arXiv subjects

Ory Schnitzer

Publications and source records attributed to Ory Schnitzer.

At least 19 recordsLinked to original sources

arXiv2026

Weakly nonlinear dynamics of a follower-force active filament in simple shear flow

We employ weakly nonlinear theory to investigate how an externally imposed simple shear flow affects the onset of spontaneous dynamics of an inertialess active filament deforming in Stokes flow. The filament, clamped to a wall at one end, is subjected to a compressive "follower force" applied tangentially at its free end. By extending my earlier weakly nonlinear analysis of the shear-free case (J. Fluid Mech., 1007 A65, 2025), we derive a generalized amplitude equation governing the near-onset dynamics under weak shear. Analysis of the amplitude equation shows that, besides inducing a steady deflection, the shear damps the filament's intrinsic oscillations. This damping arises from a subtle nonlinear resonance between the shear and the intrinsic oscillations, scales quadratically with the shear rate, and is anisotropic---stronger in the flow direction than normal to it. Without shear, stable whirling states, where the filament tip traces a circular orbit in a plane parallel to the wall, and unstable planar-beating states are known to simultaneously emerge at a critical follower-force value, with circular whirling typically observed beyond this threshold. Shear breaks this degeneracy, driving a sequence of dynamical transitions: from circular to elliptical whirling, then to transverse beating (normal to the shear), and ultimately to steady deflection.

physics.flu-dyn↗

arXiv2026

Universal square-root-log scaling for slender-body end effects

The charge on a conducting cylinder becomes uniformly distributed at large aspect ratios, albeit very slowly and with nonuniformity persisting near the ends. We show that the charge density and field magnitude are enhanced near the ends by a factor scaling as the square-root of the logarithm of the aspect ratio. This scaling is obtained by locally resumming a perturbation-series solution to the integral equation of slender-body theory. The same scaling applies to a broad class of "truncated" slender bodies -- including cylinders and shapes tapered near the ends on the cross-sectional scale -- as well as other physical setups. We validate this scaling through boundary-element simulations for cylinders with flat and hemispherical caps, and demonstrate its applicability to diffusion, plasmonics and Stokes flow.

physics.app-ph↗

arXiv2026

Effective longitudinal slip over grooves encapsulated by a nearly inviscid lubricant

We calculate the effective slip length for a rectangularly grooved periodic surface encapsulated (i.e., fully wetted) by a lubricant fluid and subjected to exterior shear flow parallel to the grooves. Our focus is the limit of a nearly-inviscid lubricant, where the ratio $\mu$ of the lubricant viscosity to that of the exterior fluid is small. This limit is singular for an encapsulated surface, indicating a dominant lubricant-flow effect - a stark contrast to superhydrophobic surfaces where the role of the lubricant is typically negligible.

physics.flu-dyn↗

arXiv2025

Slip over liquid-infused gratings in the singular limit of a nearly inviscid lubricant

We consider shear-driven longitudinal flow of an exterior fluid over a periodic array of rectangular grooves filled with an immiscible interior fluid (the "lubricant"), the grooves being formed by infinitely thin ridges protruding from a flat substrate. The ratio $\lambda$ of the effective slip length to the semi-period is a function of the ratio $\mu$ of the interior to exterior viscosities and the ratio $h$ of the grooves depth to the semi-period. We focus on the limit $\mu\ll1$, which is singular for that geometry. We find that the viscous resistance to the imposed shear is dominated by a boundary layer of exponentially small extent about the ridge tips, resulting in the effective slip length scaling as $\mu^{-1/2}$ - not $\mu^{-1}$ as implied by intuitive arguments overlooking the tip contributions (and by proposed approximations in the literature). Analyzing that exponential region in conjunction with an integral force balance, we find the simple asymptotic approximation $\lambda\approx \mu^{-1/2}$; using conformal mappings, we also calculate the leading-order correction to that result, which introduces a dependence upon $h$. The ensuing asymptotic expansion breaks down for $h=O(\mu^{1/2})$, upon transitioning to a lubrication geometry. We accordingly conduct a companion asymptotic analysis in the distinguished limit of small $\mu$ and fixed $H=h/\mu^{1/2}$, which gives $\lambda\approx \mu^{-1/2}H/(1+H)$ as well as a closed-form leading-order correction to that approximation; the intuitive $\mu^{-1}$ scaling is accordingly only relevant to the regime $H\ll1$ corresponding to extremely shallow grooves. We demonstrate excellent agreement between our predictions and numerical solutions constructed using a boundary-integral formulation.

