arXiv subjects

Ehud Yariv

Publications and source records attributed to Ehud Yariv.

6 recordsLinked to original sources

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↗

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↗

arXiv2023

Phoretic swimming with bulk absorption

We consider phoretic self-propulsion of a chemically active colloid where solute is consumed at both the colloid boundary and within the bulk solution. Assuming first-order kinetics, the dimensionless transport problem is governed by the surface Damköhler number ${\mathcal{S}}$ and the bulk Damköhler number ${\mathcal B}$. The dimensionless colloid velocity $U$, normalized by a self-phoretic scale, is a nonlinear function of these two parameters. We identify two scenarios where these numbers are linked. When the controlling physical parameter is colloid size, ${\mathcal{S}}$ is proportional to ${\mathcal B}^{1/2}$; when the controlling parameter is solute diffusivity, ${\mathcal{S}}$ is proportional to ${\mathcal B}$. In the limit of small Damköhler numbers, $U$ adopts the same asymptotic limit in both scenarios, proportional to ${\mathcal{S}}$. In the limit of large Damköhler numbers, the deviations of solute concentration from the equilibrium value are restricted to a narrow layer about the active portion of the colloid boundary. The asymptotic predictions of the associated boundary-layer problem are corroborated by an eigenfunction solution of the exact problem. The boundary-layer structure breaks down near the transition between the active and inactive portions of the boundary. The transport problem in that local region partially resembles the classical Sommerfeld problem of wave diffraction from an edge.

physics.flu-dyn↗

arXiv2015

Phoretic self-propulsion at large Peclet numbers

We analyse the self-diffusiophoresis of a spherical particle animated by a nonuniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux, and one where this flux is governed by first-order kinetics with a specified distribution of rate constant. We employ a macroscale model where the short-range interaction of the solute with the particle boundary is represented by an effective slip condition. The solute transport is governed by an advection-diffusion equation. We focus upon the singular limit of large Péclet numbers, $Pe\gg 1$. In the fixed-flux model, the excess-solute concentration is confined to a narrow boundary layer. The scaling pertinent to that limit allows to decouple the problem governing the solute concentration from the flow field. The resulting nonlinear boundary-layer problem is handled using a transformation to stream-function coordinates and a subsequent application of Fourier transforms, and is thereby reduced to a nonlinear integral equation governing the interfacial concentration. Its solution provides the requisite approximation for the particle velocity, which scales as $Pe^{-1/3}$. In the fixed-rate model, large Péclet numbers may be realized in different limit processes. We consider the case of large swimmers or strong reaction, where the Damköhler number $Da$ is large as well, scaling as $Pe$. In that double limit, where no boundary layer is formed, we obtain a closed-form approximation for the particle velocity, expressed as a nonlinear functional of the rate-constant distribution; this velocity scales as $Pe^{-2}$. Both the fixed-flux and fixed-rate asymptotic predictions agree with the numerical values provided by computational solutions of the nonlinear transport problem.

physics.flu-dyn↗

arXiv2004

Symmetry Breaking in Induced-Charge Electrophoresis

The electrophoretic motion of a conducting particle, driven by an induced charge mechanism, is analyzed. The dependence of the motion upon particle shape is embodied in four tensorial coefficients that relate the particle velocities to the externally-applied electric field. Several families of particle shapes, whose members are unaffected by the applied field, are identified via use of symmetry arguments. Other particles translate and/or rotate in response to the imposed field, even if their net electric charge vanishes. The coefficients are represented as surface integrals of the electric potential over the particle boundary, thereby eliminating the need to solve the flow field.

physics.flu-dyn↗