Interface Perturbations Research Articles

Growth of nonlinear structures on the interface between dielectric liquids in a strong vertical electric field

Nonlinear dynamics of the interface between dielectric liquids exposed to a strong vertical electric field is studied. Two types of exact solutions for quadratically nonlinear equations of motion (periodic solutions involving a finite number of Fourier harmonics and spatially localized rational solutions) are analyzed. Description of the interfacial evolution reduces to solving a finite number of ordinary differential equations either on amplitudes of harmonics, or, through the analytical continuation into the complex plane from the interface, for the poles motion. The common property of the solutions is a tendency for the growth of interface perturbations in the direction of the liquid with a lower permittivity.

Polymer-Polymer Interfacial Perturbation on the Glass Transition of Supported Low Molecular Weight Polystyrene Thin Films.

Clarifying interfacial perturbation on polymer relaxation is important for polymer material development. Herein we investigated polymer-polymer interfacial perturbation on low molecular weight (MW) polystyrene (PS) thin film (15-180 nm) glass transition by depositing various polymers atop PS films. Overall, rubbery topcoats induced Tg depression of PS thin film (below 60 nm), whileglassy topcoats induced Tg elevation of PS thin film (below 30 nm). Importantly, for the rubbery topcoat, Tg perturbation strength is largely dependent on the Tg difference between interfacial polymers and a larger Tg difference would induce stronger perturbation, while for the glassy topcoat this dependence is inconspicuous. Meanwhile, the interfacial perturbation length during PS glass transition by rubbery topcoats is estimated to be around 8 nm, while it is considered to be about 3.5 nm for glassy topcoats. The different interfacial perturbation length induced by disparate topcoats was accounted for by their different perturbation strength on adjacent PS molecules and disparate interfacial roughness. The results can promote the understanding of polymer interfacial perturbation and benefit the design and development of polymer-based materials.

Analog cosmology with two-fluid systems in a strong gradient magnetic field.

We propose an experiment combining fluid dynamics and strong magnetic field physics to simulate cosmological scenarios. Our proposed system consists of two immiscible, weakly magnetized fluids moved through a strong gradient magnetic field. The diamagnetic and paramagnetic forces thus generated amount to a time-dependent effective gravity, which allows us to precisely control the propagation speed of interface waves. Perturbations on the interface therefore experience a nonstationary effective metric. In what follows, we demonstrate that our proposed system is capable of simulating a variety of cosmological models. We then present a readily realizable experimental setup which will allow us to capture the essential dynamics of standard inflation, wherein interface perturbations experience a shrinking effective horizon and are shown to transition from oscillatory to frozen and squeezed regimes at horizon crossing.

Directional solidification of Fe-Al-Ta eutectic by electron beam floating zone melting

Fe-Al-Ta eutectic composites have been paid more attentions for high temperature application. Nevertheless, still there is a lack of research on microstructural characteristics and crystal growth mechanism of this eutectic obtained by high temperature gradient directional solidification technique. As such, Fe-Al-Ta eutectic composites were prepared by high temperature gradient electron beam floating zone melting technique in the present paper. Microstructures, solid/liquid interface morphologies and preferential orientations of the Fe-Al-Ta eutectic composites at different solidification rates were studied. Moreover, effect of interface perturbation wavelength on stability of the solid/liquid interface was calculated according to M-S theory and Kurz-Fisher model, respectively. These are consistent with the experimental results well.

Stability of the interface between two thin liquid layers under tangential high frequency vibrations

In this paper, a system of two equally thin layers of immiscible incompressible isothermal ideal liquids under high frequency horizontal harmonic vibrations is considered theoretically. The vessel containing the liquids is assumed to be closed, of rectangular form with weakly-deformable side borders and infinitely long in horizontal direction. Previous studies showed that, for significantly thin layers, the main instability in the system, oscillatory Kelvin-Helmholtz instability, should be the long-wave instability. Therefore, the problem was solved analytically using “shallow water” approximation. For all equations, a formal expansion with respect to two small parameters was used: one associated with a small ratio of the vertical to horizontal scale and another with small perturbations of the flat interface. Evolutionary equations were derived for the interface in the main order of expansion for vibration intensity less than a threshold value for oscillatory Kelvin-Helmholtz instability (subcritical area). The solutions found for these evolutionary equations correspond to traveling waves with soliton or cnoidal interfacial surface. The soliton profile is a limiting case of the cnoidal profile. The maximum speed of these waves was determined. It was demonstrated that the obtained solutions exist only in the subcritical area of parameters and from the critical level subcritical bifurcation emerges. For special case of traveling waves in a quasi-stationary mode (i.e. with static interface) also referred to as a “frozen wave”, a numerical analysis of linear stability was performed using a Fourier series expansion in a horizontal coordinate. The instability of quasi-stationary modes to small disturbances was demonstrated.