physics.flu-dyn↗

arXiv2025

Bistability and charge-density blowup in the onset of drop Quincke rotation

Particles in a sufficiently strong electric field spontaneously rotate, provided that charge relaxation is slower in the particle than in the suspending fluid. It has long been known that drops also exhibit such "Quincke rotation," with the electrohydrodynamic flow induced by electrical shear stresses at the interface leading to an increased critical field. However, the hysteretic onset of this instability, observed for sufficiently low-viscosity drops, has so far eluded theoretical understanding -- including simulations that have struggled in this regime owing to charge-density-steepening effects driven by surface convection. Here, we conduct a numerical study of the leaky-dielectric model in a simplified two-dimensional setting involving a circular drop, considering arbitrary viscosity ratios and field strengths. As the viscosity of the drop is decreased relative to the suspending fluid, the pitchfork bifurcation marking the onset of drop rotation is found to transition from supercritical to subcritical, giving rise to a field-strength interval of bistability. In this subcritical regime, the critical field is always large enough that, at the bifurcation, the symmetric base-state solution exhibits equatorial charge-density blowup singularities of the type recently described by Peng et al. (Phys. Rev. Fluids, 9 083701, 2024). As the rotation speed increases along the initially unstable solution branch from the bifurcation, the singularities gradually shift from the equator and ultimately disperse once the rotational component of the flow is strong enough to eliminate the surface stagnation points.

physics.flu-dyn↗

arXiv2024

Giant superhydrophobic slip of shear-thinning liquids

We theoretically illustrate how complex fluids flowing over superhydrophobic surfaces may exhibit giant flow enhancements in the double limit of small solid fractions ($ε\ll1$) and strong shear thinning ($β\ll1$, $β$ being the ratio of the viscosity at infinite shear rate to that at zero shear rate). Considering a Carreau liquid within the canonical scenario of longitudinal shear-driven flow over a grooved superhydrophobic surface, we show that, as $β$ is decreased, the scaling of the effective slip length at small solid fractions is enhanced from the logarithmic scaling $\ln(1/ε)$ for Newtonian fluids to the algebraic scaling $1/ε^{\frac{1-n}{n}}$, attained for $β=\mathcal{O}(ε^{\frac{1-n}{n}})$, $n\in(0,1)$ being the exponent in the Carreau model. We illuminate this scaling enhancement and the geometric-rheological mechanism underlying it through asymptotic arguments and numerical simulations.

physics.flu-dyn↗

arXiv2024

Onset of spontaneous beating and whirling in the follower force model of an active filament

We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at the other. Clarke, Hwang and Keaveny (Phys. Rev. Fluids, to appear) have recently conducted a thorough investigation of this model using methods of computational dynamical systems; inter alia, they show that the filament first loses stability via a supercritical double-Hopf bifurcation, with periodic 'planar-beating' states (unstable) and 'whirling' states (stable) simultaneously emerging at the critical follower-force value. We complement their numerical study by carrying out a weakly nonlinear analysis close to this unconventional bifurcation, using the method of multiple scales. The main outcome is an 'amplitude equation' governing the slow modulation of small-magnitude oscillations of the filament in that regime. Analysis of this reduced-order model provides insights into the onset of spontaneous dynamics, including the creation of the nonlinear whirling states from particular superpositions of linear planar-beating modes as well as the selection of whirling over planar beating in three-dimensional scenarios.

physics.flu-dyn↗

arXiv2024

Equatorial blowup and polar caps in drop electrohydrodynamics

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number $\mathrm{Re}_E$. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four -- $\mathrm{Re}_E$ and the conductivity, permittivity and viscosity ratios -- to two: a modified electric Reynolds number $\widetilde{\mathrm{Re}}$ and a charging parameter $\varpi$. In the case $\varpi<0$, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical $\widetilde{\mathrm{Re}}$ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the $-1/3$ power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging -- annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime $\widetilde{\mathrm{Re}}\gg1$, far beyond the blowup threshold. In the case $\varpi>0$, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large $\widetilde{\mathrm{Re}}$ of stagnant, perfectly conducting surface-charge caps about the drop poles.

