studied using direct particle simulations. A detailed model is proposed for a slender rod-like particle that propels itself in a viscous fluid by exerting a prescribed tangential stress on its surface, and a method is devised for the efficient calculation of hydrodynamic interactions in large-scale suspensions of such particles using slender-body theory and a smooth particle-mesh Ewald algorithm. Simulations are performed with periodic boundary conditions for various system sizes and suspension volume fractions, and demonstrate a transition to large-scale correlated motions in suspensions of rear-actuated swimmers, or Pushers, above a critical volume fraction or system size. This transition, which is not observed in suspensions of head-actuated swimmers, or Pullers, is seen most clearly in particle velocity and passive tracer statistics. These observations are consistent with predictions from our previous mean-field kinetic theory, one of which states that instabilities will arise in uniform isotropic suspensions of Pushers when the product of the linear system size with the suspension volume fraction exceeds a given threshold. We also find that the collective dynamics of Pushers result in giant number fluctuations, local alignment of swimmers and strongly mixing flows. Suspensions of Pullers, which evince no large-scale dynamics, nonetheless display interesting deviations from the random isotropic state.

Bubble-Propelled Micromotors for Enhanced Transport of Passive Tracers

Fluid convection and mixing induced by bubble-propelled tubular microengines are characterized using passive microsphere tracers. Enhanced transport of the passive tracers by bubble-propelled micromotors, indicated by their mean squared displacement (MSD), is dramatically larger than that observed in the presence of catalytic nanowires and Janus particle motors. Bubble generation is shown to play a dominant role in the effective fluid transport observed in the presence of tubular microengines. These findings further support the potential of using bubble-propelled microengines for mixing reagents and accelerating reaction rates. The study offers useful insights toward understanding the role of the motion of multiple micromotors, bubble generation, and additional factors (e.g., motor density and fuel concentration) upon the observed motor-induced fluid transport.

Geometrically Designing the Kinematic Behavior of Catalytic Nanomotors

Catalytic nanomotors with silica microbead heads and TiO(2) arms are systematically designed by dynamic shadowing growth. The swimming trajectories are fine tuned by altering the arm length and orientation exploiting geometry-dependent hydrodynamic interactions at low Reynolds number. The curvature, angular frequency, and radius of curvature of the trajectories change as a function of arm length. Simulations based on the method of regularized Stokeslets are also described and correctly capture the trends observed in the experiments.

The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation

Theory and numerical simulations are used to investigate the concentration fluctuations and the microstructure in dilute sedimenting suspensions of orientable and deformable particles at zero Reynolds number. The case of orientable particles is studied using prolate and oblate spheroids, while viscous droplets in the small deformation regime illustrate the effects of deformability. An efficient method based on a point-particle approximation and on smooth localized force representations is implemented to simulate full-scale suspensions with both periodic and slip boundaries, where the latter are used to qualitatively reproduce the effects of horizontal walls. The concentration instability predicted theoretically for suspensions of spheroids is captured in the simulations, and we find that including horizontal walls provides a mechanism for wavenumber selection, in contrast to periodic systems in which the longest wavelength set by the size of the container dominates. A theoretical model for the case of slightly deformable particles is developed, and a linear stability analysis shows that such suspensions are also unstable to concentration fluctuations under sedimentation. In the absence of diffusion, the model predicts that density fluctuations are equally unstable at all wavelengths, but we show that diffusion, whether Brownian or hydrodynamic, should damp high-wavenumber fluctuations. Simulations are also performed for deformable particles, and again an instability is observed that shows a similar mechanism for the wavenumber selection in finite containers. Our results demonstrate that all sedimentation processes of orientable or deformable particles are subject to spontaneous concentration inhomogeneities, which control the sedimentation rates in these systems.

Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow

We use Brownian dynamics to investigate the effect of chain flexibility on the cross-streamline migration of short polymers in a pressure-driven flow between two infinite flat plates. A simulation method is described that models a polymer molecule at the Kuhn step level as a chain of

Emergent vortices in populations of colloidal rollers

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Instabilities and nonlinear dynamics of concentrated active suspensions

freely jointed Brownian rods, and includes multibody hydrodynamic interactions between the chain segments and the surrounding channel walls. Our study confirms the existence of shear-induced migration away from the solid boundaries toward the channel centreline as a result of wall hydrodynamic interactions. At a fixed ratio

Nonlinear interactions in electrophoresis of ideally polarizable particles

H/R_{g}