Flow Of Thin Liquid Film Research Articles

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.

Flow of Thin Liquid Film on an Inclined Solid Surface

Flow of Thin Liquid Film on an Inclined Solid Surface

Numerical and experimental studies of thin liquid film flow between two forward-rollers

Roll coating is a widely used industrial technique to deposit a thin and uniform liquid film on a sheet or solid substrate. In this paper the three dimensional forward roll coating process has been studied by both experiments and numerical simulations. Experiments were conducted on a 2 roll coating system of pick up roll and application roll using two samples of 50% and 70% by weight aqueous glycerin solutions. The gap between the two rollers at nip was maintained at 100 microns. The coating film thickness and the distance of the film splitting point from the nip were measured during the experiments. The coating film thickness was determined for different speed ratios for both samples. 3D Numerical simulations for forward coating process have been carried out and the simulation results were verified were with experiments. They match very well, the error between them being 5% to 10%.

Flow in Inclined Thin Liquid Films with no Inertia Force

In this paper we have investigated viscous flow in symmetric thin liquid films which are inclined by an inclination angle to the horizontal for an incompressible liquids in two dimensions with no inertia force. We use the (Navier-Stocks) equations and we obtain equations that govern such flow and we solved these equations by numerical methods to obtain the thickness of the film.

A numerical model for the thermocapillary flow and heat transfer in a thin liquid film on a microstructured wall

PurposeThis paper aims to study thermocapillarity‐induced flow of thin liquid films covering heated horizontal walls with 2D topography.Design/methodology/approachA numerical model based on the 2D solution of heat and fluid flow within the liquid film, the gas above the film and the structured wall is developed. The full Navier‐Stokes equations are solved and coupled with the energy equation by a finite difference algorithm. The movable gas‐liquid interface is tracked by means of the volume‐of‐fluid method. The model is validated by comparison with theoretical and experimental data showing a good agreement.FindingsIt is demonstrated that convective motion within a film on a structured wall exists at any nonzero Marangoni number. The motion is caused by surface tension gradients induced by temperature differences at the gas‐liquid interface due to the spatial structure of the heated wall. These simulations predict that the maximal flow velocity is practically independent from the film thickness, and increases with increasing temperature difference between the wall and the surrounding gas. It is found that an abrupt change in wall temperature causes rupture of the liquid film. The thermocapillary convection notably enhances heat transfer in liquid films on heated structured walls.Research limitations/implicationsOur solutions are restricted to the case of periodic wall structure, and the flow is enforced to be periodic with a period equal to that of the wall.Practical implicationsThe reported results are useful for design of the heat transfer equipment.Originality/valueNew effects in thermocapillary convection are presented and studied using a developed numerical model.

Nucleate boiling heat transfer: possibilities and limitations of theoretical analysis

The paper considers the different ways of nucleate boiling investigation, and in particular, presents the analysis of the latest numerical studies of the nucleate boiling primary processes (isolated bubble growth, thin liquid film flow and evaporation near the nucleation site). Many features of the process that were only the hypothesis became established facts after the direct numerical simulation. However, in spite of their undoubted usefulness these investigations cannot be applied for practical calculations. The high complexity of the phenomena comprising nucleate boiling excludes practically the possibility of strict theoretical analysis of the process. Under this situation development of an approximate theory of nucleate boiling retains its validity at present. Such a theory has been developed by the author in 1988. It reveals the main regularities of the nucleate boiling and leads to the predicting equation for heat transfer, which includes two empirical numerical factors. On the basis of the model developed the method of calculation of heat transfer in boiling of binary mixtures is proposed. To improve the existing predicting equations for boiling heat transfer it seems to be especially important to ground theoretically the nucleation sites density dependence on the wall superheat and liquid properties.

Gas absorption in a thin liquid film flow on a horizontal rotating disk

An analytical model for the rate of gas absorption into laminar non-wavy film flow on a horizontal rotating disk is obtained assuming short contact times. Literature data for the oxygen mass transfer coefficient in a wavy film is correlated by means of the dimensionless numbers deriving from the model. The rate enhancement due to waves is found to vary from 6 to 13 times. It is established that the absorption process in the film on the disk as compared to that in a gravitational wavy film flow can be intensified up to 14 times by means of a moderate rotation speed.

