Publications
67 results found
Schnitzer O, 2017, Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: The small-solid-fraction singularity, Journal of Fluid Mechanics, Vol: 820, Pages: 580-603, ISSN: 1469-7645
We study the effective slip length for unidirectional flow over a superhydrophobic mattress of bubbles in the small-solid-fraction limit . Using scaling arguments and utilising an ideal-flow analogy we elucidate the singularity of the slip length as : relative to the periodicity it scales as for protrusion angles and as for . We continue with a detailed asymptotic analysis using the method of matched asymptotic expansions, where ‘inner’ solutions valid close to the solid segments are matched with ‘outer’ solutions valid on the scale of the periodicity, where the bubbles protruding from the solid grooves appear to touch. The analysis yields asymptotic expansions for the effective slip length in each of the protrusion-angle regimes. These expansions overlap for intermediate protrusion angles, which allows us to form a uniformly valid approximation for arbitrary protrusion angles . We thereby explicitly describe the transition with increasing protrusion angle from a logarithmic to an algebraic small-solid-fraction slip-length singularity.
Maling B, Schnitzer O, Craster RV, 2017, Radiation from structured-ring resonators, SIAM Journal on Applied Mathematics, ISSN: 0036-1399
We investigate the scalar-wave resonances of systems composed of identicalNeumann-type inclusions arranged periodically around a circular ring. Drawingon natural similarities with the undamped Rayleigh-Bloch waves supported byinfinite linear arrays, we deduce asymptotically the exponentially smallradiative damping in the limit where the ring radius is large relative to theperiodicity. In our asymptotic approach, locally linear Rayleigh-Bloch wavesthat attenuate exponentially away from the ring are matched to a ring-scaleWKB-type wave field. The latter provides a descriptive physical picture of howthe mode energy is transferred via tunnelling to a circularevanescent-to-propagating transition region a finite distance away from thering, from where radiative grazing rays emanate to the far field. Excluding thezeroth-order standing-wave modes, the position of the transition circlebifurcates with respect to clockwise and anti-clockwise contributions,resulting in striking spiral wavefronts.
Schnitzer O, 2017, Waves in Slowly Varying Band-Gap Media, SIAM Journal on Applied Mathematics, Vol: 77, Pages: 1516-1535, ISSN: 0036-1399
Schnitzer O, 2016, Singular effective slip length for longitudinal flow over a dense bubble mattress, Physical Review Fluids, Vol: 1, ISSN: 2469-990X
We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid,with trapped shear-free bubbles protruding between the no-slip ridges at a π/2 contact angle.Specifically, we carry out a singular-perturbation analysis in the limit ǫ ≪ 1 where the bubbles areclosely spaced, finding the effective slip length (normalised by the bubble radius) for longitudinalflow along the the ridges as π/√2ǫ − (12/π) ln 2 + (13π/24)√2ǫ + o(√ǫ), the small parameter ǫbeing the planform solid fraction. The square-root divergence highlights the strong hydrophobiccharacter of this configuration; this leading singular term (along with the third term) follows froma local lubrication-like analysis of the gap regions between the bubbles, together with generalmatching considerations and a global conservation relation. The O(1) constant term is found bymatching with a leading-order solution in the “outer” region, where the bubbles appear to betouching. We find excellent agreement between our slip-length formula and a numerical schemerecently derived using a “unified-transform” method (D. Crowdy, IMA J. Appl. Math., 80 1902,2015). The comparison demonstrates that our asymptotic formula, together with the diametric“dilute-limit” approximation (D. Crowdy, J. Fluid Mech., 791 R7, 2016), provides an elementaryanalytical description for essentially arbitrary no-slip fractions.
Schnitzer O, Giannini V, Maier SA, et al., 2016, Surface-plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol: 472, ISSN: 1364-5021
According to the hydrodynamic Drude model,surface-plasmon resonances of metallic nanostructuresblueshift owing to the nonlocal response of the metal’selectron gas. The screening length characterisingthe nonlocal effect is often small relative to theoverall dimensions of the metallic structure, whichenables us to derive a coarse-grained nonlocaldescription using matched asymptotic expansions; aperturbation theory for the blueshifts of arbitraryshaped nanometallic structures is then developed.The effect of nonlocality is not always a perturbationand we present a detailed analysis of the “bonding”modes of a dimer of nearly touching nanowires wherethe leading-order eigenfrequencies and eigenmodedistributions are shown to be a renormalisation ofthose predicted assuming a local metal permittivity.
Schnitzer O, Giannini V, Craster RV, et al., 2016, Asymptotics of surface-plasmon redshift saturation at subnanometric separations, Physical Review B, Vol: 93, ISSN: 2469-9950
Many promising nanophotonics endeavors hinge upon the unique plasmonic properties of nanometallic structures with narrow nonmetallic gaps, which support superconcentrated bonding modes that singularly redshift with decreasing separations. In this Rapid Communication, we present a descriptive physical picture, complemented by elementary asymptotic formulas, of a nonlocal mechanism for plasmon redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalization of the corresponding local ones. Specifically, the renormalization furnishes an asymptotic plasmon-frequency lower bound that scales with the 1/4 power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.
