Healing Length Research Articles

Roughness-induced fluid interface fluctuations due to polar and apolar interactions

We investigate substrate roughness-induced fluctuations on liquid films in the presence of polar (exponential) and apolar (van der Waals) interactions in the complete wetting regime. The liquid/vapor interface roughness amplitude ${\ensuremath{\sigma}}_{w}$ increases rapidly with film thickness \ensuremath{\varepsilon} above a critical thickness ${\ensuremath{\varepsilon}}_{c}$ for which the film is stable (or it does not rupture due to presence of polar interactions), and it reaches a maximum at a thickness ${\ensuremath{\varepsilon}}_{m}$ slightly larger than ${\ensuremath{\varepsilon}}_{c}$ if polar and apolar components are of comparable strength and for small polar potential ranges. As the strength of the polar interaction decreases with respect to the apolar, behavior characteristic of that of apolar interactions within the Derjaguin approximation is recovered for moderate film thicknesses $(\ensuremath{\varepsilon}>{\ensuremath{\varepsilon}}_{m});$ ${\ensuremath{\sigma}}_{w}\ensuremath{\propto}{\ensuremath{\zeta}}^{\ensuremath{-}2}$ with \ensuremath{\zeta} the healing length.

Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a `penetration depth' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.

Scanning tunneling microscope studies of the superconductor proximity effect

Scanning tunneling microscopy and spectroscopy are employed in studies of the proximity effect between normal metals and superconductors. The experimental configuration is unique, in that the tunneling current flows in parallel to the interfaces between different materials. The samples are superconducting wires consisting of ordered arrays of submicron diameter normal-metal filaments, either Cu or Ni (a ferromagnet), embedded in a NbTi superconducting matrix. By taking topographic images simultaneously with current-voltage curves, we map with nanometer resolution the local quasiparticle density of states. Two main issues are addressed in this work. The first is the spatial variation of the superconductor gap as a function of distance from the boundary between the normal-metal and the superconductor. We find that the healing length of the gap on the superconducting side is much larger than the superconductor coherence length. The second is the observation of pronounced Tomasch oscillations and bound states arising from multiple Andreev reflections of quasiparticles propagating in the plane perpendicular to the tunneling current.

Fluid interface fluctuations within the generalized Derjaguin approximation

The fluctuation properties of fluid interfaces bounded by rough surfaces are investigated within a linear generalization of the Derjaguin approximation. In the thick-film regime, the interface roughness amplitude is lower in magnitude from that obtained in the Derjaguin approximation. Nevertheless, for large healing lengths z the power-law asymptotic behavior s w;z 22 , which is observed in the Derjaguin approximation, is still preserved. Moreover, the rms local interface slope r is shown to attain small values for film thicknesses larger than the substrate roughness amplitude and to follow an asymptotic power-law behavior r;z 22 for large z. @S0163-1829~97!07436-5# Wetting phenomena of fluids on solid substrates have been an important topic of applied and fundamental research for more than a century. However, the understanding of the complexity of these phenomena is still incomplete, since wetting is highly sensitive to roughness and chemical contaminants of the solid substrates. 1‐4 In general, these types of surface disorder can have a dramatic influence on interfacial processes which are of experimental and technological interest. Various theoretical treatments 2‐4 of the influence of surface roughness on the wetting properties of liquids have been performed within the so-called Derjaguin approximation. 5 In fact, this approximation accounts for replacing the local disjoining pressure P d by that of a uniform film of thickness h(r)2z(r) @z(r) and h(r) are, respectively, the substrate and liquid-vapor surface/interface profile functions# for small substrate roughness amplitudes, and then linearize the disjoining pressure around the average film thickness « that would exist on a flat surface. 3 The average thickness « is given by the relation Dm5P d(«), with Dm the chemical potential difference between the liquid and vapor phases, and the liquid-vapor interface fluctuations are described by the

Fluctuation properties of interfaces and membranes bounded by self-affine surfaces

In this work we study fluctuation properties of fluid interfaces/membranes bounded by a rough self-affine surface. We find that the fractal character of the substrate affects the interface/membrane roughness significantly for healing lengths S\ensuremath{\xi} is the substrate roughness correlation length. However, for healing lengths S\ensuremath{\gg}:\ensuremath{\xi} the rms roughness scales as a power law \ensuremath{\propto}${\mathrm{S}}^{\mathrm{\ensuremath{-}}\mathrm{c}}$ with the exponent c characteristic of the system. Moreover, thermally induced roughness can dominate that induced from the substrate for large healing lengths S (\ensuremath{\gg}:\ensuremath{\xi}) and/or system temperatures T>${\mathrm{T}}_{\mathrm{sc}}$.

Absolute and convective instabilities and noise-sustained structures in the Couette-Taylor system with an axial flow.