Effect of Hydraulic Jump on Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk Analyzed by Integral Method

Flow and heat transfer in a liquid film flowing over the surface of a rotating disk was analyzed by integral technique. The integral analysis includes the prediction of the hydraulic jump and its effects on heat transfer. The results of this analysis are compared to the earlier results that did not include this effect. At low inlet Reynolds numbers and high Rossby numbers, corresponding to low film inertia and low rotation rates, respectively, a hydraulic jump appears on the disk surface. The location of the jump and the liquid film height at this location are predicted. A scaling analysis of the equations governing the film thickness provided a semi-empirical expression for these quantities that was found to be in very good agreement with numerical results. Heat transfer analysis shows that the Nusselt numbers for both constant disk surface temperature and constant disk surface heat flux boundary conditions are lowered in the vicinity of the hydraulic jump due to the thickened liquid film. This effect can be more pronounced for the constant heat flux case depending on the location of the hydraulic jump. The Nusselt number exhibits a turning point at the jump location and can have higher values downstream of the hydraulic jump compared to those obtained from the analysis that does not include the gravitational effects.

Effect of nanoscale bubbles on viscous flow and rupture in thin liquid films

Nanoscale bubbles between a thin liquid film and a hydrophobic solid substrate affect rupture by relaxing the no-slip boundary condition for the viscous flow in the liquid. They also cause appreciable changes in the shape of the flow domain and the value of disjoining pressure when the film thickness is comparable to the bubble size. We investigate all three effects systematically for a single gas bubble on the substrate under the liquid film in the framework of a lubrication-type model. A scaling law for film thickness versus time is found, but the scaling exponent is different from the case when no bubble is present. Rupture time is studied as a function of bubble size and disjoining pressure parameters. Presence of bubbles is shown to significantly decrease rupture time and can also be the cause of instability and rupture in otherwise stable films.

Transient film profile of thin liquid film flow on a stretching surface

In this paper we have studied a non-planar thin liquid film flow on a planar stretching surface. The stretching surface is assumed to stretch impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar flow on the stretching surface are solved analytically. It is observed that faster stretching causes quicker thinning of the film on the stretching surface. Velocity distribution in the liquid film and the transient film profile as functions of time are obtained.

Analysis of Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk by the Integral Method

An integral analysis of hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk surface is presented for both constant temperature and constant heat flux boundary conditions. The model is found to capture the correct trends of the liquid film thickness variation over the disk surface and compare reasonably well with experimental results over the range of Reynolds and Rossby numbers covering both inertia and rotation dominated regimes. Nusselt number variation over the disk surface shows two types of behavior. At low rotation rates, the Nusselt number exhibits a radial decay with Nusselt number magnitudes increasing with higher inlet Reynolds number for both constant wall temperature and heat flux cases. At high rotation rates, the Nusselt number profiles exhibit a peak whose location advances radially outward with increasing film Reynolds number or inertia. The results also compare favorably with the full numerical simulation results from an earlier study as well as with the reported experimental results.

Dynamics of a thin film with temperature-dependent viscosity on a rotating disk

The thermal effects on the dynamics of an axisymmetric flow of a non-volatile incompressible viscous thin liquid film on a rotating disk due to viscosity variation depending exponentially on temperature are considered. The nonlinear evolution equation is solved numerically. The numerical results reveal that heating the film from below enhances the rate of thinning. The increase in Biot number increases the film thickness, when the film is heated from below. Further, the relative amount of fluid retained on the substrate decreases as the film is heated from below. The results are reversed for the case of a film which is cooled from below. The rate of thinning of the film is more (less) for the case of temperature dependent viscosity when the film is heated (cooled) from below than for the case of constant viscosity of the fluid.

The flow of thin liquid films over spinning disks: Hydrodynamics and mass transfer

We study the hydrodynamics and mass transfer associated with gas absorption into a thin liquid film flowing over a spinning disk. We use the thin-layer approximation in conjunction with the Karman–Polhausen method to derive evolution equations for the film thickness and the volumetric flow rates in the radial and azimuthal directions. We also use the integral balance method to derive evolution equations for the thickness of the diffusion boundary layer as well as the concentration of solute at the disk surface. Numerical solutions of these partial differential equations, which govern the hydrodynamics and the associated mass transfer, reveal the formation of large finite-amplitude waves and elucidate their significant effect on the mass-transfer characteristics. We illustrate this dependence quantitatively by examining the effect of system parameters on the time-averaged and spatially averaged Sherwood numbers. The results are assessed by comparison with computations of the parabolized convective diffusion equation and experimental data.

Thermocapillarity-induced vortexes and liquid film dynamics on structured heated walls

Thermocapillarity-induced flow and evolution of thin liquid films on horizontal structured heated walls are studied theoretically and numerically. The steady deformation of the liquid–gas interface and the vortex flow pattern within the film are predicted for the steady continuous films in the case of grooved walls. The effect of the thickness of the gas layer above the film on the film deformation is quantified. A linear stability analysis of the film is performed. The dynamics of film evolution toward rupture is simulated numerically in the framework of the long-wave theory. The effect of the wall topography on the rupture time and on the film topology at the moment just before rupture is studied. The long-wave model is verified by comparison with full-scale numerical simulations using the volume of fluid method.

