Parallel Solid Plates Research Articles

The deformed oblate drop’s free translational oscillations

Free translational oscillations of deformable liquid droplet are considered. It is placed into a vessel filled with another liquid. This droplet has an equilibrium revolution shape. The revolution axis of this form is perpendicular two parallel solid plates – floor and cover of vessel. The arbitrary equilibrium contact angle between the interface and the solid substrate can take arbitrary values in the range 0 and π. A contact line velocity is linearly proportional to contact angle deviation from its initial position. Proportionality coefficients (Hocking’s parameters) are individual for any substrate. They characterize individual dissipation coefficient, but whole system’s dissipation is proportional to a sum of all coefficients. There are three characteristic natural frequency intervals for the case of small aspect ratio. High frequencies are the capillary wave frequencies at the interface. The middle frequency is the fundamental or main one. Low frequencies correspond to the drop oscillations with a stationary contact angle. The cylindrical droplet has the highest frequency.

The influence of difference in the surface properties on the axisymmetric oscillations of an oblate drop

The forced axisymmetric oscillations of an oblate fluid drop are investigated. A drop is cylindrical in equilibrium, surrounded by another liquid and bounded axially by two parallel solid plates. These plates have different surfaces. Hocking’s boundary conditions hold on the contact line: the velocity of the contact line motion is proportional to the deviation of the contact angle from its equilibrium value. The Hocking’s parameter (so-called wetting parameter) is the proportionality coefficient in this case and it is different for each plate. The vibration force is parallel to the symmetry axis of the drop. The solution of the boundary value problem is found using Fourier series of Laplace operator eigen functions.

Динамика зажатой капли в неоднородном электрическом поле

The forced oscillations of an incompressible liquid drop under the influence of an alternating electric field are considered. The drop is sandwiched between two homogeneous plates and surrounded by an incompressible fluid of a different density. In equilibrium, the drop has the shape of a circular cylinder which is bounded axially by parallel solid plates. These plates have different surface properties. An external electric field acts as an external force which is a reason of the motion of the contact line. A modified Hocking boundary condition is used to describe the motion of the contact line: the velocity of the contact line is proportional to the deviation of the contact angle and the rate of fast relaxation processes, the frequency of which is proportional to the doubled frequency of the electric field. Using this equation allows one to qualitatively describe the experimental dependence of the contact angle as a function of stress, in contrast to the Young – Lippmann equation. The solution to the problem is presented as a Fourier series expansion in eigen functions of the Laplace operator. Graphs of the amplitude-frequency characteristics and evolution of the drop shape are constructed for various values of the problem parameters. In the case of identical surfaces, only odd modes of droplet oscillations are excited, while for different surfaces, even harmonics additionally appear. It was found that in a wide range of parameters the shape of the side surface of the drop is close to the description by an odd function. The oscillation amplitude of even modes is significant only near resonances at the frequencies of these modes. In the case of an inhomogeneous field, azimuthal oscillations are excited, which leads to the appearance of additional resonance peaks. Travel waves propagate along the lateral surface of the drop, which are caused by vibrations of the contact line and the contact angle. The dependences of the values of the contact angle on the upper and lower surfaces on the square root of the amplitude for different values of the frequency of the electric field, which qualitatively coincide with similar graphs of experimental data, are constructed. It is possible to determine the parameters of the Hocking.

Fast liquid sheet and filament dynamics in the fluid splitting process

We consider the fluid splitting dynamics of a small fluid drop entrapped between two parallel solid plates, which are rapidly pulled apart such that a free liquid sheet is formed between them for a few milliseconds. Velocities, time scales and shear rates correspond to the lift-off of a printing cylinder from the substrate in an industrial printing process.The formation and collapse of the liquid sheets, and the filaments forming at their rim are studied. Driven by the surface tension of the liquid sheet, the filaments are accelerated towards each other, and finally collide and decay. We show that surface waves that travel on the liquid sheet have a critical impact on this collision, which may either result in a smooth unification or in a highly dynamical collapse, ending in a random emission of fluid drops. Furthermore, we discuss the relevance of the Laplace number on the propagation of these waves.We also consider the liquid sheet decay by capillarity-driven expansion of spontaneously forming holes and discuss how sheet thickness and its local variation can be detected by an anisotropic hole expansion rate measurement.

