Horizontal Liquid Layer Research Articles

Experimental determination of the critical rayleigh number in electrolyte solutions with concentration polarization

The hydrodynamic stability problem with respect to natural convection in a horizontal liquid layer of liquid electrolytes exhibiting concentration polarization only has been investigated in aqueous solutions of copper sulphate at room temperature. The stability of the system is determined by the value of the modified Rayleigh number. The critical value of this number calculated theoretically is 1707. The value determined experimentally is lower, 1130 ± 210.

Investigation of the occurrence of convection in horizontal liquid layers

The occurrence of convection in horizontal layers of ethanol, distilled water, and ethylene glycol heated from below was investigated by the interferometric method. The limits of roller-type convection and its effect on the magnitude of heat flux through the layer were determined.

Mass transfer into a horizontal layer of stagnant liquid under the action of instabilities+

AbstractThe rate of absorption into a horizontal liquid layer undergoing an assumed steady cellular convection due to a concentration gradient or to the Marangoni effect is calculated. One concludes that a roll‐cell model can explain the large increase in the rate of absorption observed experimentally and that for large times a diffusional model, with a constant diffusion coefficient much larger than the molecular one, describes adequately the above situations.

Observed flow patterns at the initiation of convection in a horizontal liquid layer heated from below

An experimental investigation has been made of the flow patterns at the initiation of convection in a layer of a high Prandtl number liquid confined between rigid, horizontal surfaces and heated from below. The experiment was designed to overcome the limitations of earlier experiments and to correspond closely to the conditions of the theory. In particular, the upper and lower rigid surfaces which enclosed the layer were made of copper which has a high thermal conductivity. To aid in the analysis of the experimental results some supplementary observations of the flow patterns were made using a glass upper plate. For small fluid depths and large temperature differences between the upper and lower surface the initial flow was in the form of hexagonal cells as predicted theoretically. With increasing Rayleigh number the cellular flow appeared to transform into rolls as predicted. For large fluid depths and small temperature differences only circular plan-form rolls were observed. This is in agreement with the results of other experimenters. It is tentatively proposed that this non-appearance of an initial cellular flow is due to the shape of the test chamber having a dominating influence on the flow pattern when the temperature gradient in the fluid is small. Measurements were also made of the development time for the flow patterns and the critical Rayleigh number.

Thermal instability of a horizontal layer of liquid with maximum density

AbstractAn investigation is carried out to determine the onset of convection of a horizontal layer of liquid subject to temperature of T1 and T2 at lower and upper surfaces, respectively. The liquid is assumed to possess a maximum density value at Tmax with Tmax between T1 and T2. The temperature‐density relationship within the temperature range |T1 — T2| can be expressed as ρ = ρmax [1 — γ1 (T — Tmax)2 — γ2 (T — Tmax)3].Both rigid‐rigid and rigid‐free surface conditions were considered. The critical Rayleigh number defined in Equations (20) and (24) is found to be dependent upon two parameters.Experimental observations on the onset of convection were made and compared with the theoretical results. The experimental work consists of the measurement of the melting rate of a block of ice with melting from both below and above. In all cases, excellent agreement between experimental and theoretical results were obtained.

Thermocapillary convection in a horizontal layer of liquid

An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.

Experimental study of flow patterns and temperature fields in horizontal free convection liquid layers

Experimental study has been made of the hydrodynamic liquid flow patterns in horizontal layers up to Ra = 1·5 × 10 6; the temperature profiles over the cell volume and of cell sizes at various Ra and heights of bed. It is shown that near the horizontal heat-transfer surface with natural convection in a large volume an eddy cell flow exists. Ra number calculated based on the height of the cellular layer near the heat-transfer surface is experimentally determined for various boundary conditions. For various boundary conditions the Rayleigh number has been experimentally determined, based on the height of the cellular layer which exists close to the heat-transfer surface.

Instability of unsteady flows or configurations Part 1. Instability of a horizontal liquid layer on an oscillating plane

A layer of viscous liquid with a free surface is set in motion by the lower boundary moving simple-harmonically in its own plane. The stability of this motion is investigated. Since the primary flow is time-dependent, the time variable cannot be separated from at least one space variable, and a new approach must be used to investigate the problem. In this paper the stability of long waves is studied by a perturbation method which has not been applied before to problems of stability of unsteady flows, and it is found that the flow under consideration can be unstable for long waves.

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Mass transfer through horizontal liquid films in wavy motion

AbstractThe effect of standing waves of controlled amplitude and frequency on the steady state rate of mass transfer through thin horizontal liquid layers is studied experimentally. The variables studied are the film thickness, the amplitude and frequency of the waves, and the spacing between the probes generating the waves. A bulk motion of complicated pattern known as drift is caused by the finite amplitude of the waves. The rate of mass transfer in the absence of imposed vibration is two to three times greater than that expected by molecular diffusion alone. Vibration increases the rate up to an order of magnitude or more, depending on the hydrodynamic conditions. The data at low frequencies are correlated by an expression of the form (i‐io)/idiff = KAf3/4h1/2L−1/2.

Natural Convection in Horizontal Liquid Layers

Natural convection in horizontal layers is examined. The eigenvalue problem yielding the characteristic Rayleigh numbers for the first ten modes is solved using linear theory. The contribution to heat transfer is determined and compared with experiment.