Viscous Liquid Film Research Articles

Deflection of a viscous liquid curtain

Surface tension and shear stress are shown to cause a viscous liquid film falling from the edge of an inclined plane to deflect toward the underside of the plane.

Approximate Equations for Long Nonlinear Waves on a Viscous Fluid

A systematic perturbation method is applied to three-dimensional long waves on a viscous liquid film, and the nonlinear evolution equation incorporating the effects of dissipation and dispersion is derived. It is shown that both the fourth-order derivative term as well as the three-dimensionality have stabilizing effects.

Stability of flow of a thin layer of viscous magnetic liquid

The laminar flow of a thin layer of heavy viscous magnetic liquid down an inclined wall is examined. The stability and control of the flow of an ordinary liquid are affected only by alteration of the angle of inclination of the solid wall and the velocity of the adjacent gas flow. When magnetic liquids are used [1, 2], an effective method of flow control may be control of the magnetic field. By using magnetic fields of various configurations it is possible to control the flow of a thin film of viscous liquid, modify the stability of laminar film flow, and change the shape of the free surface of the laminarly flowing thin film, a factor which plays a role in mass transfer, whose rate depends on the phase contact surface area. The magnetic field significantly affects the shape of the free surface of a magnetic liquid [3, 4]. In this paper the velocity profile of a layer of viscous magnetic liquid adjoining a gas flow and flowing down an inclined solid wall in a uniform magnetic field is found. It is shown that the flow can be controlled by the magnetic field. The problem of stability of the flow is solved in a linear formulation in which perturbations of the magnetic field are taken into account. The stability condition is found. The flow stability is affected by the nonuniform nature of the field and also by its direction.

Stability of a liquid film with respect to initially finite three-dimensional disturbances

The nonlinear stability of a viscous liquid film flowing steadily down an inclined plane is studied in the phase plane. Explicit expressions of the critical points of the governing differential system are obtained. The nature of the critical points and the integral curves corresponding to various flow parameters, initial conditions, and disturbance characteristics are determined numerically. Based on the phase plane analysis and the numerical results, the following conclusions are reached: The film which is unstable according to linear theory may be stable with respect to a finite three-dimensional disturbance if the initial amplitude and the side-band width are sufficiently small. The particular values of the initial amplitude and the side-band width beyond which the film becomes unstable depend on the relevant flow parameters. The film which is stable according to linear theory is also shown to be stable with respect to three-dimensional small finite amplitude disturbances with finite bandwidths.

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.

An Instability for Parallel Sliding of Solid Surfaces Separated by a Viscous Liquid Film

Thermoelastic phenomena in lubricated face type seals are analyzed for possible instabilities which may lead to large surface deformations and seal failure. Thresholds of such instabilities are found where a small, steadily moving, surface disturbance will neither grow nor decay. For a good thermal conductor sliding on a good insulator, several such thresholds exist. Only one, however, falls within a reasonable operating range, the critical sliding speed being Ucrit=hκ¯KMμαM where h¯ is the nominal film-thickness, κ the wave number of the disturbance, KM the thermal conductivity of the conductor and αM its coefficient of thermal expansion, and μ the viscosity of the oil. Expressions are given for the approximate limits of h¯ within which such a threshold lies. Finally, it is shown that, as expected, a disturbance will grow when U > Ucrit and decay when U < Ucrit.

Spreading of an elliptical film of liquid under impact

The article deals with the impact on an elliptical film of liquid, with the effect of the film shape on the punch deceleration and on the velocity of liquid spreading, and with the stability of the process. The problem is solved for the case of a slowly flowing viscous liquid as well as for an ideal liquid, but with the inertia forces taken into account. The theory is found to agree with experimental data. The inertia-free spreading of a circular film of viscous liquid has already been studied by Reynolds [1]. Interest in this problem is being shown again in connection with certain aspects of lubrication, of the punch and die operation, and with the sensitivity analysis of liquid explosives [2, 3, 4, 5, 6, 7]. Several articles deal with the impact on a circular film [3, 4, 5, 6].

THE THICKNESS OF AVISCOUS LIQUID FILM ON A ROTATING DISK

Various theoretical solutions including the author''s for the thickness of a viscous liquid film on a rotating disk are presented in terms of two dimensionless parameters and are compared with experimental results. The film thickness on the disk was measured by a micrometer which is movable with a needle used as a surface detector. The numerical solution of the equations as simplified by von Karman''s method and Bruin''s solution agree well with the experimental results in a wide range of operating conditions. Polynomial approximation with orders up to fourth and fifth degree is usable to predict the film thickness.

Undular flow of an evaporating viscous liquid film under uniform injection

The wave profile on the free surface of a thin viscous liquid film flowing along a porous surface under uniform injection is established here by the asymptotic method which has been developed in [1, 2].

Steady-state small-amplitude waves on the surface of a viscous liquid film in a coflowing gas stream (inclined channel)

Steady-state small-amplitude waves on the surface of a viscous liquid film in a coflowing gas stream (inclined channel)

Waves on a thin film of viscous liquid

AbstractIn this paper we consider the problem of the flow of a viscous incompressible fluid down an inclined wall. A solution is obtained by assuming that the free surface is a wave of low frequency. The solution is numerical and the results are compared with existing theories and available experimental results.

The shape of the air interface during the formation of viscous liquid films by withdrawal

The thickness of a viscous liquid film on a sh et decreases exponentially to a constant value during withdrawal of the sheet from a bath. The steepness of this exponential decrease is calculated as a function of the eventual film thickness. The measured interface shape agrees with the theoretically expected shape. Die Dicke eines zähflüssigen Filmes auf einer Platte nimmt exponentiell ab während des Herausziehens der Platte aus einem Bad. Die Steilheit dieser Exponentialkurve wird in Abhähgigkeit von der jeweiligen Filmdicke errechnet. Die gemessene Form der Grenzschicht stimmt mit der theoretisch erwarteten Form überein.

Flow and heat transfer in a film of viscous liquid on a rotating disk

A numerical method employing a computer is used to investigate the hydrodynamics and heat transfer of a thin film of incompressible viscous liquid on a rotating disk for the case of laminar flow when it is possible to neglect surface tension, body forces, and friction between liquid film and gas medium.

A stream-line filter

Many years ago, when employing the method of stream-line motion with thin films of viscous liquid for investigating various problems, the author suggested the use of such films for studying chemical action and the deposition of matter from solution. In taking up the subject recently and employing in his laboratory a fairly large screen, so as to give great magnification with lantern projection, it was found possible, by giving certain forms to the channels in which the liquid was made to flow under pressure, to observe the behaviour of suspended matter and, further, to actually separate the coarser from the finer particles of the suspended material. When the film was reduced in thickness beyond a certain amount, say to 1/10,000 inch, or less not only was the matter in suspension prevented from entering, but the colour bands in the stream-lines became invisible. It was, at first, thought that this was due to the extreme attenuation of the colour. As a matter of fact, the liquid itself which passed through the film was found to have lost its colour.

Sound Colour-Figures

THE great interest excited by Prof. Bell's telephone and Mr. Eddison's phonograph, in which an elastic disc or membrane faithfully takes up the highly complex vibrations due to sounds of the human voice, has directed renewed attention to the optical methods hitherto employed in studying the motion of resonant media. These have, in important instances, been based on observations of the secondary effects produced by sonorously vibrating bodies. Thus Chladni watched the behaviour of sand strewn upon sounding plates and membranes; König that of gas flames acted on by aerial vibrations. The present article describes an analogous method depending on the colours reflected from slightly viscous liquid films when thrown into sonorous vibration.