Thin Fluid Layer Research Articles

Dispersion Forces between Metal and Dielectric Plates Separated by a Magnetic Fluid

The formalism of the Lifshitz theory has been used for determining the pressure exerted by dispersion forces between metal and dielectric plates separated by a thin layer of a magnetic fluid. Numerical calculations are performed for gold and quartz glass plates and the magnetic fluid consisting of kerosene and magnetite nanoparticles at room temperature. For this purpose, we have used familiar representations of dielectric properties of gold and quartz glass along the imaginary frequency axis; corresponding representations have also been obtained for magnetite and kerosene. The dispersion pressure has been analyzed as a function of the distance between the plates, the volume fraction of magnetite particles in the magnetic fluid, and their diameter. At large separations between the plates, simple analytic expressions for this pressure have been derived. Possible application of results has been considered.

Non-linear ring waves in a thin layer of magnetic fluid with variable thickness

Non-linear ring waves in a thin layer of magnetic fluid with variable thickness

Acousto-Optic Deflector with Heat Removal from the Piezotransducer by Sound Insulation of a Heat Radiator

A method is proposed for removing heat from the transducer of an acousto-optic deflector without substantial acoustic damping. The rear surface of the transducer and the heat–radiator surface are kept in contact through a thin sound-insulating fluid layer. The method is based on the considerable difference in the complex acoustic impedances for shear vibrations of fluids and a solid (the piezotransducer) by means of efficient heat transfer through the fluid. In the experiment, a continuous operation mode of the acousto-optic deflector is achieved with an acoustic wave intensity of more than 20 W/cm2. The acousto-optic deflector has been created that operates in the Bragg diffraction mode with a phase–modulation index of 3π with an input continuous controlling electric power of 3 W. The deflector characteristics for a light wavelength of 1.06 μm are as follows: diffraction efficiency no less than 90% in the 25 MHz frequency band at an absolute scanning angle of 40 mrad.

Frictional effect on stability of discontinuity interface in tangential velocity of a shallow-water flow

We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for U>8c, with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number U/c.

Marangoni instability in a heated viscoelastic liquid film: Long-wave versus short-wave perturbations.

We investigate the Marangoni instability in a thin layer of viscoelastic fluid, confined between its deformable free surface and a substrate of low thermal conductivity. Following a theoretical analysis, we study the stability of the present system for the case when the fluid layer is subjected to heating from below. Here, we use the Maxwell model to depict the rheology of the viscoelastic fluid. Linear stability analysis of the quiescent base state reveals that, in addition to the conventional short-wave mode, a long-wave instability can also emerge in this system. We demonstrate the appearance of both the long-wave monotonic and oscillatory instabilities in such a system. We study this long-wave mode analytically using the scaling k∼sqrt[Bi] (k is the wave number and Bi is the Biot number), whereas the short-wave mode is examined numerically. The influential role of elasticity of the fluid and the other involved parameters on the stability of the system is aptly discussed, and their ranges are identified within which a particular instability mode gets critical.

Marangoni convection of a viscous fluid over a vibrating plate

This research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge–Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented.

Orbiting of Flagellated Bacteria within a Thin Fluid Film around Micrometer-Sized Particles

Bacterial motility under confinement is relevant to both environmental control and the spread of infection. Here, we report observations on Escherichia coli, Enterobacter sp., Pseudomonas aeruginosa, and Bacillus subtilis when they are confined within a thin layer of water around dispersed micrometer-sized particles sprinkled over a semisolid agar gel. In this setting, E. coli and Enterobacteria orbit around the dispersed particles. The liquid layer is shaped like a shallow tent with its height at the center set by the seeding particle, and the meniscus profile set by the strong surface tension of water. The tent-shaped confinement and the left handedness of the flagellar filaments result in exclusively clockwise circular trajectories. The thin fluid layer is resilient because of a balance between evaporation and reinforcement of fluid that permeated out of the agar. The latter is driven by the Laplace pressure caused by the concave meniscus. In short, we explain the physical mechanism of a convenient method to entrap bacteria within localized thin fluid film near a permeable surface.