physics.flu-dyn↗

arXiv2024

Spontaneous locomotion of a symmetric squirmer

The squirmer is a popular model to analyse the fluid mechanics of a self-propelled object, such as a micro-organism. We demonstrate that some fore-aft symmetric squirmers can spontaneously self-propel above a critical Reynolds number. Specifically, we numerically study the effects of inertia on spherical squirmers characterised by an axially and fore-aft symmetric `quadrupolar' distribution of surface-slip velocity; under creeping-flow conditions, such squirmers generate a pure stresslet flow, the stresslet sign classifying the squirmer as either a `pusher' or `puller.' Assuming axial symmetry, and over the examined range of the Reynolds number $Re$ (defined based upon the magnitude of the quadrupolar squirming), we find that spontaneous symmetry breaking occurs in the pusher case above $Re \approx 14.3$, with steady swimming emerging from that threshold consistently with a supercritical pitchfork bifurcation and with the swimming speed growing monotonically with $Re$.

physics.flu-dyn↗

arXiv2023

Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. II. History-dependent motion

We develop a reduced model for the slow unsteady dynamics of an isotropic chemically active particle near the threshold for spontaneous motion. Building on the steady theory developed in part I of this series, we match a weakly nonlinear expansion valid on the particle scale with a leading-order approximation in a larger-scale unsteady remote region, where the particle acts as a moving point source of diffusing concentration. The resulting amplitude equation for the velocity of the particle includes a term representing the interaction of the particle with its own concentration wake in the remote region, which can be expressed as a time integral over the history of the particle motion, allowing efficient simulation and theoretical analysis of fully three-dimensional unsteady problems. To illustrate how to use the model, we study the effects of a weak force acting on the particle, including the stability of the steady states and how the velocity vector realigns towards the stable one, neither of which previous axisymmetric and steady models were able to capture. This unsteady formulation could also be applied to most of the other perturbation scenarios studied in part I as well as the dynamics of interacting active particles.

cond-mat.soft↗

arXiv2022

Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. I. Adjoint method

In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude equation governing the particle's velocity, first assuming the canonical model in the literature of an isotropic chemically active particle and then considering general perturbations about that model. As in previous works, the amplitude equation is obtained from a solvability condition on the inhomogeneous problem at second order of a particle-scale weakly nonlinear expansion, the formulation of that problem involving asymptotic matching with a leading-order solution in a remote region where advection and diffusion are balanced. We develop a generalised solvability condition based on a Fredholm Alternative argument, which entails identifying the adjoint linear operator at the threshold and calculating its kernel. This circumvents the apparent need in earlier theories to solve the second-order inhomogeneous problem, resulting in considerable simplification and adding insight by making it possible to treat a wide range of perturbation scenarios on a common basis. To illustrate our approach, we derive and solve amplitude equations for a number of perturbation scenarios (external force and torque fields, non-uniform surface properties, first-order surface kinetics and bulk absorption), demonstrating that sufficiently near the threshold weak perturbations can appreciably modify and enrich the landscape of steady solutions.

physics.flu-dyn↗

arXiv2022

Plasmonic resonances of slender nanometallic rings

We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem governing the geometric (material- and frequency-independent) modes of a given ring structure to a 1D-periodic integro-differential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. Second, we obtain closed-form solutions to the reduced eigenvalue problem for azimuthally invariant rings (including torus-shaped rings but also allowing for non-circular cross-sectional shapes), as well as coaxial dimers and chains of such rings. For more general geometries, involving azimuthally non-uniform rings and non-coaxial structures, we solve the reduced eigenvalue problem using a semi-analytical scheme based on Fourier expansions of the reduced eigenfunctions. Third, we used the asymptotically approximated modes, in conjunction with the quasi-static spectral theory of plasmonic resonance, to study and interpret the frequency response of a wide range of nanometallic slender-ring structures under plane-wave illumination.

physics.optics↗

arXiv2022

Absorption characteristics of large acoustic metasurfaces

Metasurfaces formed of arrays of subwavelength resonators are often tuned to 'critically couple' with incident radiation, so that at resonance dissipative and radiative damping are balanced and absorption is maximised. Such design criteria are typically derived assuming an infinite metasurface, whereas the absorption characteristics of finite metasurfaces, even very large ones, can be markedly different in certain frequency intervals. This is due to the excitation of surface waves, intrinsic to resonant metasurfaces, and especially meta-resonances, namely collective resonances where the surface waves form standing-wave patterns over the planar metasurface domain. We illustrate this issue using a detailed model of a Helmholtz-type acoustic metasurface formed of cavity-neck pairs embedded into a rigid substrate, with geometric and dissipation effects included from first principles (R. Brandão and O. Schnitzer, Wave Motion, 97 102583, 2020).

physics.app-ph↗

arXiv2022

Acoustics of a partially partitioned narrow slit connected to a half-plane: case study for exponential quasi-bound states in the continuum and their resonant excitation