On instabilities of growing bi-material interfaces

This study concerns with the evolution of morphological patterns that often arise on the interface of bi-material, so called metal-precipitate phase, due to the instability of the interfaces. The instability leads to growth or retraction of small perturbation, which may determine the formation of a variety of morphological patterns initially arising on surfaces of growing precipitates at small length scales. To better understand the cause of different patterns on the bi-material interfaces, an analytical study of the stability of the precipitate-matrix interface is performed. First, a wavy interface perturbation is used to examine the spontaneous variations that occur at the precipitate-matrix interface. Then, the analysis utilises Cerruti?s solution to compute the perturbed stress field surrounding the interface. It is shown that a virtually flat interface subjected to tension is in general unstable. The amplitude of sinusoidal perturbations decays for short wave lengths and grow for longer wave lengths. Both a critical wave length for which the perturbation amplitude is unaffected and a specific ditto which obtain maximum perturbation growth rate are derived

Steric Repulsion Forces Contributed by PEGylation of Interleukin-1 Receptor Antagonist Reduce Gelation and Aggregation at the Silicone Oil-Water Interface

Silicone oil, used as a lubricating coating in pharmaceutical containers, has been implicated as a cause of therapeutic protein aggregation. After adsorbing to silicone oil-water interfaces, proteins may form interfacial gels, which can be transported into solution as insoluble aggregates if the interfaces are perturbed. Mechanical interfacial perturbation of both monomeric recombinant human interleukin-1 receptor antagonist (rhIL-1ra) and PEGylated rhIL-1ra (PEG rhIL-1ra) in siliconized syringes resulted in losses of soluble monomeric protein. However, the loss of rhIL-1ra was twice that for PEG rhIL-1ra; even though in solution, PEG rhIL-1ra had a lower ΔGunf and exhibited a more perturbed tertiary structure at the interface. Net protein-protein interactions in solution for rhIL-1ra were attractive but increased steric repulsion because of PEGylation led to net repulsive interactions for PEG rhIL-1ra. Attractive interactions for rhIL-1ra were associated with increases in intermolecular β-sheet content at the interface, whereas no intermolecular β-sheet structures were observed for adsorbed PEG rhIL-1ra. rhIL-1ra formed interfacial gels that were 5 times stronger than those formed by PEG rhIL-1ra. Thus, the steric repulsion contributed by the PEGylation resulted in decreased interfacial gelation and in the reduction of aggregation, in spite of the destabilizing effects of PEGylation on the protein’s conformational stability.

An explosive disintegration of heated fuel droplets with adding water

This work experimentally studies the processes of explosive disintegration of heated fuel droplets with variations of the added water volume. The studies are performed for typical liquid fuels burnt in power plants, as well as flammable liquids being the main fuel component: kerosene, diesel, gasoline, oil, turbine and automobile oil. The minimum (sufficient for the explosive breakup of droplets) heating temperature and the ratio of concentrations of water and flammable liquid are determined. The optical method of Planar Laser Induced Fluorescence (with the operation principle based on the laser illumination of a drop or a liquid film with the introduction of a fluorophore dye) is used to determine temperatures at the inter-component boundary that are sufficient for the micro-explosion of a two-liquid drop. The influence of laser action on the drop on the processes of its heating, evaporation, transformation and breakup is evaluated. The effect of the laser on the mode of explosive disintegration of droplets, the time of its heating and destruction, and the minimum (limiting) temperature of droplet disintegration is determined. Laser irradiation intensifies heating and breakup of fuel droplets as a result of three processes: an additional radiative heat flux; the perturbation (deformation) of the medium interface; and a considerable temperature gradient on the inter-component boundaries, leading to high velocity of convection flows and the formation of vortex structures in the vicinity of the medium interface. The technology of fuel droplets disintegration is proposed.

