Experiments on the flow of a thin liquid film over a horizontal stationary and rotating disk surface

Experiments on characterization of thin liquid films flowing over stationary and rotating disk surfaces are described. The thin liquid film was created by introducing deionized water from a flow collar at the center of an aluminum disk with a known initial film thickness and uniform radial velocity. Radial film thickness distribution was measured using a non-intrusive laser light interface reflection technique that enabled the measurement of the instantaneous film thickness over a finite segment of the disk. Experiments were performed for a range of flow rates between 3.0 lpm and 15.0 lpm, corresponding to Reynolds numbers based on the liquid inlet gap height and velocity between 238 and 1,188. The angular speed of the disk was varied from 0 rpm to 300 rpm. When the disk was stationary, a circular hydraulic jump was present in the liquid film. The liquid-film thickness in the subcritical region (downstream of the hydraulic jump) was an order of magnitude greater than that in the supercritical region (upstream of the hydraulic jump) which was of the order of 0.3 mm. As the Reynolds number increased, the hydraulic jump migrated toward the edge of the disk. In the case of rotation, the liquid-film thickness exhibited a maximum on the disk surface. The liquid-film inertia and friction influenced the inner region where the film thickness progressively increased. The outer region where the film thickness decreased was primarily affected by the centrifugal forces. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. At high rotational speeds, spiral waves were observed on the liquid film. It was also determined that the angle of the waves which form on the liquid surface was a function of the ratio of local radial to tangential velocity.     

Diffusion to a particle covered with a liquid film

Formulas are established for calculating the influx of a substance to the surface of a liquid film on a particle in a laminar flow of an incompressible liquid with small Reynolds numbers. It is assumed that there is complete absorption of the diffusing substance at the surface of the film. An expression derived in [1] is used to solve the problem of the field of the flow velocities. The results obtained generalize expressions for the influx of substance to a drop found in [2].     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

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.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Mass transfer with gas desorption from the surface of a liquid film in the presence of a cocurrent flow

Results of a thcoretical and experimental study of dynamics and mass transfer during desorption of a gas from a liquid film in the presence of a cocurrent air flow are presented. The calculation model is based on solving integral momentum and diffusion relations for the gaseous and liquid phascs. Both laminar and turbulent regimes of the film flow are analyzed. The experimental study of mass transfer was conducted for carbon dioxide desorption from a water film. Criterial relations for mass transfer in the gaseous and liquid phases are obtained. The experiments showed that the heat-transfer coefficients for the case under study are one order of magnitude grcater than those for the flow of a smooth film. Possible mechanisms of such an appreciable intensification of the liquid-film mass transfer in a cocurrent gas flow are discussed. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 131–138, July–August, 2000.     

Shear flow over a porous particle

Linear axisymmetric Stokes flow over a porous spherical particle is investigated. An exact analytic solution for the fluid velocity components and the pressure inside and outside the porous particle is obtained. The solution is generalized to include the cases of arbitrary three-dimensional linear shear flow as well as translational-shear Stokes flow. As the permeability of the particle tends to zero, the solutions obtained go over into the corresponding solutions for an impermeable particle. The problem of translational Stokes flow around a spherical drop (in the limit a gas bubble or an impermeable sphere) was considered, for example, in [1,2]. A solution of the problem of translational Stokes flow over a porous spherical particle was given in [3]. Linear shear-strain Stokes flow over a spherical drop was investigated in [2].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–120, May–June, 1995.     

Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

Magnetohydrodynamic laminar boundary-layer flow over a porous wedge with thermophoresis particle deposition in the presence of variable stream conditions

An analysis is presented to investigate the effects of thermophoresis variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by local non-similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Capillary effects on a particle rolling on a plane surface in the presence of a thin liquid film

An experimental study has been performed of the effects of a liquid film on a particle rolling on a planar surface using a combination of laser-induced fluorescence and particle-image velocimetry. Contact angle hysteresis leads to asymmetry of the liquid meniscus, resulting in a difference in contact angle between the front and rear sections of the meniscus relative to the rolling particle. This asymmetry results in a capillary torque that resists the rolling motion of the particle. The particle rolling motion also induces a viscous transport of fluid from the front to the rear of the particle, which acts to shift the location of the contact point. The laser-induced fluorescence method is used to characterize the meniscus asymmetry and the resulting change in contact angle on the two sides of the particle. Particle-image velocimetry in various horizontal and vertical cross-sectional planes is used to examine the flow trajectories and velocity magnitude within the meniscus in the presence of rolling. All experiments are conducted at small capillary number, so that the meniscus is approximately circular in shape.     

Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.     

Hydro-thermodynamics of a liquid film with crystals on the body surface in an air flow containing ice particles

This paper presents a physicomathematical model for the effect of air flow containing ice crystals on a water film moving along the surface of a solid body. Numerical studies were carried out for the case of a cylinder in transverse flow. The influence of the effective viscosity of the suspension of crystals in the carrier water and the finite time of their melting on the hydro-thermodynamics of the solidifying film. In this case, the employed model is nonlocal.     

Advective flow in a rotating liquid film

This paper presents a new exact solution of the Navier–Stokes equations in the Boussinesq approximation that describes thermocapillary advective flow in a slowly rotating horizontal layer of incompressible fluid with free boundaries. Such flow occurs in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution at the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.     

Detached flow over a step with the formation of a turbulent wake

A method of calculating the plane turbulent layer behind a step interacting with a free potential flow of incompressible fluid is developed. The method includes consideration of the initial boundary layer and injection (or suction) in the isobaric bottom region. Friction on the wall behind the step is neglected, which corresponds to symmetric quasisteady flow behind the straight edge of a plate. The inviscid flow is represented by the Keldysh-Sedov integral equations; the flow in the wake with a one-parameter velocity profile is represented by three first-order differential equations—the equations of momentum for the wake and motion along its axis and the equation of interaction (through the displacement thickness) of the viscous flow with the external potential flow. The turbulent friction in the wake is given, accurate to the single empirical constant, by the Prandtl equation. The different flow regions — on the plate behind the step, the isobaric bottom region, and the wake region — are joined with the aid of the quasi-one-dimensional momentum equation for viscous flow. The momentum equation for the flow as a whole serves as the closure condition. The obtained integrodifferential system of equations is approximated by a system of nonlinear finite-difference equations, whose solution is obtained on a computer by minimization of the sum of the squares of the discrepancies. The results of the calculations agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1977.We are grateful to V. I. Kuptsov for consultation and help in programming and to Z. A. Donskova who assisted in the calculations and preparation of the paper.     

Three-dimensional surface characteristics of a falling liquid film

Optical methods are described for examining the three-dimensional character of waves on a falling liquid film. This involved monitoring the motion of the local film surface normal through the use of laser beam refraction. The wavy motion was found to be primarily of a two-dimensional nature only for Re (equal to 4Q/v) less than 1500.

Surface characteristics were examined for Reynolds numbers from 217 to 4030 and for different distances along the direction of flow.