A detailed study of the Couette-Taylor system with axial flow in the range of Reynolds number Re up to 4.5, which is characterized by the propagating Taylor-vortices (PTV's) state, is presented. Two methods to measure the convective instability line are described. Comparative studies of the PTV's in the absolutely and convectively unstable regions are given. It was found that at Re1 the PTV's appear first at the outlet at the absolute instability transition. At Re>1 the PTV's are also sustained in the convectively unstable region, but the properties of the PTV's in the absolutely and convectively unstable regions differ distinctively. In both regions the PTV's are characterized by the existence of an interface separating the pattern state from the Couette-Poiseuille flow. The interface is stationary in the absolutely unstable region and fluctuates in the convectively unstable region. The distance from the inlet to the interface changes as both control parameters \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} and Re are varied, where \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} is the distance from the convective line. This dependence is, however, different in both regions. In the absolutely unstable region the healing length is scaled with the PTV's group velocity at all values of \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{} and Re, and diverges at the absolute instability transition line. In the convectively unstable region the healing length does not obey the general scaling but is about inversely proportional to \ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{}. The most distinctive difference in the PTV's behavior in the two regions is a different sensitivity to noise.A time-dependent spatial profile of the PTV's leads to a broadband power spectrum of the velocity in the convectively unstable region near the outlet. The PTV's velocity power spectrum in the absolutely unstable region is, on the other hand, noise-free. The different sensitivity to noise was used as an experimental criterion to locate the absolute instability line for Re>1. The wave-number selection is also found to be different in both regions. As a result, we concluded that the PTV's in the convectively unstable region are noise-sustained structures (NSS's) which were recently considered theoretically and observed in numerical simulations. The selective spatial amplification of an external noise and the characteristic dependence of the healing length on the control parameters and on the aspect ratio confirm our suggestion that the mechanism of NSS generation is a selective spatial amplification of a permanent noise at the inlet. An interaction of the noise with the NSS's leads to a noise modulation of the PTV's velocity.

Analysis and interpretation of critical current experiments for bismuth-based high-temperature superconductors made by powder-in-tube processing

Abstract Current distribution and voltage drop were analyzed for a composite conductor composed of a layer of bismuth-based high-temperature superconductor (BSCCO) bonded to a silver substrate. The analytical model assumes that the silver strip is continuous, and the superconductor is periodically discontinuous. The resistance at the discontinuities in the superconductor is assumed to be much greater than that of the silver substrate. The results show that if the BSCCO is superconducting, the solution depends on only one dimensionless parameter, λ s L 2 , which is equal to the square root of the ratio of the resistance of the silver to the interfacial resistance between the silver and the BSCCO. When λ s L 2 is very high ( > 100), most of the current returns to the superconductor after it has been diverted to the silver substrate by the discontinuity. When λ s L 2 is very low ( 0.1 λ s L 2 . All of the current returns to the superconductor only if λ s L 2 approaches infinity. The situation most likely to occur in an experiment is when λ s L 2 is high but finite and there is some small dissipation in the system. In this case, the healing length (defined as the length at which most of the current has returned to the superconductor) is shown to be proportional to the characteristic length 1 λ s , which depends on the properties of the silver and that of the BSCCO/silver interface. Voltage in the BSCCO is found to be equal to one-half the voltage drop in the silver over a length of L . The present results suggest that the critical current of an experiment is that of the composite conductor (BSCCO plus Ag). It also suggests that in fabricating this type of composite conductor, such as those made by powder-in-tube processing, it is desirable to reduce the interfacial parameter to below a certain value, thus ensuring that most of the current returns to the superconductor and reducing the amount of resistive heating (and healing length) in the composite conductor. The results of the analysis can be applied to interpret critical current density experiments if the discontinuities in the superconductor are considered to be grain boundaries, and the results can also be employed to predict the effect of transverse cracks on critical current density if the discontinuities are considered to be transverse cracks generated by axial strains.

Stability of vortex rings in a model of superflow

Stability of an isolated vortex ring is studied in the framework of the Ginzburg-Landau model using the nonlocal equation of motion. It is shown that an instability which might have been caused by nonlocal effects in the long-scale theory falls into the range of wavelengths comparable with the healing length. A higher-order effect of acoustic emission is found to play a stabilizing role, since the dissipation of the energy of perturbations by isotropic emission is sufficiently strong to restore the circular shape with only a small loss of the momentum.

Spatially resolved study of the dynamics of Josephson tunnel junctions.