An Unusual Presentation of Tuberculosis

The normal pericardium is a fibroelastic sac containing a thin layer of fluid that surrounds the heart. Cardiac tamponade, which may be acute or subacute, is characterized by the accumulation of pericardial fluid under pressure. Tuberculous pericarditis is a complication of tuberculosis which is often diagnose late due to the difficulty in establishing this diagnosis. We present a case of pericardial tuberculosis diagnosed in a 20-year-old young retroviral disease patient who presented with signs of cardiac tamponade. His clinical condition improved post-pericardial tapping and he was discharged with antituberculosis medications. This case highlight the importance of having a high level of suspicion as this condition is easily curable.

Non-equilibrium thermodynamics beyond linearity: sliding friction

Nevertheless, sliding friction is frequent and it was the first irreversible process we were faced in the school, very rare effort has been aimed to develop its non-equilibrium thermodynamic theory if ever. The reason may be guessed as Coulomb’s (Amonton’s 3rd) law is often taught as if it where the final solution, even the velocity dependence of the friction force is rarely mentioned in textbooks or in papers, looking away from its direction. On the other hand, the phenomenon cannot be accounted with a linear theory even in the Onsagerian sense. Coulomb’s law displays a strong singularity at equilibrium, which is, at least, extremely rare in nature. On the ground of the thermodynamic theory of rheology, one can guess, that the singularity is virtual. The friction force does depend on the magnitude of the velocity and the function is continuous but it starts so steeply and falls back at practically very low values that to observe it is really difficult. If the two solids are separated by a thin layer of a non-Newtonian fluid the thermodynamic theory of the latter can be applied. This is not a nonsense; the independence of the friction force on the contact area is explained—by rather widely accepted ideas—with plastic flow of the materials at the surface region. In the last decades, the interest has increased and several theories was published and experimentally verified that explain friction and wear at different circumstances and the results are not like to each other nor to Coulomb’s law. Applying Onsager’s thermodynamics beyond the realm of linearity is more or less like guessing. Not a free brainstorm, but severely limited by observations. Here a germ of a thermodynamic theory is sketched without acquiring generality and restricted to stationary sliding. Here the most simple model is looked for to eliminate the gap between static and kinetic friction. It is not a complete idea at all—the transients have been put aside—but may be a guideline for further modeling. The fork the train of thoughts stops at gives way to several kinds of possibilities, a number of which—by the author's opinion—may have their own realm of application. Finally, an accurately accountable model is given that may be assumed friction if we pretend not knowing its origin and the law differs significantly from the nearly exclusively used Coulomb’s law. This example supports the idea that friction cannot be described in a simple and uniform theory.

A dam break driven by a moving source: a simple model for a powder snow avalanche

We study the two-dimensional, irrotational flow of an inviscid, incompressible fluid injected from a line source moving at constant speed along a horizontal boundary, into a second, immiscible, inviscid fluid of lower density. A semi-infinite, horizontal layer sustained by the moving source has previously been studied as a simple model for a powder snow avalanche, an example of an eruption current, Carroll et al. (Phys. Fluids, vol. 24, 2012, 066603). We show that with fluids of unequal densities, in a frame of reference moving with the source, no steady solution exists, and formulate an initial/boundary value problem that allows us to study the evolution of the flow. After considering the limit of small density difference, we study the fully nonlinear initial/boundary value problem and find that the flow at the head of the layer is effectively a dam break for the initial conditions that we have used. We study the dynamics of this in detail for small times using the method of matched asymptotic expansions. Finally, we solve the fully nonlinear free boundary problem numerically using an adaptive vortex blob method, after regularising the flow by modifying the initial interface to include a thin layer of the denser fluid that extends to infinity ahead of the source. We find that the disturbance of the interface in the linear theory develops into a dispersive shock in the fully nonlinear initial/boundary value problem, which then overturns. For sufficiently large Richardson number, overturning can also occur at the head of the layer.

Self-similar solution for power-law liquid flow down an inclined plane

Within the Stokes film approximation, unsteady plane-parallel spreading of a thin layer of a heavy non-Newtonian fluid along an inclined solid surface is studied. The forced spreading regime induced by mass supply is considered. An evolution equation for the film thickness is derived. The group classification problem is solved. Self-similar solution is constructed for the power time dependence on mass supply.

