Layer Of Viscous Fluid Research Articles

Propagation of Waves in an Elastic Half-Space Interacting with a Viscous Liquid Layer

The problem of the propagation of acoustic waves in a layer of a compressible viscous fluid that interacts with an elastic half-space is solved using the three-dimensional linear equations of classical elasticity theory for the solid and the three-dimensional linearized Navier–Stokes equations for the compressible viscous fluid. The problem statement and approach based on the application of the general solutions of linear equations for elastic bodies and linearized equations for the fluid are employed. The dispersion equation describing the propagation of quasi-Lamb waves in the hydroelastic system is derived. Dispersion curves for normal waves in a wide frequency range are plotted. The effect of the thickness of the liquid layer on the phase velocities and attenuation coefficients of acoustic waves is analyzed. It is shown that the influence of fluid viscosity on the parameters of the wave process is associated with the properties of wave localization. Using the developed approach and obtained results, the limits of the applicability of the models of wave processes based on the model of an ideal fluid are established. The numerical results are presented in the form of graphs and analyzed.

Dynamics of a High-Order Generalized Lorenz Model for Magnetoconvection

In this paper, we present a 6D generalized Lorenz model for magnetoconvection of an electrically conducting viscous fluid layer subjected to horizontally imposed uniform magnetic field. It generalizes the 4D generalized Lorenz model of Macek and Strumik [Phys. Rev. E 82, 027301 (2010)] taking into account high-wavenumber vertical Fourier modes of the temperature profile. These additional modes not only increase the feedback loop of the system but also subsequently affect the transitional processes. The boundedness, stability of solutions, bifurcation patterns enroute to chaos for the new 6D model are explored. Studies reveal that the stability of the quiescent state does not alter. But the stability of the steady convective state differs in comparison to the 4D model. The regions of aperiodic oscillation are suppressed which results in stabilization of the convective motion. Some new organized periodic structures embedded in chaotic domain appear in parameter space of the 6D model, and the transitional route to hyperchaos is altered owing to the inclusion of the high-order modes.

Hydroelastic response of a circular sandwich plate interacting with a liquid layer

We considered the formulation and solution of the forced oscillations hydroelasticity problem for a three-layered circular plate contacting with a viscous incompressible fluid layer, the pressure in which varies according to the harmonic law. The plate is the bottom wall of a narrow channel completely filled with a viscous fluid. The axisymmetric coupled hydroelasticity problem consisting of the plate dynamics equation, the viscous fluid layer dynamics equation, and their corresponding boundary conditions was investigated. We obtained the plate dynamics equations taking into account inertia forces in the radial and normal directions in the framework of zigzag kinematic theory. In these equations, the load was expressed by the stresses of the viscous fluid contacting with the three-layered circular plate. The fluid dynamics equations were represented by the Navier-Stokes equations and continuity equation written for the case of creeping fluid flow in a channel. We obtained the forced radial and bending hydroelastic oscillations equations of the circular three-layered plate using the perturbation method. The solution of these equations was represented by a series of eigenfunctions of the corresponding Sturm-Liouville problem. We have also presented the numerical study results of the radial and bending vibrations amplitude dependence on the frequency for the main steady oscillations mode of the plate.

Гидроупругая реакция трехслойной пластины со сжимаемым заполнителем, взаимодействующей со штампом через слой вязкой жидкости

Гидроупругая реакция трехслойной пластины со сжимаемым заполнителем, взаимодействующей со штампом через слой вязкой жидкости

Long-distance Transport in Bacterial Swarms Revealed by Single Nanoparticle Tracking.

During swarming, high density flagella-driven bacteria migrate collectively in a swirling pattern on wet agar surfaces, immersed in a thin viscous fluid layer called "swarm fluid". Though the fluid environment has essential role in the emergence of swarming behavior, the microscopic mechanisms of it in mediating the cooperation of bacteria populations are not fully understood. Here, instead of micro-sized tracers used in previous research, we use gold nanorods as single particle tracers to probe the dynamics of the swarm fluid. This protocol includes five major parts: (1) the culture of swarming bacterial colony; (2) the preparations of gold nanorod tracers and the micro-spraying technique which are used to put the nanotracers into the upper fluid of bacterial swarms; (3) imaging and tracking; (4) other necessary control experiments; (5) data analysis and fitting of physical models. With this method, the nano-sized tracers could move long distances above motile cells without direct collisions with the bacteria bodies. In this way, the microscopic dynamics of the swarm fluid could be tracked with high spatiotemporal resolution. Moreover, the comprehensive analysis of multi-particle trajectories provides systematic visualization of the fluid dynamics. The method is promising to probe the fluid dynamics of other natural or artificial active matter systems.