By scanning superconducting Nb/${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$/Nb tunnel junctions of various geometries with an electron beam at low temperatures we have obtained spatially resolved two-dimensional images related with the dynamics of the junctions. In a current-biased junction the local thermal perturbation effected by the beam results in a voltage change \ensuremath{\Delta}V representing a convenient imaging-response signal. The spatial resolution is limited by a characteristic thermal healing length with a value of about 2 \ensuremath{\mu}m in our experiments. We analyze our results in terms of the sine-Gordon equation. For the interpretation of the spatially resolved voltage signal \ensuremath{\Delta}V we extend the energetic analysis of the perturbed sine-Gordon system of McLaughlin and Scott by including the beam-induced local thermal perturbation. Our model allows the quantitative comparison of our experimental two-dimensional images with the local dynamics expected from the perturbed sine-Gordon equation. Our experiments include the observation of single-mode and multiple-mode cavity resonances, soliton oscillations, and flux-flow behavior.

Theory for the atomic force microscopy of layered elastic surfaces

The authors present a first-principles theory of atomic force microscopy (AFM) on layered elastic surfaces. Substrate distortions due to the AFM tip and intercalant impurities are described within continuum elasticity theory, using elastic constants determined from ab initio density functional calculations. They apply this theory to graphite and calculate local distortions in the vicinity of an AFM tip and/or an intercalant atom. Using this formalism, they discuss the effect of a finite size tip (or a graphite flake attached to the tip) on the substrate distortions and the resulting AFM image. The authors calculations show that the AFM should be a unique tool to determine the local surface rigidity and the healing length of graphite near structural impurities.

Static relaxations of puckering distortions in intercalated layered solids

Layered solids have been qualitatively characterized according to their transverse layer rigidity with respect to point-like puckering distortions. In this scheme graphite is a ‘floppy’ layer system, layered aluminosilicates contain ‘rigid’ layers and layer dichalcogenides fall between these extremes. The primary signature of layer rigidity is the dependence of the basal spacing, d( x), on composition, x, in a ternary systems A 1− x B x L where L represents the host layers while A and B are distinct guest species with radii r A < r B. Previous attempts to quantify the layer rigidity (i.e. account for d( x)) using models which employed infinitely rigid layers have been singularly unsuccessful. In the present paper a one-parameter finite layer rigidity model, which yields an extremely good fit to the composition dependent basal spacing of a wide variety of layered solids which includes the floppy and rigid extremes, is described. In this model, a healing length is introduced to quantify the static spatial relaxation of a point-like puckering distortion. Both a discrete and continuous version of the model are presented and shown to yield equivalent results. It is found that, as expected, the more rigid the host layer, the larger the healing length, the values of which are deduced for several important layered solids.

Thin liquid films on rough or heterogeneous solids.

We study the conformation of thin liquid films on rough or heterogeneous solid substrates. The liquid-substrate interaction dominates for sufficiently thin films, and heterogeneity roughens the liquid interface. As the film thickens, surface tension becomes increasingly important, and the liquid interface flattens. A general equation for the equilibrium interface shape is derived. Analytic results are obtained in the limit of weak disorder for rough or self-affine surfaces as well as chemically heterogeneous solids. The effect of disorder depends strongly on the wave vector. Fluctuations at scales smaller than the film thickness or a ``healing length'' \ensuremath{\xi} produce little roughness. At larger wavelengths, the film conforms to the local fluctuations. Exact numerical solutions of the general equation are presented for surfaces with square grooves. These confirm the qualitative predictions of the analytic theory, and are in quantitative agreement when the depth of the grooves is small. The variation of roughness with film thickness, as well as the calculated adsorption isotherms, are compared to recent experimental results. We show that previously measured isotherms can be reproduced by corrugated surfaces with a single characteristic length scale, and do not necessarily imply that the surfaces studied were self-similar.

Dual percolation threshold in two-dimensional microporous media.

We have constructed a lattice model to probe the two-dimensional (2D) microporosity of intercalated layered systems of the type ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$L, where A and B are two types of intercalants sandwiched between host layers L. Percolation of a probe particle in this 2D microporous medium has been studied analytically and by Monte Carlo simulation. Depending on the transverse layer rigidity, which is characterized by a healing length \ensuremath{\lambda}, we find two ``normal'' percolation thresholds that coalesce for a particular value of \ensuremath{\lambda}=${\ensuremath{\lambda}}_{1}$. However, percolation at this point belongs to a different universality class compared with the site percolation in 2D system even though the correlations are of short range. In fact, for \ensuremath{\lambda}=${\ensuremath{\lambda}}_{1}$, the percolation is hull percolation which has been studied earlier by Saleur and Duplantier. Anomalous diffusion on these systems has also been investigated for \ensuremath{\lambda}=${\ensuremath{\lambda}}_{1}$ using analytic and simulation methods.