Waves and Ripples in Liquid Films

In this paper we present a mathematical model for two- dimensional incompressible flow in a symmetric thin liquid films with the viscosity forces, which can be very small, compared with surface tension and inertia forces. We obtain the governing differential equation for such flow, we also determine the solution of equations and also we consider an inviscid waves in thin films.

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver.Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography.Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function.An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.

Experiments on Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk

An experimental study of heat transfer into a thin liquid film on a rotating heated disk is described. Deionized water was introduced at the center of a heated, horizontal disk with a constant film thickness and uniform radial velocity. Radial distribution of the disk surface temperatures was measured using a thermocouple/slip ring arrangement. Experiments were performed for a range of liquid flow rates between 3.0 lpm and 15.0 lpm. The angular speed of the disk was varied from 0 rpm to 500 rpm. The local heat transfer coefficient was determined based on the heat flux supplied to the disk and the temperature difference between the measured disk surface temperature and the liquid entrance temperature onto the disk. The local heat transfer coefficient was seen to increase with increasing flow rate as well as increasing angular velocity of the disk. Effect of rotation on heat transfer was largest for the lower liquid flow rates with the effect gradually decreasing with increasing liquid flow rates. Semi-empirical correlations are presented in this study for the local and average Nusselt numbers.

Steady and traveling flows of a power-law liquid over an incline

The slow flow of thin liquid films on solid surfaces is an important phenomenon in nature and in industrial processes, and an intensive effort has been made to investigate it. So far research has been focused mainly on Newtonian fluids, notwithstanding that often in the real situations as well as in the experiments, the rheology of the involved liquid is non-Newtonian. In this paper we investigate within the lubrication approximation the family of traveling wave solutions describing the flow of a power-law liquid on an incline. We derive general formulae for the traveling waves, that can be of several kinds according to the value of the propagation velocity c and of an integration constant j 0 related to the difference between c and the averaged velocity of the fluid u. There are exactly 17 different kinds of solutions. Five of them are the steady solutions ( c=0). In addition there are eight solutions that correspond to different downslope traveling waves, and four that describe waves traveling upslope.

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5⩽ Q⩽2 ml/s), rotation rates f (33⩽ f⩽100 Hz), and volume concentrations ρ s of the surface active protein BSA (10 −4⩽ ρ s ⩽4×10 −4 wt%) in the far field of large radii r (11⩽ r⩽25 cm). With these parameters, ranges of the Reynolds number Re (0.48⩽ Re⩽4.3), Weber number We (22.3⩽ We⩽1,410), and surface elasticity numbers ζ or E (0.02⩽ ζ⩽62; 0.1⩽ E⩽1.4) were covered. The ratio Re/ Re crit varied between values ⪡1 and 15,000. Surface waves were induced with a constant gas jet directed onto the rotating liquid film in order to investigate their propagation velocities. Measured data are in fairly good agreement with linear and nonlinear theories. The damping effect of surfactants was studied using self-excited waves. It could be shown that the adsorbing monolayer is not in thermodynamic equilibrium at small radii r, but approaches equilibrium at larger r. Assuming the validity of linear stability theory with respect to wave damping, the adsorption kinetics of BSA on the flowing film could be traced. The determination of the transition radius from wavy to smooth film surfaces provides a tool to estimate local film pressures in situ.

Thin film of non-Newtonian fluid on an incline.

The slow flow of thin liquid films on solid surfaces is an important phenomenon in nature and in industrial processes, and an intensive effort has been made to investigate it. It is well known that the contact line of currents on an inclined surface may become unstable and then a pattern of "fingers" develops that affects the quality of the coatings. This instability has been intensively studied due to its relevance for the technology of various industrial processes. So far the theoretical and numerical research has been focused on Newtonian fluids, notwithstanding that often in the real situations as well as in the experiments, the rheology of the involved liquid is non-Newtonian. Using the lubrication approximation, we derive the governing equations for a current of a power law non-Newtonian fluid on an inclined plane under the action of gravity and the viscous stresses. We show that surface tension effects can be included in the theory by a slight modification of the governing equations, that can then be used as a starting point to investigate the influence of rheology on the fingering instability and other phenomena of interest. We consider the one-dimensional case and we present three families of traveling wave solutions: two running downwards and the other upwards.