The nonlinear stability regime of the viscous Faraday wave problem

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for horizontally periodic flows. This problem gives rise to flat but vertically oscillating equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of these equilibria in certain parameter regimes. We prove that both with and without surface tension there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t = 0 t = 0 give rise to global-in-time solutions that decay to equilibrium at an identified quantitative rate.

Mathematical Model of Oscillations of a Three-Layered Channel Wall Possessing a Compressible Core and Interacting with a Pulsating Viscous Liquid Layer

The paper deals with the formulation of a mathematical model to study a dynamics interaction of a three-layered channel wall with a pulsating viscous fluid layer in a channel. The narrow channel formed by two parallel walls was considered. The lower channel wall was a three-layered plate with a compressible core, and the upper one was absolutely rigid. The face sheets of the three-layered plate satisfied Kirchhoff's hypotheses. The plate core was considered rigid taking into account its compression in the transverse direction. Plate deformations were assumed to be small. The continuity conditions of displacements are satisfied at the layers' boundaries of the three-layered plate. The oscillations of the three-layered channel wall occurred under the action of a given law of pressure pulsation at the channel edges. The dynamics of the viscous incompressible fluid layer within the framework of a creeping motion was considered. The formulated mathematical model consisted of the dynamics equations of the three-layered plate with compressible core, Navier --- Stokes equations, and the continuity equation. The boundary conditions of the model were the conditions at the plate edges, the no-slip conditions at the channel walls and the conditions for pressure at the channel edges. The steady-state harmonic oscillations were investigated and longitudinal displacements and deflections of the plate face sheets were determined. Frequency-dependent distribution functions of amplitudes of plate layers displacements were introduced. These functions allow us to investigate the dynamic response of the channel wall and the fluid pressure change in the channel. The elaborated model can be used for the evolution of non-destructive testing of elastic three-layered elements contacting with a viscous fluid layer and being part of the lubrication, damping or cooling systems of modern instruments and units.

Equations of Symmetric MHD-Boundary Layer of Viscous Fluid with Ladyzhenskaya Rheology Law

One considers flow past a body in an electrically conductive viscous fluid in magnetic field, the fluid being subject to a nonlinear rheological law. Solutions of the corresponding system of magnetohydrodynamic boundary layer are examined in a neighborhood of a frontal critical point.

Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows

Abstract The nonlinear dynamics of two immiscible superposed viscous fluid layers in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The flow is driven by an imposed axial pressure gradient. Working on the assumption that one of the layers is thin, a weakly-nonlinear evolution equation for the interfacial shape is derived that couples the dynamics in the two layers via a nonlocal integral term whose kernel is determined by solving the linearised Navier–Stokes equations in the thicker fluid. The model equation incorporates salient physical effects including inertia, gravity, and surface tension, and allows for comparison with DNS at finite Reynolds numbers. Direct comparison of travelling-wave solutions obtained from the model equation and from DNS show good agreement for both stably and unstably stratified flows. Both the model and the DNS indicate regions in parameter space where unimodal, bimodal and trimodal waves co-exist. Nevertheless, the asymptotic model cannot capture the dynamics for a sufficiently strong unstable density stratification when interfacial break-up and eventual dripping occurs. In this case, complicated interfacial dynamics arise from the dominance of the gravitational force over the shear force due to the underlying flow, and this is investigated in detail using DNS.

Asymptotics of the Spectrum of One-Dimensional Natural Vibrations in a Layered Medium Consisting of Viscoelastic Material and Viscous Fluid

The spectrum of one-dimensional natural vibrations propagating through a two-phase layered medium in the direction of the normal to the layers is investigated. The medium considered consists of many periodically alternating layers of isotropic viscoelastic material and viscous compressible fluid. It is found that the spectrum mentioned above consists of the roots of transcendental equations whose number is proportional to the number of the layers of original medium. As the initial approximations of the roots for solving these equations numerically, it is proposed to use the points of the spectrum of one-dimensional natural vibrations of the corresponding homogenized medium. These points represent the roots of linear fractional equations. It is shown that the points at which the denominators of fractions in the linear fractional equations vanish should be also taken as the initial approximations. The accuracy of the initial approximations is proved to increase when the number of layers of the original medium increases and the layer thickness decreases simultaneously.

