Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

Weakly nonlinear stability analysis of a falling film with countercurrent gas–liquid flow has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear and nonlinear stability solutions for the film flow system. The results show that both supercritical stability and subcritical instability are possible for a film flow system when the gas flows in the countercurrent direction. The stability characteristics of the film flow system are strongly influenced by the effects of interfacial shear stress when the gas flows in the countercurrent direction. The effect of countercurrent gas flow in a falling film is to stabilize the film flow system.     

Two-fluid modeling in analyzing the interfacial stability of liquid film flows

The area-averaged two-fluid model formulation of a separated two-phase flow system is used to investigate interfacial stability of liquid film flows. The analysis takes into account the effects of phase change at the interface as well as the dynamic effects of the adjacent vapor flow on the interfacial stability. Wave formation and instability criteria are established in terms of the generalized fluid and flow parameters. The criteria are applied to investigate the stability of laminar liquid film flow with interfacial shear and phase change. The influence of various dimensionless parameters characterizing film thickness, gravity, phase change and interfacial shear are studied with respect to the neutral stability, temporal growth factor and the wave propagation velocity. The results of the present study indicate that the interfacial stability analysis developed within the frame of the two-fluid model formulation proves to be quite accurate as judged by comparing its results with the available experimental data and with the results of much longer and more complex analytical investigations which are valid only for the liquid film free of interfacial shear.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Measurements of velocity,temperature and velocity fluctuation distributions in falling liquid films

The velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples. The interfacial shear was caused by cocurrent air flow.The results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000. Mixing motion occurs in the vicinity of the interface; however, the flow near the wall surface exhibits no sign of such eddy motions, as predicted by the wall law for single phase turbulent flow. Although velocity fluctuation is observed within films with interfacial shear, mean velocity profiles are approximately the same as those obtained by the laminar film prediction.     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

The two-dimensional elastic wave propagation in an infinite layered structure with nonlinear interlayer interfaces is analyzed theoretically to investigate the second-harmonic generation due to interfacial nonlinearity. The structure consists of identical isotropic linear elastic layers that are bonded to each other by spring-type interfaces possessing identical linear normal and shear stiffnesses but different quadratic nonlinearity parameters. Explicit analytical expressions are derived for the second-harmonic amplitudes when a single monochromatic Bloch mode propagates in the structure in arbitrary directions by applying the transfer-matrix approach and the Bloch theorem to the governing equations linearized by a perturbation method. The second-harmonic generation by a single nonlinear interface and by multiple consecutive nonlinear interfaces are shown to be profoundly influenced by the band structure of the layered structure, the fundamental Bloch wave mode, and its propagation direction. In particular, the second harmonics generated at multiple consecutive interfaces are found to grow cumulatively with the propagation distance when the phase matching occurs between the Bloch modes at the fundamental and double frequencies.     

Tensile and mixed-mode strength of a thin film-substrate interface under laser induced pulse loading

Laser induced stress waves are used to characterize intrinsic interfacial strength of thin films under both tensile and mixed-mode conditions. A short-duration compressive pulse induced by pulsed-laser ablation of a sacrificial layer on one side of a substrate is allowed to impinge upon a thin test film on the opposite surface. Laser-interferometric measurements of test film displacement enable calculation of the stresses generated at the interface. The tensile stress at the onset of failure is taken to be the intrinsic tensile strength of the interface. Fused-silica substrates, with their negative nonlinear elasticity, cause the compressive stress wave generated by the pulse laser to evolve a decompression shock, critical for generation of the fast fall times needed for significant loading of surface film interfaces. By allowing the stress pulse to mode convert as it reflects from an oblique surface, a high amplitude shear wave with rapid fall time is generated and used to realize mixed-mode loading of thin film interfaces. We report intrinsic strengths of an aluminum/fused silica interface under both tensile and mixed-mode conditions. The failure mechanism under mixed-mode loading differs significantly from that observed under pure tensile loading, resulting in a higher interfacial strength for the mixed-mode case. Inferred strengths are found to be independent, as they should be, of experimental parameters.     

Pure-shear Failure of Thin Films by Laser-induced Shear Waves

The measurement of mode-dependent thin film interfacial properties is important in evaluating the quality of the interfaces between thin films and substrates. Previous work has proved that tensile and mixed-mode strength of a thin film/substrate interface can be evaluated using a laser-induced thin film spallation technique. To further examine the application regime of this technique and identify the individual roles of the tensile and shear stress in the resulting interfacial failure, a special sample design is adopted in the current work to realize pure-shear loading at the thin film/substrate interface. Our result demonstrates that for sufficiently high stress amplitude, interfacial failure can be induced solely by the in-plane shear stress and the stress can be quantitatively determined from optical interferometric measurements. Together with the previous tensile and mixed-mode studies, a complete picture of the mode-dependent thin film interfacial strength can now be reliably determined using the laser-induced thin film spallation techniques.     

