arXiv subjects

Saverio E. Spagnolie

Publications and source records attributed to Saverio E. Spagnolie.

At least 19 recordsLinked to original sources

arXiv2026

Autonomous route to the strange attractor: the many life stages of the chaotic bubblewheel

A body floating atop a supersaturated fluid may accumulate bubbles along its underbelly, which can render the body rotationally unstable. But rotation can strip the surface of these bubbles when they make contact with the air above. To explore this coupling we perform experiments using cylinders floating on carbonated water. The cylinders exhibit an array of distinct dynamics, including constant rolling, periodic and aperiodic oscillation, chaos, and intermittent capsizing, which can be tuned by body size, mass distribution, and gas concentration. A continuum model for the bubble density dynamics, and Galerkin projection, tie the experiment to the generalized Lorenz system and its famed chaotic attractor. Even an extremely small center-of-mass offset can have a qualitative impact on the dynamics, and an offset of as little as a few percent can fully stabilize the system. The experiment represents a highly accessible physical realization of the Lorenz system, which, owing to continuous gas loss from the fluid to the air above, sweeps slowly without intervention across a classical bifurcation diagram in time.

physics.flu-dyn↗

arXiv2025

Morphogenesis of bacterial colonies in liquid crystalline environments

Natural bacterial habitats are often complex fluids with viscoelastic and anisotropic responses to stress; for example, they can take the form of liquid crystals (LCs), with elongated microscopic constituents that collectively align while still retaining the ability to flow. However, laboratory studies typically focus on cells in simple liquids or complex fluids with randomly-oriented constituents. Here, we show how interactions with LCs shape bacterial proliferation in multicellular colonies. Using experiments, we find that in a nematic LC, cells generically form aligned single-cell-wide "chains" as they reproduce. As these chains lengthen, they eventually buckle in a highly localized manner. By combining our measurements with a continuum mechanical theory, we demonstrate that this distinctive morphogenetic program emerges because cells are kept in alignment due to the LC's elasticity; as each chain lengthens, growth-induced viscous stresses along its contour eventually overcome the elasticity of the surrounding nematic, leading to buckling. Our work thus reveals and provides mechanistic insight into the previously-overlooked role of LCs in sculpting bacterial life in complex environments.

cond-mat.soft↗

arXiv2025

Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow

A body immersed in a nematic liquid crystal disturbs the fluid's preferred molecular configuration and increases its stored elastic energy. In an active nematic, the fluid components also generate a stress in the bulk fluid. By introducing either an immersed body or boundary, a large scale flow can be triggered due to anchoring boundary conditions alone -- a global pressure built by active stresses at equilibrium is instantly released everywhere. The fluid then imposes viscous, elastic, and active stresses on such surfaces which, if compliant, may result in a surface deformation. We study the deformations and stresses of a linearly elastic body placed in an active nematic in two dimensions. Using complex variables techniques, exact expressions for the fluid flow, director field, surface tractions, and body deformation are derived. Qualitative differences between elastic and active stress-driven deformations are identified, depending on an active Ericksen number, anchoring conditions, and body material properties, thereby suggesting a new method for measuring mechanical stresses in active anisotropic environments. Flow profiles, external confinement, and anchoring-induced stirring are also addressed.

cond-mat.soft↗

arXiv2025

Arrested development and traveling waves of active suspensions in nematic liquid crystals

Active particles in anisotropic, viscoelastic fluids experience competing stresses which guide their trajectories. An aligned suspension of particles can trigger a hydrodynamic bend instability, but the elasticity of the fluid can drive particle orientations back towards alignment. To study these competing effects, we examine a dilute suspension of active particles in an Ericksen-Leslie model nematic liquid crystal. An anchoring strength linking the active and passive media tunes the system between active suspension theory in Newtonian fluids in one limit, and active nematic theory in another. For extensile active stresses, beyond a critical active Ericksen number or particle concentration, the suspension first comes into alignment, then buckles via a classical bend instability. Rather than entering the fully developed roiling state observed in isotropic fluids, the development is arrested into a steady, flowing state by fluid elasticity. Arrested states of higher wavenumber appear at yet larger extensile activity, and a phase transition is identified at finite anchoring strength. If the active particles are motile, the particles can surf along the bent environment of their own creation. More exotic states are also observed, including a oscillatory 'thrashing' mode. Moment equations are derived, compared to kinetic theory simulations, and analyzed in asymptotic limits which admit exact expressions for the traveling wave speed and both particle orientation and director fields in the first arrested state.