Controlling the diffusive boundary layer thickness above the sediment–water interface in a thermostated rotating‐disk reactor

AbstractThe diffusive boundary layer (DBL) is a thin layer of fluid at the interface with a solid surface in which frictional forces cause molecular diffusion to become the dominant mode of solute transport. The thickness of the DBL is a function of the nature and roughness of sediment substrates, as well as the bottom‐current speed. In low‐energy natural aquatic environments, such as abyssal plains or lakes, the thickness of the DBL can reach several millimeters and significantly impede the diffusive rate of solutes through the sediment–water interface (SWI). Thus, precisely reproducing the DBL in the laboratory is required to simulate benthic diffusive fluxes similar to those encountered in situ. Yet, an experimental apparatus allowing precise control of the DBL thickness at the SWI in the laboratory has not been described in the literature. Here, we present a simple temperature‐controlled rotating‐disk system, which is suitable for the use with natural sediments and that is capable of generating thick DBLs. Water overlying the rotating sediment can be sampled discretely or continuously to monitor the chemical reaction progress. We tested the validity of the reactor by dissolving a foraminiferal sand bed in natural seawater. We find that (1) measured dissolution fluxes agree with those predicted by theory and (2) the dissolution of calcite in these seafloor‐like hydrodynamic conditions is controlled by mass transfer across the DBL above the bed. Guidelines for best practices under various experimental conditions, possible future developments, and the theoretical equations to compute the DBL thickness and diffusive fluxes in this reactor are described.

Turbulent drag reduction by compliant lubricating layer

We propose a physically sound explanation for the drag reduction mechanism in a lubricated channel, a flow configuration in which an interface separates a thin layer of less-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{1}$) from a main layer of a more-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{2}$). To single out the effect of surface tension, we focus initially on two fluids having the same density and the same viscosity ($\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=1$), and we lower the viscosity of the lubricating layer down to $\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=0.25$, which corresponds to a physically realizable experimental set-up consisting of light oil and water. A database comprising original direct numerical simulations of two-phase flow channel turbulence is used to study the physical mechanisms driving drag reduction, which we report between 20 and 30 percent. The maximum drag reduction occurs when the two fluids have the same viscosity ($\unicode[STIX]{x1D706}=1$), and corresponds to the relaminarization of the lubricating layer. Decreasing the viscosity of the lubricating layer ($\unicode[STIX]{x1D706}<1$) induces a marginally decreased drag reduction, but also helps sustaining strong turbulence in the lubricating layer. This led us to infer two different mechanisms for the two drag-reduced systems, each of which is ultimately controlled by the outcome of the competition between viscous, inertial and surface tension forces.

Separated rows structure of vortex streets behind triangular objects

We discuss two distinct spatial structures of vortex streets. The ‘conventional mushroom’ structure is commonly discussed in many experimental studies, and the exotic ‘separated rows’ structure is characterized by a thin layer of irrotational fluid between two rows of vortices. In a two-dimensional soap film channel, we generate the exotic vortex arrangement by using triangular objects. This setting allows us to vary the thickness of boundary layers and their separation distance independently. We find that the separated rows structure appears only when the boundary layer is thinner than 40 % of the separation distance. We also discuss two physical mechanisms of the breakdown of vortex structures. The conventional mushroom structure decays due to the mixing, and the separated rows structure decays because its arrangement is hydrodynamically unstable.

Hydroelastic Oscillations of a Three-layer Plate Interacting with Vibrating Stamp

Longitudinal and bending oscillations of a three-layer plate interacting with vibrating stamp through a thin layer of a viscous incompressible fluid are investigated. We study the plane problem. The plate is considered as a three-layer package consisting of two bearing layers with an incompressible filler between them. The broken normal hypothesis is used to cinematically describe a three-layer package. A mathematical model including Navier-Stokes equations, continuity equation and three-layer plate dynamics equations with the corresponding boundary conditions is developed. No-slip conditions, pressure conditions at the channel edges and simply supported plate edges conditions are selected as boundary ones. The hydrodynamic parameters distribution laws of the liquid layer and the elastic displacements of the three-layer plate are found by mines of the perturbation method.