Experimental study on the cavity dynamics of oblique impact of sphere on a viscous liquid floating on water

Abstract Oblique water entry of marine structure involves complex hydrodynamics phenomena including splash formation, asymmetrical cavity and pinch-off that have been observed in previous systematic experiments. However, very few studies focus on such phenomena induced by oblique impact of object in a two-layer liquid system. In this paper, we present an experimental investigation of oblique entry of a sphere into a deep pool of water within a layer of highly viscous dimethicone floating on the water. In the experiment, a high speed digital camera is established to obtain the instantaneous cavity and motion trajectories for both qualitative and quantitative analysis. The results show that the upper-layer viscous liquid introduces a significant change in the splash formation mechanism and the special behaviors are characterized by stratified splash and corresponding asymmetrical shrinkage structures. Meanwhile, it is observed that the difference in splash characteristics caused by different thicknesses of viscous fluid layer is obvious, and the pinch-off depth is independent of the thickness value which studied in our experiments. In addition, it is found that increasing the horizontal impact velocity will cause a delay in the splash closure and the vertical displacement of the sphere during the dimethicone-water enter process is independent of the horizontal impact velocity. Hydrodynamic force model is established to explain the trajectory of the sphere. Furthermore, the splash angle, pinch-off depth, pinch-off time and the water entry depth at pinch-off locations and the corresponding change tendency are obtained qualitatively and quantitatively. These results indicate that the dimethicone layer is critical in determining the cavity dynamics, especially splash formation and pinch-off characteristics.

Analysis and computations of a non-local thin-film model for two-fluid shear driven flows.

This paper is concerned with analysis and computations of a non-local thin-film model developed in Kalogirou & Papageorgiou (J. Fluid Mech. 802, 5-36, 2016) for a perturbed two-layer Couette flow when the thickness of the more viscous fluid layer next to the stationary wall is small compared to the thickness of the less viscous fluid. Travelling wave solutions and their stability are determined numerically, and secondary bifurcation points are identified in the process. We also determine regions in parameter space where bistability is observed with two branches being linearly stable at the same time. The travelling wave solutions are mathematically justified through a quasi-solution analysis in a neighbourhood of an empirically constructed approximate solution. This relies in part on precise asymptotics of integrals of Airy functions for large wave numbers. The primary bifurcation about the trivial state is shown rigorously to be supercritical, and the dependence of bifurcation points, as a function of Reynolds number R and the primary wavelength 2πν -1/2 of the disturbance, is determined analytically.

A viscous magnetohydrodynamic Kelvin–Helmholtz instability in the interface of two fluid layer: Part II. An application to the atmosphere of the Sun

The main aim of this submission is to investigate the effects of some parameters like wave number, shear velocity, magnetic field and temperature for the growth rate of the magnetized Kelvin-Helmholtz instability (KHI) with incessant profiles through interface of two viscous fluid layer occurred in the solar atmosphere using the model of Hoshoudy, Cavus and Mahdy (2019). In this examination, the presence of KHI is identified for the various cases of wave number, magnetic field, shear velocity and temperature in the solar atmosphere. The sensible values of these parameters were acquired.

On the nonlinear stability of the thermodiffusive equilibrium for the magnetic Bénard problem

In this paper we study the nonlinear Lyapunov stability of the termodiffusive equilibrium of a viscous electroconducting horizontal fluid layer heated from below. We reformulate the nonlinear stability problem, in terms of poloidal and toroidal fields, by projecting the initial perturbation evolution equations on some suitable orthogonal subspaces of the kinematically admissible functions. In such a way, if the principle of exchange of stabilities holds, we obtain, in the classical L 2 -norm, the coincidence of linear and nonlinear stability bounds.