cond-mat.soft↗

arXiv2025

Geometric dependence of curvature-induced rigidity

Bending the edge of a thin elastic material promotes rigidity far from its clamped boundary. However, this curvature-induced rigidity can be overwhelmed by gravity or other external loading, resulting in elastic buckling and large deformations. We consider the role of body geometry on this competition using experiments, numerical simulations, and reduced-order models. Finite element simulations are performed using a model nonlinear hyperelastic material, and a theoretical framework is proposed that incorporates small lateral curvatures, large longitudinal rotations, and a varying cross-sectional width. A particular focus is on the comparison between rectangular and triangular sheets, and trapezoidal sheets in between. Sheet geometry affects downward tip deflection by changing the relative importance of the sheet's weight and the rigidity provided by curvature, often in subtle ways. In extreme cases, non-monotonic deflection is observed with increasing sheet length, and a region of hysteretic bistability emerges, becoming more pronounced with rectangular sheets and large imposed curvatures. These findings demonstrate the profound impact of geometry on the competition between curvature-induced rigidity and gravity-induced deformation in thin elastic materials.

cond-mat.soft↗

arXiv2024

Exact and approximate solutions for elastic interactions in a nematic liquid crystal

Anisotropic fluids appear in a diverse array of systems, from liquid-crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium's orientational order, however, resulting in a stored elastic energy within the bulk. As a consequence, multiple immersed bodies interact at equilibrium through fluid-mediated forces and torques, which depend on the bodies' positions, orientations, and shapes. We provide the equilibrium configuration of a model nematic liquid crystal with multiple immersed bodies or inclusions in two-dimensions, as well as the associated body forces, torques, and surface tractions. A complex variables approach is taken which leans on previous work by Crowdy (2020) for describing solutions with multiply-connected domains. Free periods of a complex director field, which correspond to topological defect positioning and net topological charge, are determined numerically to minimize a global stored elastic energy, including a contribution of a weak (finite) anchoring strength on the body surfaces. Finally, a general, analytical description of two-body far-field interactions is provided, along with examples using two cylindrical inclusions of arbitrary position and size, and two triangles of arbitrary position and orientation.

cond-mat.soft↗

arXiv2024

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.

physics.flu-dyn↗

arXiv2023

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 dynamically evolving flagellar orientation field, we derive the Euler-Poincar{é} equations governing dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium {\it 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.

cond-mat.soft↗

arXiv2023

A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox

We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two-dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local tractions, forces, and torques on the body are discussed in a general setting. For weak (finite) anchoring strengths, an effective boundary technique is proposed which is used to determine asymptotic solutions. The energy-minimizing locations of topological defects on the body surface are also discussed. A number of examples are provided, including circular and triangular bodies, and a Janus particle with hybrid anchoring conditions. Analogues to classical results in fluid dynamics are identified, including d'Alembert's paradox, Stokes' paradox, and the Kutta condition for circulation selection.

cond-mat.soft↗

arXiv2022

Swimming in Complex Fluids

We review the literature on swimming in complex fluids. A classification is proposed by comparing the length and time scales of a swimmer with those of nearby obstacles, interpreted broadly, extending from rigid or soft confining boundaries to molecules which confer the bulk fluid with complex stresses. A third dimension in the classification is the concentration of swimmers, which incorporates fluids whose complexity arises purely by the collective motion of swimming organisms. For each of the eight system classes which we identify we provide a background and describe modern research findings. While some classes have seen a great deal of attention for decades, others remain uncharted waters still open and awaiting exploration.

physics.flu-dyn↗

arXiv2022

Swinging and tumbling of multicomponent vesicles in flow

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations we develop a reduced order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane in two dimensions with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid body tumbling behavior. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.

cond-mat.soft↗

arXiv2021

Helical trajectories of swimming cells with a flexible flagellar hook

The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum in Stokes flow are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.