Schnitzer O, Yariv E, 2016, Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion, Journal of Fluid Mechanics, Vol: 786, Pages: 84-109, ISSN: 1469-7645
We employ the moderate-P´eclet-number macroscale model developed in part 2 of this sequence(Schnitzer, Frankel & Yariv, J. Fluid Mech., vol. 704, 2012, pp. 109–136) towardsthe calculation of electroviscous forces on charged solid particles, engendered by an imposedrelative motion between these particles and the electrolyte solution in which theyare suspended. In particular, we are interested in the kinematic irreversibility of theseforces, stemming from the diffusio-osmotic slip which accompanies the salt-concentrationpolarisation induced by that imposed motion. We illustrate the electroviscous irreversibilityusing two prototypic problems, one involving side-by-side sedimentation of two sphericalparticles, and the other involving a force-free spherical particle suspended in the vicinityof a planar wall and exposed to a simple shear flow. We focus upon the pertinent limitof near-contact configurations, where use of lubrication approximations provides closedformexpressions for the leading-order lateral repulsion. In this approximation schemethe need to solve the advection–diffusion equation governing the salt-concentration polarisationis circumvented.
Schnitzer O, 2015, Singular perturbations approach to localized surface-plasmon resonance: Nearly touching metal nanospheres, Physical Review. B, Condensed Matter, Vol: 92, ISSN: 0163-1829
Metallic nano-structures characterised by multiple geometric length scales support low-frequencysurface-plasmon modes, which enable strong light localisation and field enhancement. We suggestto study such configurations using singular perturbation methods, and demonstrate the efficacyof this approach by considering, in the quasi-static limit, a pair of nearly touching metallic nanospheressubjected to an incident electromagnetic wave polarised with the electric field along the lineof sphere centres. Rather than attempting an exact analytical solution, we construct the pertinent(longitudinal) eigen-modes by matching relatively simple asymptotic expansions valid in overlappingspatial domains. We thereby arrive at an effective boundary eigenvalue problem in a half-spacerepresenting the metal region in the vicinity of the gap. Coupling with the gap field gives rise to amixed-type boundary condition with varying coefficients, whereas coupling with the particle-scalefield enters through an integral eigenvalue selection rule involving the electrostatic capacitance ofthe configuration. By solving the reduced problem we obtain accurate closed-form expressions forthe resonance values of the metal dielectric function. Furthermore, together with an energy-likeintegral relation, the latter eigen-solutions yield also closed-form approximations for the induceddipolemoment and gap-field enhancement under resonance. We demonstrate agreement between theasymptotic formulae and a semi-numerical computation. The analysis, underpinned by asymptoticscaling arguments, elucidates how metal polarisation together with geometrical confinement enablesa strong plasmon-frequency redshift and amplified near-field at resonance.
Schnitzer O, Yariv EY, 2015, The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description, Journal of Fluid Mechanics, Vol: 773, Pages: 1-33, ISSN: 0022-1120
While the Taylor–Melcher electrohydrodynamic model entails ionic charge carriers, it addresses neither ionic transport within the liquids nor the formation of diffuse space-charge layers about their common interface. Moreover, as this model is hinged upon the presence of non-zero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis published by Baygents & Saville (Third International Colloquium on Drops and Bubbles, AIP Conference Proceedings, vol. 7, 1989, American Institute of Physics, pp. 7–17) we systematically derive here the macroscale description appropriate for leaky dielectric liquids, starting from the primitive electrokinetic equations and addressing the double limit of thin space-charge layers and strong fields. This derivation is accomplished through the use of matched asymptotic expansions between the narrow space-charge layers adjacent to the interface and the electro-neutral bulk domains, which are homogenized by the strong ionic advection. Electrokinetic transport within the electrical ‘triple layer’ comprising the genuine interface and the adjacent space-charge layers is embodied in effective boundary conditions; these conditions, together with the simplified transport within the bulk domains, constitute the requisite macroscale description. This description essentially coincides with the familiar equations of Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). A key quantity in our macroscale description is the ‘apparent’ surface-charge density, provided by the transversely integrated triple-layer microscale charge. At leading order, this density vanishes due to the expected Debye-layer screening; its asymptotic correction provides the ‘interfacial’ surface-charge density appearing in the Taylor–Melcher model. Our unified electrohydrodynamic treatment provides a
Schnitzer O, Morozov M, 2015, A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations, Journal of Chemical Physics, Vol: 142, ISSN: 1089-7690
Schnitzer O, 2015, Slender-body approximations for advection-diffusion problems, JOURNAL OF FLUID MECHANICS, Vol: 768, ISSN: 0022-1120
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- Citations: 6
Schnitzer, Yariv, 2015, Osmotic self-propulsion of slender particles, Physics of Fluids, Vol: 27, ISSN: 1089-7666
Schnitzer O, 2015, Ray-theory approach to electrical-double-layer interactions, PHYSICAL REVIEW E, Vol: 91, ISSN: 1539-3755
