19 results found
Mingarelli L, Keaveny EE, Barnett R, 2016, Simulating infinite vortex lattices in superfluids, Journal of Physics: Condensed Matter, Vol: 28, Pages: 285201-285201, ISSN: 0953-8984
Delmotte B, Keaveny EE, 2015, Simulating Brownian suspensions with fluctuating hydrodynamics
© 2015 AIP Publishing LLC. Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint needs only to be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation.
Delmotte B, Keaveny EE, Plouraboué F, et al., 2015, Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method, Journal of Computational Physics, Vol: 302, Pages: 524-547, ISSN: 0021-9991
© 2015 Elsevier Inc. We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (10 4 -10 5 ) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.
Kalogirou A, Keaveny EE, Papageorgiou DT, 2015, An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol: 471, Pages: 20140932-20140932, ISSN: 1364-5021
Keaveny EE, 2014, Fluctuating force-coupling method for simulations of colloidal suspensions, Journal of Computational Physics, Vol: 269, Pages: 61-79, ISSN: 0021-9991
Keaveny EE, Walker SW, Shelley MJ, 2013, Optimization of Chiral Structures for Microscale Propulsion, NANO LETTERS, Vol: 13, Pages: 531-537, ISSN: 1530-6984
Walker SW, Keaveny EE, 2013, Analysis of Shape Optimization for Magnetic Microswimmers, SIAM Journal on Control and Optimization, Vol: 51, Pages: 3093-3126, ISSN: 0363-0129
Majmudar T, Keaveny EE, Zhang J, et al., 2012, Experiments and theory of undulatory locomotion in a simple structured medium., J R Soc Interface, Vol: 9, Pages: 1809-1823
Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics.
Keaveny EE, Shelley MJ, 2011, Applying a second-kind boundary integral equation for surface tractions in Stokes flow, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 230, Pages: 2141-2159, ISSN: 0021-9991
Keaveny EE, Shelley MJ, 2009, Hydrodynamic mobility of chiral colloidal aggregates, PHYSICAL REVIEW E, Vol: 79, ISSN: 1539-3755
Liu D, Keaveny EE, Maxey MR, et al., 2009, Force-coupling method for flows with ellipsoidal particles, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 228, Pages: 3559-3581, ISSN: 0021-9991
Keaveny EE, Maxey MR, 2008, Modeling the magnetic interactions between paramagnetic beads in magnetorheological fluids, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 227, Pages: 9554-9571, ISSN: 0021-9991
Keaveny EE, Maxey MR, 2008, Interactions between comoving magnetic microswimmers, PHYSICAL REVIEW E, Vol: 77, ISSN: 1539-3755
Keaveny EE, Maxey MR, 2008, Spiral swimming of an artificial micro-swimmer, JOURNAL OF FLUID MECHANICS, Vol: 598, Pages: 293-319, ISSN: 0022-1120
Keaveny EE, Pivkin IV, Maxey M, et al., 2005, A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows, JOURNAL OF CHEMICAL PHYSICS, Vol: 123, ISSN: 0021-9606
Bao Y, Rachh M, Keaveny E, et al., A fluctuating boundary integral method for Brownian suspensions
We present a fluctuating boundary integral method (FBIM) for BrownianDynamics of suspensions of rigid particles of complex shape immersed in aStokes fluid. We develop a linear-scaling algorithm to generate, together, boththe deterministic (mean) component of the particle linear and angularvelocities that arise in response to the applied forces and torques, as well asthe stochastic (fluctuating) Brownian displacements that arise in response tothe thermal fluctuations in the fluid. In this work we restrict our attentionto two-dimensional periodic domains, however, our key ideas can be extended tothree dimensions and confined suspensions. Our approach relies on a first-kindboundary integral formulation of a Stochastic Stokes Boundary Value Problem(SSBVP) in which a random surface velocity is prescribed on the particlesurface. This random surface velocity has zero mean and covariance proportionalto the Green's function for the Stokes flow (Stokeslet). We demonstrate thatthe Brownian displacements generated by solving this SSBVP obey thefluctuation-dissipation balance relation. Furthermore, we demonstrate thatdiscretizing the first-kind formulation using standard boundary integraltechniques leads to an efficient numerical method that strictly preservesdiscrete fluctuation-dissipation balance (DFDB). Near-field contributions tothe Brownian displacements are efficiently approximated by iterative methods inreal space, while far-field contributions are rapidly generated by fastFourier-space methods based on fluctuating hydrodynamics. FBIM provides the keyingredient for time integration of the overdamped Langevin equations forBrownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB byperforming equilibrium BD simulations of suspensions of starfish-shaped bodiesusing a random finite difference temporal integrator.
Delmotte B, Keaveny EE, Climent E, et al., Simulations of Brownian tracer transport in squirmer suspensions
In addition to enabling movement towards environments with favourable livingconditions, swimming by microorganisms has also been linked to enhanced mixingand improved nutrient uptake by their populations. Experimental studies haveshown that Brownian tracer particles exhibit enhanced diffusion due to theswimmers, while theoretical models have linked this increase in diffusion tothe flows generated by the swimming microorganisms, as well as collisions withthe swimmers. In this study, we perform detailed simulations based on theforce-coupling method and its recent extensions to the swimming and Brownianparticles to examine tracer displacements and effective tracer diffusivity insquirmer suspensions. By isolating effects such as hydrodynamic or stericinteractions, we provide physical insight into experimental measurements of thetracer displacement distribution. In addition, we extend results to thesemi-dilute regime where the swimmer-swimmer interactions affect tracertransport and the effective tracer diffusivity no longer scales linearly withthe swimmer volume fraction.
Mingarelli L, Keaveny EE, Barnett R, Vortex Lattices in Binary Mixtures of Repulsive Superfluids
We present an extension of the framework introduced in  to treatmulticomponent systems, showing that new degrees of freedom are necessary inorder to obtain the desired boundary conditions. We then apply this extendedframework to the coupled Gross-Pitaevskii equations to investigate the groundstates of two-component systems with equal masses thereby extending previouswork in the lowest Landau limit  to arbitrary interactions withinGross-Pitaevskii theory. We show that away from the lowest-Landau level limit,the predominant vortex lattice consists of two interlaced triangular lattices.Finally, we derive a linear relation which accurately describes the phaseboundaries in the strong interacting regimes.
Schoeller SF, Keaveny EE, From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions
Swimming cells and microorganisms are as diverse in their collective dynamicsas they are in their individual shapes and propulsion mechanisms. Even forsperm cells, which have a stereotyped shape consisting of a cell body connectedto a flexible flagellum, a wide range of collective dynamics is observedspanning from the formation of tightly packed groups to the display oflarger-scale, turbulence-like motion. Using a detailed mathematical model thatresolves flagellum dynamics, we perform simulations of sperm suspensionscontaining up to 1000 cells and explore the connection between individual andcollective dynamics. We find that depending on the level of variation inindividual dynamics from one swimmer to another, the sperm exhibit either astrong tendency to aggregate, or the suspension exhibits large-scale swirling.Hydrodynamic interactions govern the formation and evolution of both states. Inaddition, a quantitative analysis of the states reveals that the flowsgenerated at the time-scale of flagellum undulations contribute significantlyto the overall energy in the surrounding fluid, highlighting the importance ofresolving these flows.
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