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

Taylor instability in a thin fluid layer

Summary The Stokes-Taylor instability of a thin fluid layer is studied by the usual first order perturbation method. The density of the layer is assumed to be constant or to vary exponentially through it. It is bounded on either side by media of constant density. Particular attention is paid to determining the exponential rates of growth of perturbations at the two interfaces, and the effect of the layer in reducing the instability of the interface between the bounding media formed in the absence of the layer. When the layer is of variable density and the acceleration acts in the direction of increasing density, there is an infinity of modes of internal instability which do not affect the interfaces. There are also two modes of interfacial instability which are similar to those occurring when the layer is of constant density.     

Mixed-mode failure of thin films using laser-generated shear waves

A new test method is developed for studying mixed-mode interfacial failure of thin films using laser generated stress waves. Guided by recent parametric studies of laser-induced tensile spallation, we successfully extend this technique to achieve mixed-mode loading conditions. By allowing an initial longitudinal wave to mode convert at an oblique surface, a high amplitude shear wave is generated in a fused silica substrate and propagated toward the thin-film surface. A shear wave is obtained with amplitude large enough to fail an Al film/fused silica interface and the corresponding shear stress calculated from high-speed interferometric displacement measurements. Examination of the interfaces failed under mixed-mode conditions reveals significant wrinkling and tearing of the film, in great contrast to blister patterns observed in similar Al films failed under tensile loading.     

Energy redistribution dynamics in coupled Couette–Poiseuille flows using large-Eddy simulation

The problem of turbulent Couette flow driven by a statistically steady external wind is studied in the framework of spatially filtered Navier–Stokes equations. The phenomenon of wind-driven flow of water is represented by a layer of air modeled as Poiseuille flow (air sub-domain), coupled to a layer of water modeled as Couette flow (water sub-domain). We focus on changes in the statistics in either the air or the water sub-domain, due to the coupling with the other sub-domain. We also highlight dynamic flow structures forming near the air-water interface. Simulations based on different Reynolds numbers in the air and the water sub-domains are compared to computationally less demanding simulations with equal Reynolds numbers. Results of these simulations indicate strong similarities, i.e., the flow is well approximated by simulating air and water at the same Reynolds numbers. Further analysis shows that the flow in the water domain shares important features with classical Couette flows. The horizontal turbulent mixing renders a thinner boundary layer in the water sub-domain. Moreover, an increased intermittency in the flow velocities is observed, which may be linked to so-called splat events near the air-water interface. These splats characterize the interaction of coherent structures across the interface, being stronger in the water phase. An analysis of the pressure-strain correlation near the air-water interface on the water side shows that such splats are responsible for redistributing energy from the streamwise and spanwise directions, to the vertical direction. This behavior, although qualitatively similar to wall-bounded flows, differ mainly on the fact that most of the energy drained comes from the streamwise direction: in wall-bounded the main contributor is the spanwise direction. The boundary layers near the air-water interface show inclined vortical structures. Unlike in coupled Couette–Couette flow, the peak in the Reynolds stress is displaced from the channel’s center into the buffer region of the water sub-domain.     

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.     

Traction–separation laws and stick–slip shear phenomenon of interfaces between cellulose nanocrystals

Cellulose nanocrystals (CNCs) are one of nature's most abundant structural material building blocks and possess outstanding mechanical properties including a tensile modulus comparable to Kevlar. It remains challenging to upscale these properties in CNC neat films and nanocomposites due to the difficulty of characterizing interfacial bonding between CNCs that governs stress transfer under deformation. Here we present new analyses based on atomistic simulations of shear and tensile failure of the interfaces between Iβ CNCs, providing new insight into factors governing the mechanical behavior of hierarchical nanocellulose materials. We compare the two most relevant crystal interfaces and find that hydrogen bonded surfaces have greater tensile strength compared to the surfaces governed by weaker interactions. On the contrary, shearing simulations reveal that friction between the atomic interfaces depends not only on surface energy but also the energy landscape along the shear direction. While being a weaker interface, the intersheet plane exhibits greater energy barriers to shear. The molecular roughness of this interface, characterized by a greater energy barrier, exhibits stick–slip deformation behavior as opposed to a more continuous sliding and rebonding mechanism observed for the interfaces with hydrogen bonds. Analytical models to describe the energy landscapes are developed using energy scaling relations for van der Waals surfaces in combination with a modification of the Prandtl–Tomlinson model for atomic friction. Our simulations pave the way for tailoring hierarchical CNC materials by taking a similar approach to techniques employed for describing metals, where mechanical properties can be tuned through a deeper understanding of grain boundary physics and nanoscale interfaces.     