Control of the liquid jet formation through the symmetric and asymmetric collapse of a single bubble generated between two parallel solid plates

The liquid jet formation can be induced by the asymmetric collapse of the cavitation bubble located nearby boundaries. The jet translational direction and speed can be influenced by the type of the boundary, e.g. solid boundary, free surface or elastic boundary, and the relative locations of the cavitation bubble and the boundary. The mechanisms of the liquid jet formation of a single bubble generated between two parallel solid plates are investigated through the strobe photography experimental method and numerical simulations. It is found that there are two conditions for the bubble to split into two smaller bubbles, which could collapse respectively toward the boundary closer to them and form the liquid jet. The first condition is that the proportion of the maximum bubble diameter to the distance of the two plates, which is denoted as ρ, surpasses the threshold of 0.78. The distance of the bubble center to one of the plates, which is closer to the bubble, is denoted as d. The proportion of d to the maximum bubble radius is denoted as γ. The second condition is that γ surpasses the minimum value, which decreases from 1.1 to 0.3 as ρ grows from 0.78 to 1.35. The size of the separated bubble, that locates closer to one of the plates, decreases as the original bubble moves from the middle toward the other plate. Furthermore, it is found that the maximum jet speed of about 100 m/s appeared when the optimum relative bubble size equals to 1.09 and for the bubble located at the middle of the plates. Therefore, the jet speed and diameter could be adjusted by the relative size and generation position of the bubble between the plates. In this way, the laser energy can be controllably transformed into the directional mechanical force through bubble interactions with a pair of solid plates.

All-optical monitoring of acoustic waves guided by confined micro-fluidic layers

The study of the elastic properties of liquid micro-layers is of importance in biology and in micro-technology. Generation of the ultrasonic waves by sub-nanosecond pump laser provides opportunities for non-contact and non-destructive evaluation of materials at spatial scales from micrometer to a few tens of micrometers. Here, we report on the application of this all-optical technique for the study of acoustic properties of liquid layers of micrometric thickness confined by two parallel solid plates.

Thick-Film Deposition of High-Viscous Liquid Photopolymer

There are high interests among the researchers and industries for effective deposition of thick layer liquid photo-resists with applications such as fabrication of microfluidics and polymeric membranes using lithography. In this paper, we study performance of different techniques of coating for thick layers of SU-8 using spin coating, self planarization and a technique of sandwiching the resin between two parallel solid plates. Deposition using spin coaters for SU-8 2075 is limited hardly to around 250 µm with some irregularities such as edge-beads. Self-planarization requires enough resting time. We have achieved a thickness of around 1 mm in a single coating but is limited to only thick layers in reasonable time. The sandwich technique can be used for any thickness and is very fast. We present here a comparison of the three mentioned methods according to our observed data of the coating time, uniformity of the coating surface and capability of coating thick layers for a high viscosity SU-8 2075 that is employed in fabrication of microfluidics micro-structures.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Effect of confinement on the critical specific heat of liquid helium near the lambda point

Close study is devoted to the order-parameter fluctuations. When the temperature approaches the lambda-point temperature the magnitude of these fluctuations increases, leading to the divergence in the specific heat. When, on the other hand, the liquid helium is confined between parallel solid plates, the growth of the fluctuations is impeded and the divergence in the specific heat is suppressed. By an extension of the epsilon expansion to three-dimensional space we find good agreement between our calculation of the effect of confinement and the data from both earth-based and space experiments.

Transient viscous heating of liquid layers under intense shear

Viscous heating under high shear has been proposed as a possible cause for the accidental ignition of liquid monopropellants. A typical experiment consists of the rapid compression of a drop of liquid between two parallel solid plates. This process is simulated numerically by solving a boundary-layer version of the Navier-Stokes equations. It is found that allowing for the decrease of viscosity with increasing temperature leads to a major reduction in the estimated peak temperature. On the basis of these results, it would seem that accidental ignition by viscous heating is an unlikely event. The effect of wall slip is also briefly considered.

Stability of bounded rapid shear flows of a granular material

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

Dynamic contact angles

Abstract An apparatus and procedure is described for growing a bubble of one fluid with constant radial velocity between parallel solid plates, so displacing a second fluid. The process can be reversed, so that both advancing and receding angles can be studied as a function of the interfacial velocity. Results are given for the displacement of saturated air by water between siliconed glass plates at 22° and 42°C., and between polyethylene plates at 22°C. The displacement of a water-saturated hydrocarbon oil between siliconed glass plates by oil-saturated water, and by an aqueous potassium laurate solution, has also been studied at 22°C. In all systems, a definite dependence of the advancing and receding contact angles upon the interfacial velocity is found, except at very low speeds, and a provisional interpretation is given.

Properties of Sandwich-Type Structures as Acoustic Windows

The acoustic transmission of a sandwich consisting of a pair of plane parallel solid plates immersed in a liquid has been investigated theoretically and experimentally. Not only the dilatational waves, but also the shear waves, are considered. Results show greatly improved transmission characteristics over those of single thick metal plates with respect to dependence on both frequency and angle of incidence. Theoretical transmission curves for a sandwich of two steel plates have been prepared to exhibit the dependence of transmission on frequency, on ratio of plate thickness to wavelength and separation to wavelength, and on angle of incidence, respectively. Calculated transmission curves for single steel plates, including half-wave plates, are shown for comparison. An experimental test was made on a steel sandwich with lateral dimensions of the order of two wavelengths and plate thickness-to-wavelength (in the steel) ratio equal to 0.05. The measured transmission losses are within ±4 db of the calculated values.