Asymptotic analysis of a viscous fluid layer separated by a thin stiff stratified elastic plate

A three-dimensional model for a viscous fluid layer separated in two parts by a thin stratified stiff plate is considered. This problem depends on a small parameter ϵ, which is the ratio of the thickness of the plate and that of each of the two parts of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate's Young modulus is of order , i.e. it is great, while its density is of order 1. At the solid–fluid interfaces, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is established for the partial sums of the asymptotic expansion. The limit problem contains a non-standard interface condition for the Stokes equations. The existence, uniqueness and regularity of its solution are proved.

A viscous magnetohydrodynamic Kelvin–Helmholtz instability in the interface of two fluid layers: Part I. Basic mechanism

This study investigates the combined effect of density, velocity and magnetic field gradients on the Kelvin–Helmholtz instability of two viscous fluid layers. For the linear phase of instability that refers to the early stage of development of Kelvin–Helmholtz instability, the linear growth rate and frequency are presented. With respect to our selected variables and the Atwood number, the behaviour of growth rate and frequency are analysed. It is found that, the behaviour of frequency is not affected by the magnetic field and viscous term. The velocity gradient with the small Atwood numbers tends to stabilize KHI flows, while the velocity gradient with the large Atwood numbers has destabilizing effect on KHI. The growth rate reduces with the constant magnetic field and viscous term, while it enhances with magnetic field gradient.

Virtual wave stress and transient mean drift in spatially damped long interfacial waves

Abstract The mean drift in spatially damped long gravity waves at the boundary between two layers of immiscible viscous fluids is investigated theoretically by applying a Lagrangian description of motion. The focus of the paper is on the development of the drift near the interface. The initial drift (inviscid Stokes drift + viscous boundary-layer terms) associated with the instantaneously imposed wave field does not generally fulfill the conditions at the common boundary between the layers. Hence, transient Eulerian mean currents develop on both sides of the interface to ensure continuity of velocities and viscous stresses. The development of strong jet-like Eulerian currents increasing with time in this problem is related to the action of the virtual wave stress (VWS). Very soon (after a few wave periods) the transient Eulerian part dominates in the Lagrangian mean current. This effect is similar to that found for the drift in short gravity waves with a film-covered surface. A new relation is derived showing that the difference between the VWS’s at the interface is given by the divergence of the total horizontal wave momentum flux in a two-layer system. Our analysis with spatially damped waves also yields the Lagrangian change of the mean surface level and mean interfacial level (the divergence effect) due to periodic baroclinic wave motion.

Hydroelastic response of three-layered beam resting on winkler foundation

The hydroelastic oscillations problem of the sandwich beam resting on elastic foundation and interacting with the pulsating fluid layer was investigated. The three-layered beam with an incompressible lightweight filler was considered. The broken normal hypothesis for the three-layered beam and the model of viscous incompressible fluid, as well as Winkler model for elastic foundation, was chosen to study hyroelastic problem. A mathematical model of the considered mechanical system consists of dynamic equations of the three-layered beam with incompressible lightweight filler and the Navier-Stokes equations with continuity equation for the pulsating viscous fluid layer. The no-slip conditions and pressure coincidence at the edges with the given pressure into edges cavities were selected as boundary ones. The plane problem of hydroelastic beam bending oscillations for the regime of steady harmonic ones were considered. The solution of the hydroelastic problem was carried out by the perturbations method using proposed small parameters of the hydroelastic problem. As a result, the laws of three-layered beam elastic deflections and the hydrodynamic parameters of pulsating viscous fluid layer were obtained.

Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants

In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present both at the free surface and in the bulk of the fluid, and that conversion from one species to the other is possible. The surfactants couple to the fluid dynamics through the coefficient of surface tension, which depends on the surface density of surfactants. Gradients in this concentration give rise to Marangoni stress on the free surface. In turn, the fluid advects the surfactants and distorts their concentration through geometric distortions of the free surface. We model the surfactants in a way that allows absorption and desorption of surfactant between the surface and bulk. We prove that small perturbations of the equilibrium solutions give rise to global-in-time solutions that decay to equilibrium at an exponential rate. This establishes the asymptotic stability of the equilibrium solutions.

Об акустических волнах в слое вязкой жидкости, взаимодействующем с упругим полупространством

Об акустических волнах в слое вязкой жидкости, взаимодействующем с упругим полупространством