Role of droplet bridging on the stability of particle-containing immiscible polymer blends

The effect of micron-sized hydrophobic calcium carbonate particles on the stabilization of polydimethylsiloxane (PDMS)/polyisobutylene (PIB) immiscible model blends is investigated in this study. The analytical splitting of bulk and liquid–liquid interface contributions from the droplet bridging one is successfully performed due to the negligible contribution of hydrophobic microparticles to the bulk rheology of phases. The presence of particles at the fluid–fluid interface is supported by wetting parameter calculation and verified by optical microscopy observations. Moreover, direct visualizations shows that particles are able to form clusters of droplets by simultaneously adsorbing at two fluid–fluid interfaces and glue-dispersed droplets together, probably due to the patchy interactions induced by heterogeneous distribution of particles along the interface. Rheological studies show that the flow-induced coalescence is slowed down upon addition of particles and almost suppressed with the addition of 4 wt% particles. The linear viscoelastic response is modeled to estimate interfacial tension by considering the contribution of particle-induced droplet aggregation in addition to bulk and droplet deformation ones. From linear and nonlinear viscoelastic responses, the improved stability of filled polymer blends is attributed to the interfacial rheology and/or the bridged structure of droplets, even though the interfacial area is not fully covered by particles. Furthermore, Doi–Ohta scaling relations are investigated by employing stress growth response upon step-up of shear flow.     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

全固态锂电池界面的机械失效模型综述

全固态锂电池具有高能量密度和高安全性能等优点,有望替代传统锂电池成为下一代可移动储备．然而,全固态结构也给这种新型电池的应用带来全新的挑战,阻碍其商业化的进程,其中很重要的一个挑战就是机械不稳定性．首先,尽管固态电解质具有较高刚度与强度,理论上应该可以阻挡锂枝晶的穿透,但在其使用过程中仍能观察到锂枝晶的生长,这与高刚度电解质可抵制锂枝晶生长的理论相悖．其次,与液态电解质相比,固态电解质刚度大,在电极活性材料充放电时不能始终保持与活性材料的有效接触,可能导致活性颗粒和电解质的界面分层．因此,解释这些现象并提供解决策略对促进全固态锂电池的广泛应用至关重要．本文旨在总结近年来关于全固态锂电池不同界面处机械失效的力化耦合模型,主要包括以下两个方面：(1) 锂金属负极与固态电解质界面处锂枝晶的形成与生长;(2) 活性颗粒锂化/脱锂化引起的界面分层和破裂．本文从理论模型的角度总结了全固态锂离子电池中不同界面上的机械失效行为,旨在为全固态锂离子电池的模型建立与结构优化提供借鉴思路．     

Small Reynolds number instabilities in two-layer Couette flow

Instabilities in two-layer Couette flow are investigated from a small Reynolds number expansion of the eigenvalue problem governing linear stability. The wave velocity and growth rate are given explicitly, and previous results for long waves and short waves are retrieved as special cases. In addition to the inertial instability due to viscous stratification, the flow may be subject to the Rayleigh–Taylor instability. As a result of the competition of these two instabilities, inertia may completely stabilise a gravity-unstable flow above some finite critical Froude number, or conversely, for a gravity-stable flow, inertia may give rise to finite wavenumber instability above some finite critical Weber number. General conditions for these phenomena are given, as well as exact or approximate values of the critical numbers. The validity domain of the many asymptotic expansions is then investigated from comparison with the numerical solution. It appears that the small-Re expansion gives good results beyond Re = 1, with an error less that 1%. For Reynolds numbers of a few hundred, we show from the eigenfunctions and the energy equation that the nature of the instability changes: instability still arises from the interfacial mode (there is no mode crossing), but this mode takes all the features of a shear mode. The other modes correspond to the stable eigenmodes of the single-layer Couette flow, which are recovered when one fluid is rigidified by increasing its viscosity or surface tension.     

Thin films with self-assembled monolayers embedded on their surfaces

We have recently shown that the capillarity-based process for self-assembling particle monolayers on fluid–liquid interfaces can be improved by applying an electric field in the direction normal to the interface. In this paper, we present a technique for freezing these monolayers onto the surface of a flexible thin film. The technique involves assembling the monolayer on the interface between a UV-curable resin and a fluid which can be air or another liquid, and then curing the resin by applying UV light. The monolayer becomes embedded on the surface of the solidified resin film.