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- Citations: 2
Schnitzer O, Yariv E, 2014, Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis, PHYSICS OF FLUIDS, Vol: 26, ISSN: 1070-6631
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- Citations: 37
Yariv E, Schnitzer O, 2014, Ratcheting of Brownian swimmers in periodically corrugated channels: A reduced Fokker-Planck approach, PHYSICAL REVIEW E, Vol: 90, ISSN: 1539-3755
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- Citations: 23
Schnitzer O, Frankel I, Yariv E, 2014, Electrophoresis of bubbles, JOURNAL OF FLUID MECHANICS, Vol: 753, Pages: 49-79, ISSN: 0022-1120
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- Citations: 29
Schnitzer O, 2014, Fast penetration of megagauss fields into metallic conductors, PHYSICS OF PLASMAS, Vol: 21, ISSN: 1070-664X
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- Citations: 12
Schnitzer O, Yariv E, 2014, Strong electro-osmotic flows about dielectric surfaces of zero surface charge, PHYSICAL REVIEW E, Vol: 89, ISSN: 1539-3755
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- Citations: 19
Schnitzer O, Yariv E, 2014, Nonlinear oscillations in an electrolyte solution under ac voltage, PHYSICAL REVIEW E, Vol: 89, ISSN: 1539-3755
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- Citations: 16
Schnitzer O, Frankel I, Yariv E, 2013, Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers, JOURNAL OF FLUID MECHANICS, Vol: 734, ISSN: 0022-1120
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- Citations: 2
Feicht SE, Schnitzer O, Khair AS, 2013, Asymptotic analysis of double-carrier, space-charge-limited transport in organic light-emitting diodes, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 469, ISSN: 1364-5021
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- Citations: 2
Schnitzer O, Yariv E, 2013, Electric conductance of highly selective nanochannels, PHYSICAL REVIEW E, Vol: 87, ISSN: 1539-3755
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- Citations: 11
Schnitzer O, Yariv E, 2013, Nonlinear electrokinetic flow about a polarized conducting drop (vol 87, 041002, 2013), PHYSICAL REVIEW E, Vol: 87, ISSN: 1539-3755
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- Citations: 3
Schnitzer O, Zeyde R, Yavneh I, et al., 2013, Weakly nonlinear electrophoresis of a highly charged colloidal particle, PHYSICS OF FLUIDS, Vol: 25, ISSN: 1070-6631
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- Citations: 45
Schnitzer O, Yariv E, 2013, Nonlinear electrokinetic flow about a polarized conducting drop, PHYSICAL REVIEW E, Vol: 87, ISSN: 1539-3755
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- Citations: 10
Schnitzer O, Yariv E, 2013, Comment on "On the flow field about an electrophoretic particle" [Phys. Fluids 24, 102001 (2012)], PHYSICS OF FLUIDS, Vol: 25, ISSN: 1070-6631
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- Citations: 2
Yariv E, Schnitzer O, 2013, The electrophoretic mobility of rod-like particles, JOURNAL OF FLUID MECHANICS, Vol: 719, ISSN: 0022-1120
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- Citations: 5
Yariv E, Schnitzer O, 2013, Electrokinetic particle-electrode interactions at high frequencies, PHYSICAL REVIEW E, Vol: 87, ISSN: 1539-3755
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- Citations: 7
Schnitzer O, Frankel I, Yariv E, 2013, Electrokinetic flows about conducting drops, Journal of Fluid Mechanics, Vol: 722, Pages: 394-423, ISSN: 0022-1120
We consider electrokinetic flows about a freely suspended liquid drop, deriving a macroscale description in the thin-double-layer limit where the ratio δ between Debye width and drop size is asymptotically small. In this description, the electrokinetic transport occurring within the diffuse part of the double layer (the 'Debye layer') is represented by effective boundary conditions governing the pertinent fields in the electro-neutral bulk, wherein the generally non-uniform distribution of ζ, the dimensionless zeta potential, is a priori unknown. We focus upon highly conducting drops. Since the tangential electric field vanishes at the drop surface, the viscous stress associated with Debye-scale shear, driven by Coulomb body forces, cannot be balanced locally by Maxwell stresses. The requirement of microscale stress continuity therefore brings about a unique velocity scaling, where the standard electrokinetic scale is amplified by a δ-1 factor. This reflects a transition from slip-driven electro-osmotic flows to shear-induced motion. The macroscale boundary conditions display distinct features reflecting this unique scaling. The effective shear-continuity condition introduces a Lippmann-type stress jump, appearing as a product of the local charge density and electric field. This term, representing the excess Debye-layer shear, follows here from a systematic coarse-graining procedure starting from the exact microscale description, rather than from thermodynamic considerations. The Neumann condition governing the bulk electric field is inhomogeneous, representing asymptotic matching with transverse ionic fluxes emanating from the Debye layer; these fluxes, in turn, are associated with non-uniform tangential 'surface' currents within this layer. Their appearance at leading order is a manifestation of dominant advection associated with the large velocity scale. For weak fields, the linearized macroscale equations admit an analytic solution, yielding a c
Schnitzer O, Yariv E, 2012, Induced-charge electro-osmosis beyond weak fields, PHYSICAL REVIEW E, Vol: 86, ISSN: 1539-3755
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- Citations: 46
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