Publications 2015-present

A model of stokesian peristalsis and vesicle transport in a three-dimensional closed cavity.
by V. Aranda, R. Cortez and L. Fauci
in J. Biomechanics, Vol. 48 (9):1631-8 (2015)

Abstract: The complexity of the mechanics involved in the mammalian reproductive process is evident. Neither an ovum nor an embryo is self-propelled, but move through the oviduct or uterus due to the peristaltic action of the tube walls, imposed pressure gradients, and perhaps ciliary motion. Here we use the method of regularized Stokeslets to model the transport of an ovum or embryo within a peristaltic tube. We represent the ovum or embryo as a spherical vesicle of finite volume - not a massless point particle. The outer membrane of the neutrally-buoyant vesicle is discretized by nodes that are joined by a network of springs. The elastic moduli of these springs are chosen large enough so that a spherical shape is maintained. For simplicity, here we choose an axisymmetric tube where the geometry of the two-dimensional cross-section along the tube axis reflects that of the sagittal cross-section of the uterine cavity. Although the tube motion is axisymmetric, the presence of the vesicle within the tube requires a fully three-dimensional model. As was found in Yaniv et al., 2009 and Yaniv et al., 2012 for a 2D closed channel, we find that the flow dynamics in a 3D peristaltic tube are strongly influenced by the closed end and the manner in which the peristaltic wave damps out towards the closure. In addition, we demonstrate that the trajectory of a vesicle of finite volume can greatly differ from the trajectory of a massless fluid particle initially placed at the vesicle's centroid.

A fully three-dimensional model of the interaction of driven elastic filaments in a Stokes flow with applications to sperm motility.
by J. Simons, L. Fauci and R. Cortez
in J. Biomechanics, Vol. 48 (9):1639-1651(2015)

Abstract: In many animals,sperm flagella exhibit primarily planar waveforms. An isolated sperm with a planar flagellar beat in a three-dimensional unbounded fluid domain would remain in a plane. However, because sperm must navigate through complex,three-dimensional confined spaces along with other sperm, forces that bend or move the flagellum out of its current beat plane develop. Here we present an extension of previous models of an elastic sperm flagellar filament whose shape change is driven by the pursuit of a preferred curvature wave. In particular,we extend the energy of the generalized elastica to include a term that penalizes out-of-plane motion. We are now able to study the interaction of free- swimmers in a 3D Stokes flow that do not start out beating in the same plane. We demonstrate the three-dimensional nature of swimming behavior as neighboring sperm swim close to each other and affect each others' trajectories via fluid-structure coupling.

The effect of intrinsic muscular nonlinearities on the energetics of locomotion in a computational model of an anguilliform swimmer.
by C. Hamlet, L. Fauci and E.D. Tytell
in J. Theor. Biol., Vol. 385:119-129 (2015)

Abstract: Animals move through their environments using muscles to produce force. When an animal's nervous system activates a muscle, the muscle produces different amounts of force depending on its length, its shortening velocity, and its time history of force production. These muscle forces interact with forces from passive tissue properties and forces from the external environment. Using an integrative computational model that couples an elastic, actuated model of an anguilliform, lamprey-like swimmer with a surrounding Navier-Stokes fluid, we study the effects of this coupling between the muscle force and the body motion. Swimmers with different forms of this coupling can achieve similar motions, but use different amounts of energy. The velocity dependence is the most important property of the ones we considered for reducing energy costs and helping to stabilize oscillations. These effects are strongly influenced by how rapidly the muscle deactivates; if force decays too slowly, muscles on opposite sides of the body end up fighting each other, increasing energy cost. Work-dependent deactivation, an effect that causes a muscle to deactivate more rapidly if it has recently produced mechanical work, works together with the velocity dependence to reduce the energy cost of swimming.

Flow Induced by Bacterial Carpets and Transport of Microscale Loads
by A. Buchmann, L. Fauci, K. Leiderman, E. Strawbridge and L. Zhao
in in Applications of Dynamical Systems in Biology and Medicine, IMA Volumes, 158:35-53(2015)

Abstract: In this paper we utilize the method of regularized Stokeslets to explore flow fields induced by `carpets' of rotating flagella. We model each flagellum as a rigid, rotating helix attached to a wall, and study flows around both a single helix and a small patch of multiple helices. To test our numerical method and gain intuition about flows induced by a single rotating helix, we first perform a numerical time-reversibility experiment. Next, we investigate the hypothesis put forth in (Darnton et al., Biophys J 86, 1863-1870, 2004) that a small number of rotating flagella could produce "whirlpools" and "rivers" a small distance above them. Using our model system, we are able to produce "whirlpools" and "rivers" when the helices are rotating out of phase. Finally, to better understand the transport of microscale loads by flagellated microorganisms, we model a fully coupled helix-vesicle system by placing a finite-sized vesicle held together by elastic springs in fluid near one or two rotating helices. We compare the trajectories of the vesicle and a tracer particle initially placed at the centroid of vesicle and find that the two trajectories can diverge significantly within a short amount of time. Interestingly, the divergent behavior is extremely sensitive to the initial position within the fluid.

