Levitation and dynamics of bodies in supersaturated fluids.

A body immersed in a supersaturated fluid like carbonated water can accumulate a dynamic field of bubbles upon its surface. If the body is mobile, the attached bubbles can lift it upward against gravity, but a fluid-air interface can clean the surface of these lifting agents and the body may plummet. The process then begins anew, and continues for as long as the concentration of gas in the fluid supports it. In this work, experiments using fixed and free immersed bodies reveal fundamental features of force development and gas escape. A continuum model which incorporates the dynamics of a surface buoyancy field is used to predict the ranges of body mass and size, and fluid properties, for which the system is most dynamic, and those for which body excursions are suppressed. Simulations are then used to probe systems which are dominated by a small number of large bubbles. Body rotations at the surface are critical for driving periodic vertical motions of large bodies, which in turn can produce body wobbling, rolling, and damped surface 'bouncing' dynamics.

Self-buckling and self-writhing of semi-flexible microorganisms.

The twisting and writhing of a cell body and associated mechanical stresses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a flagellar orientation field, we derive the Euler-Poincaré equations governing the dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Proteus mirabilis. A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. These studies highlight a practical requirement for the stiffness of bacteria below which self-buckling occurs and cell motility becomes ineffective.

Protein-induced membrane curvature in coarse-grained simulations.

Using the endosomal sorting complex required for transport (ESCRT)-III membrane remodeling complex as an example, we analyze three popular coarse-grained models (the regular MARTINI, polarizable MARTINI (POL-MARTINI), and big multipole water MARTINI (BMW-MARTINI)) for the description of membrane curvature sensing and generation activities of peripheral proteins. Although the three variants of the MARTINI model provide consistent descriptions for the protein-protein interface in a linear filament model of ESCRT-III, they differ considerably in terms of protein-membrane interface and therefore membrane curvature sensing and generation behaviors. In particular, BMW-MARTINI provides the most consistent description of the protein-membrane interface as compared to all-atom simulations, whereas the regular MARTINI is most consistent with atomistic simulations in terms of the qualitative sign of membrane curvature sensing and generation. With POL-MARTINI, the ESCRT-III model interacts weakly with the membrane and therefore does not exhibit any curvature-sensitive activities. Analysis suggests that the incorrect membrane curvature activities predicted by BMW-MARTINI are due to overestimated insertion depth of an amphipathic helix and incorrect sign for the spontaneous curvature of anionic lipids. These results not only point to ways that coarse-grained models can be improved but also explicitly highlight local lipid composition and insertion depth of protein motifs as essential regulatory factors for membrane curvature sensing and generation.

Dynamic and reversible shape response of red blood cells in synthetic liquid crystals.

Mammalian cells are soft, and correct functioning requires that cells undergo dynamic shape changes in vivo. Although a range of diseases are associated with stiffening of red blood cells (RBCs; e.g., sickle cell anemia or malaria), the mechanical properties and thus shape responses of cells to complex viscoelastic environments are poorly understood. We use vapor pressure measurements to identify aqueous liquid crystals (LCs) that are in osmotic equilibrium with RBCs and explore mechanical coupling between RBCs and LCs. When transferred from an isotropic aqueous phase into a LC, RBCs exhibit complex yet reversible shape transformations, from initially biconcave disks to elongated and folded geometries with noncircular cross-sections. Importantly, whereas the shapes of RBCs are similar in isotropic fluids, when strained by LC, a large variance in shape response is measured, thus unmasking cell-to-cell variation in mechanical properties. Numerical modeling of LC and cell mechanics reveals that RBC shape responses occur at constant cell membrane area but with membrane shear moduli that vary between cells from 2 to 16 × 10-6 N/m. Temperature-dependent LC elasticity permits continuous tuning of RBC strains, and chemical cross-linking of RBCs, a model for diseased cells, leads to striking changes in shape responses of the RBCs. Overall, these results provide insight into the coupling of strain between soft mammalian cells and synthetic LCs, and hint at new methods for rapidly characterizing mechanical properties of single mammalian cells in a population and thus cell-to-cell variance.

Shaving and breaking bacterial chains with a viscous flow.

Some food and ferment manufacturing steps such as spray-drying result in the application of viscous stresses to bacteria. This study explores how a viscous flow impacts both bacterial adhesion functionality and bacterial cell organization using a combined experimental and modeling approach. As a model organism we study Lactobacillus rhamnosus GG (LGG) "wild type" (WT), known to feature strong adhesive affinities towards beta-lactoglobulin thanks to pili produced by the bacteria on cell surfaces, along with three cell-surface mutant strains. Applying repeated flows with high shear-rates reduces bacterial adhesive abilities up to 20% for LGG WT. Bacterial chains are also broken by this process, into 2-cell chains at low industrial shear rates, and into single cells at very high shear rates. To rationalize the experimental observations we study numerically and analytically the Stokes equations describing viscous fluid flow around a chain of elastically connected spheroidal cell bodies. In this model setting we examine qualitatively the relationship between surface traction (force per unit area), a proxy for pili removal rate, and bacterial chain length (number of cells). Longer chains result in higher maximal surface tractions, particularly at the chain extremities, while inner cells enjoy a small protection from surface tractions due to hydrodynamic interactions with their neighbors. Chain rupture therefore may act as a mechanism to preserve surface adhesive functionality in bacteria.