physics.bio-ph↗

arXiv2018

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 which also describes the Saffman-Taylor instability in a Hele-Shaw cell, or Rayleigh-Taylor instability in 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 which is non-monotonic 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.

cond-mat.soft↗

arXiv2017

A generalized traction integral equation for Stokes flow, with applications to near-wall particle mobility and viscous erosion

A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere (or hemisphere for wall-bounded flows). The derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free-space and wall-bounded domains. Two sample applications of the method are discussed: we study the tractions on an ellipsoid moving near a plane wall, which provides a more detailed understanding of the well-studied glancing and reversing trajectories in the context of particle sedimentation, and the erosion of bodies by a viscous flow, in which the surface is ablated at a rate proportional to the local viscous shear stress. Simulations and analytical estimates suggest that a spherical body in a uniform flow first reduces nearly but not exactly to the drag minimizing profile and then vanishes in finite time. The shape dynamics of an eroding body in a shear flow and near a wall are also investigated. Stagnation points on the body surface lead generically to the formation of cusps, whose number depends on the flow configuration and/or the presence of nearby boundaries.

physics.flu-dyn↗

arXiv2016

Microorganism Billiards

Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of a body with this empirical reflection law inside a regular polygon and show that the dynamics can settle on a stable periodic orbit or can be chaotic, depending on the swimmer's departure angle and the domain geometry. The dynamics are often found to be robust to the introduction of weak random fluctuations. The Lyapunov exponent of swimmer trajectories can be positive or negative, can have extremal values, and can have discontinuities depending on the degree of the polygon. A passive sorting device is proposed that traps swimmers of different departure angles into separate bins. We also study the external problem of a microorganism swimming in a patterned environment of square obstacles, where the departure angle dictates the possibility of trapping or diffusive trajectories.

nlin.CD↗

arXiv2016

A locally gradient-preserving reinitialization for level set functions

The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the interface gradient. The gradient of the level set function represents the stretching of the interface, which is of critical importance in many physical applications. The proposed locally gradient-preserving reinitialization (LGPR) method involves the solution of three PDEs of Hamilton-Jacobi type in succession; first the signed distance function is found using a traditional reinitialization technique, then the interface gradient is extended into the domain by a transport equation, and finally the new level set function is achieved with the solution of a generalized reinitialization equation. We prove the well-posedness of the Hamilton-Jacobi equations, with possibly discontinuous Hamiltonians, and propose numerical schemes for their solutions. A subcell resolution technique is used in the numerical solution of the transport equation to extend data away from the interface directly with high accuracy. The reinitialization technique is computationally inexpensive if the PDEs are solved only in a small band surrounding the interface. As an important application, the LGPR method will enable the application of the local level set approach to the Eulerian Immersed boundary method.

math.NA↗

arXiv2015

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 either by transverse or longitudinal 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. The behavior is quantitatively and qualitatively well-approximated by a hexatic liquid crystal except in the cases of small Ericksen number and in a nematic fluid with tumbling parameter near the transition to a flow-aligning nematic, where anisotropic effects dominate. 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.

cond-mat.soft↗

arXiv2015

Sedimentation of spheroidal bodies near walls in viscous fluids: glancing, reversing, tumbling, and sliding

The sedimentation of a rigid particle near a wall in a viscous fluid has been studied numerically by many authors, but analytical solutions have been derived only for special cases such as the motion of spherical particles. In this paper the method of images is used to derive simple ordinary differential equations describing the sedimentation of arbitrarily oriented prolate and oblate spheroids at zero Reynolds number near a vertical or inclined plane wall. The differential equations may be solved analytically in many situations, and full trajectories are predicted which compare favorably with complete numerical simulations. The simulations are performed using a novel double layer boundary integral formulation, a method of stresslet images. The conditions under which the glancing and reversing trajectories, first observed by Russel et al. (1977), occur are studied for bodies of arbitrary aspect ratio. Several additional trajectories are also described: a periodic tumbling trajectory for nearly spherical bodies, a linearly stable sliding trajectory which appears when the wall is slightly inclined, and three-dimensional glancing, reversing, and wobbling.

physics.flu-dyn↗