Hydroelastic Oscillations of a Three-layer Plate Interacting with Vibrating Stamp

Longitudinal and bending oscillations of a three-layer plate interacting with vibrating stamp through a thin layer of a viscous incompressible fluid are investigated. We study the plane problem. The plate is considered as a three-layer package consisting of two bearing layers with an incompressible filler between them. The broken normal hypothesis is used to cinematically describe a three-layer package. A mathematical model including Navier-Stokes equations, continuity equation and three-layer plate dynamics equations with the corresponding boundary conditions is developed. No-slip conditions, pressure conditions at the channel edges and simply supported plate edges conditions are selected as boundary ones. The hydrodynamic parameters distribution laws of the liquid layer and the elastic displacements of the three-layer plate are found by mines of the perturbation method.

Numerical Analysis of Lubrication Layer Characteristics in a Supporting Slider Bearing under Reverse Motion

A plane isothermal problem of the internal contact between elastic cylindrical bodies separated by a thin layer of a viscous lubricating fluid under constant load and reverse motion is considered. To determine the deformations of the contacting bodies, solutions of the plane problems of the elasticity theory for a cylinder and a space with a cylindrical cut are used. Extreme cases of low load, high load, small and long periods of reverse motion are considered. The dependences of lubricant layer thickness and pressure on the angular coordinate at different times, as well as the dependence of the eccentricity and the minimum lubricant layer thickness on time are presented. It is shown that the minimum lubricant layer thickness as a function of time exhibits a decrease when braking the cylinder and continues to decrease for some time after a change in the direction of rotation and an increase in speed. It has been established that at the times when the speed is low, under high loads, the gap has narrow spots at the boundaries of the high-pressure area, preventing the lubricant from leaking out of the gap. At a low load and a long period of reverse motion, the maximum pressure in the lubricant layer can increase more than twice.

Impacts of chemical reaction on MHD double diffusive flow with suction/blowing and slip

Unsteady double diffusive chemically reactive MHD thin fluid layer flow near the surface of an electrically conducting fluid with incompressibility past a flat surfaced plate is investigated by similarity analysis. The mathematically formulated PDEs are converted into ODEs by utilizing the similarity transforms. Then the numerical solution is determined for ODEs by operating Runge-Kutta method together with shooting technique. The impacts of varieties of parameters are scrutinized on stream velocity, energy distribution and solute dispensation through portraits. The inspection for the magnitude of local skin drag, rate of energy and solute transfer is executed through table.

Numerical study of the dynamics of a droplet in a T-junction microchannel using OpenFOAM

The mechanisms of droplet breakup in a Microfluidic T-junction are mainly influenced by the capillary number Ca and the ratio between the length of the droplet and the transverse dimension of the microchannel (lo/w). This work presents numerical simulations of an isolated Taylor droplet in a rectangular T-junction microchannel in the range of 0.0096 to 0.0904 of capillary numbers and viscosity ratio of the dispersed and continuous phases, that is, μd/μc=0.125. The numerical simulations were carried out with OpenFOAM 2.4 by using the S-CLSVOF methodology which was implemented for this study. The snappyHexMesh tool was used for grid refinement near the microchannel wall in order to correctly model the thin fluid layer between the wall and the drop. It was verified that in this range of the capillary numbers, parasitic currents could affect the dynamics of the droplet in the microchannel. The use of S-CLSVOF, the time step control and mesh resolution enabled a better capture of the interface dynamics. A mathematical correlation was obtained in the obstructed breakup regime for the dimensionless thickness of the droplet (δ/w) in relation to Ca, dimensionless time (τ∗=Udt/w) and droplet length (lo/w). Two types of non-obstructed breakup were observed in the simulations, namely, partially obstructed, and with permanent tunnel. The results showed that the mechanisms of a droplet breakup inside a T-junction are in good agreement with literature.

Rayleigh–Bénard convection with a melting boundary

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.