Hydrodynamic interactions of sheets vs filaments: synchronization, attraction, and alignment
by S.D. Olson and L. Fauci
in Physics of Fluids, Vol. 27: 12901(2015)

Abstract: The synchronization of nearby sperm flagella as they swim in a viscous fluid was observed nearly a century ago. In the early 1950s, in an effort to shed light on this intriguing phenomenon, G.I. Taylor initiated the mathematical analysis of the fluid dynamics of microorganism motility. Since then, models have investigated sperm hydrodynamics where the flagellum is treated as a waving sheet (2D) or as a slender waving filament (3D). Here we study the interactions of two finite length, flexible filaments confined to a plane in a 3D fluid, and compare these to the interactions of the analogous pair of finite, flexible sheets in a 2D fluid. Within our computational framework using regularized Stokeslets, this comparison is easily achieved by choosing either the 2D or 3D regularized kernel to compute fluid velocities induced by the actuated structures. We find, as expected, that two flagella swimming with a symmetric beatform will synchronize (phase-lock) on a fast time scale and attract towards each other on a longer time scale in both 2D and 3D. For a symmetric beatform, synchronization occurs faster in 2D than 3D for sufficiently stiff swimmers. In 3D, a greater enhancement in efficiency and swimming velocity is observed for attracted swimmers relative to the 2D case. We also demonstrate the tendency of two asymmetrically beating filaments in a 3D fluid to align - in tandem - exhibiting an efficiency boost for the duration of their sustained alignment.

Regularized image system for Stokes flow outside a solid sphere
by J. Wrobel, R. Cortez, D. Varela and L. Fauci
in J. Comp. Physics, Vol. 317: 165-184(2016)

Abstract: The image system for a three-dimensional flow generated by regularized forces outside a solid sphere is formulated and implemented as an extension of the method of regularized Stokeslets. The method is based on replacing a point force given by a delta distribution with a smooth localized function and deriving the exact velocity field produced by the forcing. In order to satisfy zero-flow boundary conditions at a solid sphere, the image system for singular Stokeslets is generalized to give exact cancellation of the regularized flow at the surface of the sphere. The regularized image system contains the same elements as the singular counterpart but with coefficients that depend on a regularization parameter. As this parameter vanishes, the expressions reduce to the image system of the singular Stokeslet. The expression relating force and velocity can be inverted to compute the forces that generate a given velocity boundary condition elsewhere in the flow. We present several examples within the context of biological flows at the microscale in order to validate and highlight the usefulness of the image system in computations.

Enhanced flagellar swimming through a compliant viscoelastic network in Stokes flow
by J. Wrobel, S. Lynch, A. Barrett, L. Fauci and R. Cortez
in J. Fluid Mech., Vol. 792: 775-797(2016)

Abstract: In many physiological settings, microorganisms must swim through viscous fluids with suspended polymeric networks whose length scales are comparable to that of the organism. Here we present a model of a flagellar swimmer moving through a compliant viscoelastic network immersed in a three-dimensional viscous fluid. The swimmer moves with a prescribed gait, exerting forces on the fluid and the heterogeneous network. The viscoelastic structural links of this network are stretched or compressed in response to the fluid flow caused by these forces, and these elastic deformations also generate forces on the viscous fluid. Here we track the swimmer as it leaves a region of Newtonian fluid, enters and moves through a heterogeneous network and finally enters a Newtonian region again. We find that stiffer networks give a boost to the velocity of the swimmer. In addition, we find that the efficiency of swimming is dependent upon the evolution of the compliant network as the swimmer progresses through it.

Role of body stiffness in undulatory swimming: Insights from robotic and computational models
by E.D. Tytell, M.C. Leftwich, C.-Y. Hsu, B.E. Griffith, A.H. Cohen, A.J. Smits, C. Hamlet and L. Fauci
in Phys. Rev. Fluids, Vol. 1:073202(2016)

Abstract: In an effort to understand the locomotion dynamics of a simple vertebrate, the lamprey, both physical and computational models have been developed. A key feature of these models is the ability to vary the passive stiffness of portions of the swimmer, focusing on highly flexible models similar in material properties to lampreys and other anguilliform fishes. The physical model is a robotic lamprey-like swimmer that is actuated along most of its length but has passively flexible tails of different stiffnesses. The computational model is a two-dimensional model that captures fluid-structure interactions using an immersed boundary framework. This simulated lamprey is passively flexible throughout its length, and is also actuated along most of its length by the activation of muscle forces. Although the three-dimensional robot and the two-dimensional computational swimmer are such different constructs, we demonstrate that the wake structures generated by these models share many features and examine how flexibility affects these features. Both models produce wakes with two or more same-sign vortices shed each time the tail changes direction (a `2P' or higher-order wake). In general, wakes become less coherent as tail flexibility increases. We examine the pressure distribution near the tail tip and the timing of vortex formation in both cases and find good agreement. Because we include flexibility, we are able to estimate resonant frequencies for several of the robotic and computational swimmers. We find that actuation at the resonant frequency dramatically increases the distance traveled per tail-beat cycle with only a small increase in the lost kinetic energy in the wake, suggesting that the resonant swimmers are more efficient.

Interaction of toroidal swimmers in Stokes flow
by J. Huang and L. Fauci
in Phys. Rev. E, Vol. 95:043102(2017)

Abstract: A doughnut-shaped object supporting surface rotations was a hypothetical construct proposed by both Taylor and Purcell as a swimmer that would be able to propel itself in a Stokesian fluid because of the irreversibility of its stroke. Here we numerically examine the hydrodynamic interaction of pairs and trios of these free toroidal swimmers. First, we study the axisymmetric case of two toroidal swimmers placed in tandem, and show that a single torus of a corotating pair is more efficient than when it swims alone, but less efficient when paired with a counterrotating partner. Using a regularized Stokeslet framework, we study the nonaxisymmetric case of toroidal swimmers whose axes are initially parallel, but not collinear. These perturbed in tandem swimmers can exhibit qualitatively different trajectories that may, for instance, repel the swimmers or have them settle into a periodic state. We also illustrate interesting dynamics that occur for different initial configurations of three tori.

Dynamics of a macroscopic elastic fibre in a polymeric cellular flow
by Qiang Yang and L. Fauci
in J. Fluid Mech., Vol. 817:388-405(2017)

Abstract: We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds- number flow using the Navier-Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre's ability to traverse multiple cells in the domain.