Faraday waves on a cylindrical fluid filament – generalised equation and simulations

We perform linear stability analysis of an interface separating two immiscible, inviscid, quiescent fluids subject to a time-periodic body force. In a generalised, orthogonal coordinate system, the time-dependent amplitude of interfacial perturbations, in the form of standing waves, is shown to be governed by a generalised Mathieu equation. For zero forcing, the Mathieu equation reduces to a (generalised) simple harmonic oscillator equation. The generalised Mathieu equation is shown to govern Faraday waves on four time-periodic base states. We use this equation to demonstrate that Faraday waves and instabilities can arise on an axially unbounded, cylindrical capillary fluid filament subject to radial, time-periodic body force. The stability chart for solutions to the Mathieu equation is obtained through numerical Floquet analysis. For small values of perturbation and forcing amplitude, results obtained from direct numerical simulations (DNS) of the incompressible Euler equation (with surface tension) show very good agreement with theoretical predictions. Linear theory predicts that unstable Rayleigh–Plateau modes can be stabilised through forcing. This prediction is borne out by DNS results at early times. Nonlinearity produces higher wavenumbers, some of which can be linearly unstable due to forcing and thus eventually destabilise the filament. We study axisymmetric as well as three-dimensional perturbations through DNS. For large forcing amplitude, localised sheet-like structures emanate from the filament, suffering subsequent fragmentation and breakup. Systematic parametric studies are conducted in a non-dimensional space of five parameters and comparison with linear theory is provided in each case. Our generalised analysis provides a framework for understanding free and (parametrically) forced capillary oscillations on quiescent base states of varying geometrical configurations.

Effects of sleep loss on the cortical microstructure

Silicone oil, used as a lubricating coating in pharmaceutical containers, has been implicated as a cause of therapeutic protein aggregation. After adsorbing to silicone oil-water interfaces, proteins may form interfacial gels, which can be transported into solution as insoluble aggregates if the interfaces are perturbed. Mechanical interfacial perturbation of both monomeric recombinant human interleukin-1 receptor antagonist (rhIL-1ra) and PEGylated rhIL-1ra (PEG rhIL-1ra) in siliconized syringes resulted in losses of soluble monomeric protein. However, the loss of rhIL-1ra was twice that for PEG rhIL-1ra; even though in solution, PEG rhIL-1ra had a lower ΔGunf and exhibited a more perturbed tertiary structure at the interface. Net protein-protein interactions in solution for rhIL-1ra were attractive but increased steric repulsion because of PEGylation led to net repulsive interactions for PEG rhIL-1ra. Attractive interactions for rhIL-1ra were associated with increases in intermolecular β-sheet content at the interface, whereas no intermolecular β-sheet structures were observed for adsorbed PEG rhIL-1ra. rhIL-1ra formed interfacial gels that were 5 times stronger than those formed by PEG rhIL-1ra. Thus, the steric repulsion contributed by the PEGylation resulted in decreased interfacial gelation and in the reduction of aggregation, in spite of the destabilizing effects of PEGylation on the protein’s conformational stability.

Magneto-hydrodynamic stability of a liquid metal battery in discharge

All liquid three-layer batteries are intended as large-scale electrical energy storage. The paper investigates long-wave interfacial instabilities driven by the electromagnetic forces during dynamic phases of the battery charging/discharging. The liquid metal battery of 20 cm size with sodium metal anode, which is a candidate for experimental and commercial implementation, is shown to be unstable at the discharge state when the top metal layer depth is reduced below a critical level. The numerical model includes the effects of viscous friction and the horizontal wave velocities. The instability does not depend on the initial interface perturbation type.

Global Regularity for 2d Water Waves with Surface Tension

We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows us to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, we are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.

Growth of liquid-gas interfacial perturbations driven by acoustic waves

Motivated by ultrasound-induced pulmonary hemorrhage, we computationally study acoustic waves in water interacting with a perturbed water-air interface. We demonstrate that baroclinic vorticity due to the misaligned pressure (waves) and density (interface) gradients drives the perturbation growth.