Localised wave oscillations in an open system that do not decay or grow in time, despite their frequency lying within a continuous spectrum of radiation modes carrying energy to or from infinity, are known as bound states in the continuum (BIC). Small perturbations from the typically delicate conditions for BIC almost always result in the waves weakly coupling with the radiation modes, leading to leaky states called quasi-BIC that have a large quality factor. We study the asymptotic nature of this weak coupling in the case of acoustic waves interacting with a rigid substrate featuring a partially partitioned slit -- a setup that supports quasi-BIC that exponentially approach BIC as the slit is made increasingly narrow. In that limit, we use the method of matched asymptotic expansions in conjunction with reciprocal relations to study those quasi-BIC and their resonant excitation. In particular, we derive a leading approximation for the exponentially small imaginary part of each wavenumber eigenvalue (inversely proportional to quality factor), which is beyond all orders of the expansion for the wavenumber eigenvalue itself. Furthermore, we derive a leading approximation for the exponentially large amplitudes of the states in the case where they are resonantly excited by a plane wave at oblique incidence. These resonances occur in exponentially narrow wavenumber intervals and are physically manifested in cylindrical-dipolar waves emanating from the slit aperture and exponentially large field enhancements inside the slit. The asymptotic approximations are validated against numerical calculations.

physics.flu-dyn↗

arXiv2022

Leidenfrost levitation of a spherical particle above a liquid bath: evolution of the vapour-film morphology with particle size

We consider a spherical particle levitating above a liquid bath owing to the Leidenfrost effect, where the vapour of either the bath or sphere forms an insulating film whose pressure supports the sphere's weight. Starting from a reduced formulation based on a lubrication-type approximation, we use matched asymptotics to describe the morphology of the vapour film assuming that the sphere is small relative to the capillary length (small Bond number) and that the densities of the bath and sphere are comparable. We find that this regime is comprised of two formally infinite sequences of distinguished limits which meet at an accumulation point, the limits being defined by the smallness of an intrinsic evaporation number relative to the Bond number. These sequences of limits reveal a surprisingly intricate evolution of the film morphology with increasing sphere size, starting from the formation of a neck-bubble morphology typical of a Leidenfrost drop levitating above a flat solid substrate and ultimately reaching a uniform-film morphology similar to that in the case of a large liquid drop levitating above a liquid bath.

physics.flu-dyn↗

arXiv2020

Spontaneous dynamics of two-dimensional Leidenfrost wheels

Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics (A. Bouillant et al., Nature Physics, 14 1188-1192, 2018). Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface, which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: $R_1$ for a free drop and $R_2>R_1$ for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical-pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration $αg$, where $α$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $α$ exhibits a maximum with respect to the drop radius, at a radius increasing with the temperature difference between the surface and the drop.

physics.flu-dyn↗

arXiv2020

Acoustic impedance of a cylindrical orifice

We use matched asymptotics to derive analytical formulae for the acoustic impedance of a subwavelength orifice consisting of a cylindrical perforation in a rigid plate. In the inviscid case, an end correction to the length of the orifice due to Rayleigh is shown to constitute an exponentially accurate approximation in the limit where the aspect ratio of the orifice is large; in the opposite limit, we derive an algebraically accurate correction, depending upon the logarithm of the aspect ratio, to the impedance of a circular aperture in a zero-thickness screen. Viscous effects are considered in the limit of thin Stokes boundary layers, where a boundary layer analysis in conjunction with a reciprocity argument provides the perturbation to the impedance as a quadrature of the basic inviscid flow. We show that for large aspect ratios the latter perturbation can be captured with exponential accuracy by introducing a second end correction whose value is calculated to be in between two guesses commonly used in the literature; we also derive an algebraically accurate approximation in the small-aspect-ratio limit. The viscous theory reveals that the resistance exhibits a minimum as a function of aspect ratio, with the orifice radius held fixed. It is evident that the resistance grows in the long-aspect-ratio limit; in the opposite limit, resistance is amplified owing to the large velocities close to the sharp edge of the orifice. The latter amplification arrests only when the the plate is as thin as the Stokes boundary layer. The analytical approximations derived in this paper could be used to improve circuit modelling of resonating acoustic devices.

physics.flu-dyn↗

arXiv2020

Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits

We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of Holley & Schnitzer (Wave Motion, 91 102381, 2019), who considered a single-slit configuration assuming an idealised formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic-acoustic analogy is preserved up to a single physics-dependent parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.

physics.flu-dyn↗