NMR and axial magnetic field textures in stationary and rotating superfluid3He-B

We have performed NMR measurements on the flare-out texture of superfluid3He-B in a cylindrical container of 5 mm diameter in axial magnetic fields of 28.4 and 56.9 mT. The transverse cw NMR spectra have been analyzed both with respect to their overall shape and the spin-wave absorption peaks close to the Larmor frequency. Our analysis of the stationary state spectra, based on texture computations, yields the longitudinal resonance frequency v L (T), the magnetic healing length ξ H (T), and the dipolar length ξ D (T), which we report for pressures below 29 bar. A lattice of quantized vortex lines appears in the rotating state, and two additional textural free energy terms have to be included in the analysis. One of the terms is linear in the applied magnetic field and arises from the spontaneous magnetization of the vortex cores. The second term is quadratic in magnetic field; it is generated both by the superflow field v s (r) about the vortex core and the difference in the induced magnetizations of the vortex-core and the bulk superfluids. The rotational orienting effects have been studied for rotation speedsβ up to 2red/sec.

Composition-drivenc-axis expansion of intercalated layered solids: 1D non–Vegard’s-law behavior in a 2D solid solution

We show that a layer rigidity model which includes the effects of elastic deformations of the host layers can account for the composition dependence of the c-axis lattice expansion of a variety of layered intercalation compounds. Rigidity parameters deduced from this model for each of the three classes of layered solids are reflective of structurally derived rigidity as are the healing lengths computed on the basis of discrete and continuum analyses. The layer rigidity model provides the first quantitative explanation for the 1D non--Vegard's-law behavior of a 2D solid solution.

Healing length near the lambda point in liquid helium.

Viscous shear waves have been used to probe the spatial variation and healing of the viscosity and superfluid density near a solid wall in bulk He i, bulk He ii, and in saturated superfluid films with thicknesses from 14 to 24 nm. The shear waves were generated at 20 and 34 MHz with an AT-cut quartz crystal resonator, and the transverse-acoustic impedance of the helium was measured at temperatures T close to the \ensuremath{\lambda} point at ${T}_{\ensuremath{\lambda}}$. In bulk He ii the results confirm a previous measurement of the healing length a(T)=(0.094\ifmmode\pm\else\textpm\fi{}0.002)${\ensuremath{\epsilon}}^{\mathrm{\ensuremath{-}}2/3}$ nm, where \ensuremath{\epsilon}=\ensuremath{\Vert}1-T/${T}_{\ensuremath{\lambda}}$\ensuremath{\Vert}. In bulk He i the measurements suggest that the viscosity exhibits healing above ${T}_{\ensuremath{\lambda}}$ near a solid wall with a similar healing length as in He ii. Healing effects were observed below the superfluid transition temperature in the films and are also described by the same healing length as in the bulk liquid.

Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid3He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid3He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial “non-Leggett configuration.” The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.

Healing and relaxation in flows of helium II. V. Thermodynamic potential and applications

This paper determines the fundamental thermodynamic potential of the healing and relaxation theory for helium II developed in previous papers in this series. The potential is founded on experimental data drawn from a variety of sources, e.g., neutron scattering, calorimetry,etc. This energy function is used in the calculation of the healing length near a plane wall and the vortex core parameter for a rectilinear line vortex over a wide range of the density-temperature plane for helium II. The coefficients of a cubicB-spline representation of the free energy is given over the same range, and a BASIC program is provided for the evaluation of that energy from the coefficients.

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R−iX of dilute solutions of3He in superfluid4He has been measured at a frequency (ω/2π) of 20.5 MHz at temperaturesT from 30 mK to the λ transition at Tλ. The3He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the λ point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of3He quasiparticles, and in the collisionless limit, ωτ≫1 (τ is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient α(c, T) and τ(c, T). The relaxation times were in good agreement with previous work, while α(c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the3He quasiparticles and the thermally excited rotons are in the hydrodynamic region, ωτ≪1. Values of the total viscosity η(c, T) were obtained and analyzed to give the3He gas viscosity and the3He-3He and roton-3He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the λ point we founda=(0.1±0.03)e−2/3 nm, where e=1−T/Tλ, proportional to the phase coherence length ξ. Our data are consistent with the hypothesis that ξρs/T is a universal constant for superfluid dilute solutions, where ρ s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in3He-4He films.

Healing Lengths Near Tλ in Liquid Helium

The λ-transition has been studied in bulk liquid 4He and in saturated films (thickness 14<d<23 nm) using viscous shear waves (penetration depth ≃20 nm) as a probe of the spatial variation of the super fluid density and viscosity near a solid/liquid interface and in superfluid films. The order parameter in Hell has a healing length a=0.1 ε-2/3 nm, where ε=|1-T/Tλ|, for ε<10-2. Above Tλ the viscosity near a wall also exhibits a spatial variation on the same length scale.