Molecular Simulation of Mechanical Properties and Membrane Activities of the ESCRT-III Complexes.

The endosomal sorting complex required for transport (ESCRT) machinery carries out the membrane scission reactions that are required for many biological processes throughout cells. How ESCRTs bind and deform cellular membranes and ultimately produce vesicles has been a matter of active research in recent years. In this study, we use fully atomistic molecular dynamics simulations to scrutinize the structural details of a filament composed of Vps32 protomers, a major component of ESCRT-III complexes. The simulations show that both hydrophobic and electrostatic interactions between monomers help maintain the structural stability of the filament, which exhibits an intrinsic bend and twist. Our findings suggest that the accumulation of bending and twisting stresses as the filament elongates on the membrane surface likely contributes to the driving force for membrane invagination. The filament exposes a large cationic surface that senses the negatively charged lipids in the membrane, and the N-terminal amphipathic helix of the monomers not only acts as a membrane anchor but also generates significant positive membrane curvature. Taking all results together, we discuss a plausible mechanism for membrane invagination driven by ESCRT-III.

Active matter invasion of a viscous fluid: Unstable sheets and a no-flow theorem.

We investigate the dynamics of a dilute suspension of hydrodynamically interacting motile or immotile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities, governed at small times by an equation that also describes the Saffman-Taylor instability in a Hele-Shaw cell, or the Rayleigh-Taylor instability in a two-dimensional flow through a porous medium. Thin sheets of aligned pusher particles are always unstable, while sheets of aligned puller particles can either be stable (immotile particles), or unstable (motile particles) with a growth rate that is nonmonotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow everywhere and for all time.

Straining soft colloids in aqueous nematic liquid crystals.

Liquid crystals (LCs), because of their long-range molecular ordering, are anisotropic, elastic fluids. Herein, we report that elastic stresses imparted by nematic LCs can dynamically shape soft colloids and tune their physical properties. Specifically, we use giant unilamellar vesicles (GUVs) as soft colloids and explore the interplay of mechanical strain when the GUVs are confined within aqueous chromonic LC phases. Accompanying thermal quenching from isotropic to LC phases, we observe the elasticity of the LC phases to transform initially spherical GUVs (diameters of 2-50 µm) into two distinct populations of GUVs with spindle-like shapes and aspect ratios as large as 10. Large GUVs are strained to a small extent (R/r < 1.54, where R and r are the major and minor radii, respectively), consistent with an LC elasticity-induced expansion of lipid membrane surface area of up to 3% and conservation of the internal GUV volume. Small GUVs, in contrast, form highly elongated spindles (1.54 < R/r < 10) that arise from an efflux of LCs from the GUVs during the shape transformation, consistent with LC-induced straining of the membrane leading to transient membrane pore formation. A thermodynamic analysis of both populations of GUVs reveals that the final shapes adopted by these soft colloids are dominated by a competition between the LC elasticity and an energy (∼0.01 mN/m) associated with the GUV-LC interface. Overall, these results provide insight into the coupling of strain in soft materials and suggest previously unidentified designs of LC-based responsive and reconfigurable materials.

Microscale locomotion in a nematic liquid crystal.

Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated by small-amplitude traveling waves in a three-dimensional nematic liquid crystal without twist. We calculate the swimming speed and entrained volumetric flux as a function of the swimmer's stroke properties as well as the elastic and rheological properties of the liquid crystal. These results are then compared to previous results on an analogous swimmer in a hexatic liquid crystal, indicating large differences in the cases of small Ericksen number and in a nematic fluid when the tumbling parameter is near the transition to a shear-aligning nematic. We also propose a novel method of swimming or pumping in a nematic fluid by passing a traveling wave of director oscillation along a rigid wall.

Bacterial transport of colloids in liquid crystalline environments.

We describe the controlled transport and delivery of non-motile eukaryotic cells and polymer microparticles by swimming bacteria suspended in nematic liquid crystals. The bacteria push reversibly attached cargo in a stable, unidirectional path (or along a complex patterned director field) over exceptionally long distances. Numerical simulations and analytical predictions for swimming speeds provide a mechanistic insight into the hydrodynamics of the system. This study lays the foundation for using cargo-carrying bacteria in engineering applications and for understanding interspecies interactions in polymicrobial communities.

Geometric capture and escape of a microswimmer colliding with an obstacle.