Inherent flexibility of CLIC6 revealed by crystallographic and solution studies

Chloride intracellular channels (CLICs) are a family of unique proteins, that were suggested to adopt both soluble and membrane-associated forms. Moreover, following this unusual metamorphic change, CLICs were shown to incorporate into membranes and mediate ion conduction in vitro, suggesting multimerization upon membrane insertion. Here, we present a 1.8 Å resolution crystal structure of the CLIC domain of mouse CLIC6 (mCLIC6). The structure reveals a monomeric arrangement and shows a high degree of structural conservation with other CLICs. Small-angle X-ray scattering (SAXS) analysis of mCLIC6 demonstrated that the overall solution structure is similar to the crystallographic conformation. Strikingly, further analysis of the SAXS data using ensemble optimization method unveiled additional elongated conformations, elucidating high structural plasticity as an inherent property of the protein. Moreover, structure-guided perturbation of the inter-domain interface by mutagenesis resulted in a population shift towards elongated conformations of mCLIC6. Additionally, we demonstrate that oxidative conditions induce an increase in mCLIC6 hydrophobicity along with mild oligomerization, which was enhanced by the presence of membrane mimetics. Together, these results provide mechanistic insights into the metamorphic nature of mCLIC6.

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275031, 11475034, 11575033, and 11274026) and the National Basic Research Program of China (Grant No. 2013CB834100).

Rayleigh–Taylor instability (RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear (WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough, the WN results in planar geometry are recovered.

Dripping retardation with corrugated ceiling

The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.

Formation of Singularities at the Interface of Liquid Dielectrics in a Horizontal Electric Field in the Presence of Tangential Velocity Discontinuity

Nonlinear dynamics of the interface of dielectric liquids under the conditions of suppression of the Kelvin–Helmholz instability by a tangential electric field has been investigated. Two broad classes of exact analytical solutions to the equations of motion describing the evolution of spatially localized and periodic interface perturbations have been found. Both classes of solutions tend to the formation of strong singularities: interface discontinuities with formally infinite amplitudes. The discontinuity sign is determined by the sign of liquid velocity jump at the interface.

Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries

This paper concerns the reflection of high-frequency, monochromatic linear waves of wavenumber k(≫ 1) from smooth boundaries which are O(k−1/2) perturbations away from either a specified near-planar boundary or else from a given smooth, two-dimensional curve of general O(1) curvature. For each class of perturbed boundary, we will consider separately plane and cylindrical wave incidence, with general amplitude profiles of each type of incident field. This interfacial perturbation scaling is canonical in the sense that a ray approach requires a modification to the standard WKBJ ‘ray ansatz’ which, in turn, leads to a leading-order amplitude (or ‘transport’) equation which includes an extra term absent in a standard application of the geometrical theory of diffraction. This extra term is unique to this scaling, and the afore-mentioned modification that is required is an application of a generalised type of ray expansion first posed by F. G. Friedlander and J. B. Keller (1955 Commun. Pure Appl. Math.6, 387–394).

Dynamics and Stability of Air Bubbles in a Porous Medium

A numerical method is developed for reliably computing the evolution of the boundary of a multiply connected water-saturated domain with air bubbles in the case when the pressure inside them depends on the bubble volume. It is assumed that the distance between the gas bubbles is comparable with their size. Gas bubbles can be near an extended phase transition boundary separating a porous medium flow and a domain saturated with a mixture of air and water vapor. The numerical method is verified by comparing the numerical solution of a test problem with its analytical solution. Caused by finite-amplitude perturbations of the phase interface, the deformation of an air bubble in an extended horizontal water-saturated porous layer with a constant pressure gradient is studied. It is shown that the instability of the bubble boundary with respect to finite perturbations leads to the splitting of the bubble. An analysis of the numerical solution shows that, although all circular bubbles move at the same velocity irrespective of their size, nevertheless, due to instability, a portion of the bubble boundary where the air displaces the fluid moves faster than an opposite portion where the fluid displaces the air. As a result, nearby bubbles are capable of merging before splitting.

Формирование особенностей на поверхности раздела жидких диэлектриков в горизонтальном электрическом поле при наличии тангенциального разрыва скоростей

AbstractNonlinear dynamics of the interface of dielectric liquids under the conditions of suppression of the Kelvin–Helmholz instability by a tangential electric field has been investigated. Two broad classes of exact analytical solutions to the equations of motion describing the evolution of spatially localized and periodic interface perturbations have been found. Both classes of solutions tend to the formation of strong singularities: interface discontinuities with formally infinite amplitudes. The discontinuity sign is determined by the sign of liquid velocity jump at the interface.