Motivated by recent experiments, we consider the hydrodynamic capture of a microswimmer near a stationary spherical obstacle. Simulations of model equations show that a swimmer approaching a small spherical colloid is simply scattered. In contrast, when the colloid is larger than a critical size it acts as a passive trap: the swimmer is hydrodynamically captured along closed trajectories and endlessly orbits around the colloidal sphere. In order to gain physical insight into this hydrodynamic scattering problem, we address it analytically. We provide expressions for the critical trapping radius, the depth of the "basin of attraction," and the scattering angle, which show excellent agreement with our numerical findings. We also demonstrate and rationalize the strong impact of swimming-flow symmetries on the trapping efficiency. Finally, we give the swimmer an opportunity to escape the colloidal traps by considering the effects of Brownian, or active, diffusion. We show that in some cases the trapping time is governed by an Ornstein-Uhlenbeck process, which results in a trapping time distribution that is well-approximated as inverse-Gaussian. The predictions again compare very favorably with the numerical simulations. We envision applications of the theory to bioremediation, microorganism sorting techniques, and the study of bacterial populations in heterogeneous or porous environments.

Stability and dynamics of magnetocapillary interactions.

Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads, and bead collisions. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.

Locomotion and transport in a hexatic liquid crystal.

The swimming behavior of bacteria and other microorganisms is sensitive to the physical properties of the fluid in which they swim. Mucus, biofilms, and artificial liquid-crystalline solutions are all examples of fluids with some degree of anisotropy that are also commonly encountered by bacteria. In this article, we study how liquid-crystalline order affects the swimming behavior of a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor's swimming sheet: an infinite line undulating with small-amplitude transverse or longitudinal traveling waves. The fluid is a two-dimensional hexatic liquid-crystalline film. We calculate the power dissipated, swimming speed, and flux of fluid entrained as a function of the swimmer's wave form as well as properties of the hexatic film, such as the rotational and shear viscosity, the Frank elastic constant, and the anchoring strength. The departure from isotropic behavior is greatest for large rotational viscosity and weak anchoring boundary conditions on the orientational order at the swimmer surface. We even find that if the rotational viscosity is large enough, the transverse-wave swimmer moves in the opposite direction relative to a swimmer in an isotropic fluid.

Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes.

The motion of a rotating helical body in a viscoelastic fluid is considered. In the case of force-free swimming, the introduction of viscoelasticity can either enhance or retard the swimming speed and locomotive efficiency, depending on the body geometry, fluid properties, and the body rotation rate. Numerical solutions of the Oldroyd-B equations show how previous theoretical predictions break down with increasing helical radius or with decreasing filament thickness. Helices of large pitch angle show an increase in swimming speed to a local maximum at a Deborah number of order unity. The numerical results show how the small-amplitude theoretical calculations connect smoothly to the large-amplitude experimental measurements.

Hydrodynamics of the double-wave structure of insect spermatozoa flagella.

In addition to conventional planar and helical flagellar waves, insect sperm flagella have also been observed to display a double-wave structure characterized by the presence of two superimposed helical waves. In this paper, we present a hydrodynamic investigation of the locomotion of insect spermatozoa exhibiting the double-wave structure, idealized here as superhelical waves. Resolving the hydrodynamic interactions with a non-local slender body theory, we predict the swimming kinematics of these superhelical swimmers based on experimentally collected geometric and kinematic data. Our consideration provides insight into the relative contributions of the major and minor helical waves to swimming; namely, propulsion is owing primarily to the minor wave, with negligible contribution from the major wave. We also explore the dependence of the propulsion speed on geometric and kinematic parameters, revealing counterintuitive results, particularly for the case when the minor and major helical structures are of opposite chirality.

Comparative hydrodynamics of bacterial polymorphism.

Most bacteria swim through fluids by rotating helical flagella which can take one of 12 distinct polymorphic shapes, the most common of which is the normal form used during forward swimming runs. To shed light on the prevalence of the normal form in locomotion, we gather all available experimental measurements of the various polymorphic forms and compute their intrinsic hydrodynamic efficiencies. The normal helical form is found to be the most efficient of the 12 polymorphic forms by a significant margin--a conclusion valid for both the peritrichous and polar flagellar families, and robust to a change in the effective flagellum diameter or length. Hence, although energetic costs of locomotion are small for bacteria, fluid mechanical forces may have played a significant role in the evolution of the flagellum.

Rehinging biflagellar locomotion in a viscous fluid.

A means of swimming in a viscous fluid is presented, in which a swimmer with only two links rotates around a joint and then rehinges in a periodic fashion in what is here termed rehinging locomotion. This two-link rigid swimmer is shown to locomote with an efficiency similar to that of Purcell's well-studied three-link swimmer, but with a simpler morphology. The hydrodynamically optimal stroke of an analogous flexible biflagellated swimmer is also considered. The introduction of flexibility is found to increase the swimming efficiency by up to 520% as the body begins to exhibit wavelike dynamics, with an upper bound on the efficiency determined by a degeneracy in the limit of infinite flexibility.