Falling Liquid Film Research Articles

Liquid Film Thickness in Vertical Circular Pipes Under Flooding Conditions at the Top End

In our previous study, we measured the void fraction α, pressure gradient dP/dz, and countercurrent flow limitation in a vertical circular pipe (diameter D = 20 mm) under flooding conditions at the square top end and working fluids of air and water to obtain the wall friction factor fw and the interfacial friction factor fi based on the annular flow model. The thickness of the falling liquid film δ obtained from the measured α was relatively well expressed by the correlation for the free-falling film, and the obtained fw was well expressed by the Fanning friction factor f for a circular pipe. Measurements of α in vertical pipes under flooding conditions are few. In this study, therefore, we evaluated α and δ from the measured dP/dz under flooding at the square top end reported by Bharathan et al. with D = 50.8 mm and air-water and by Ilyukhin et al. with D = 20 mm and working fluids of steam and water at pressures of P = 0.6 to 4.1 MPa. As a result, we found that δ obtained from the measured dP/dz and the correlation of fw = f were well correlated in terms of the liquid Reynolds number ReL. The obtained δ was well expressed by the Nusselt’s correlation for the free-falling film in the region of laminar flows, but the obtained δ was larger than the Feind’s correlation for the free-falling film in the region of turbulent flows due to the interfacial friction. We also discussed effects of the diameter and fluid properties on the interfacial friction factor fi.

Falling film thickness measurement using air-coupled ultrasonic transducer

In this work, a new, non-intrusive, increased sensitivity technique based on air-coupled ultrasonics was developed to measure the falling liquid film thickness. Air-coupled transducer of frequency 1 MHz was used to make static and dynamic measurements of water level/film thickness. The air-coupled method were compared with a metal-side contact ultrasonic approach as well as calculating water levels in the collection tank. The falling film thickness measurement over inclined plate was used in this study. Measurement of film thickness was taken at flow rates in the range of 0.34–0.9 lpm. Relatively good agreement was found between the readings, which validates the dynamic measurement capability of the new technique. The technique was applied to measure the horizontal tube falling film thickness for falling film Reynolds number ranging from 130 to 350, at different circumferential angles ranging from 40° to 130° and at tube spacing of 5 mm and 15 mm. Measurements were compared with correlations available in the literature and found to be in good agreement.

Thermocapillary rivulets in a locally heated falling liquid film

The formation of a three-dimensional rivulet structure in a heated falling liquid film is investigated theoretically. For a description of the dynamics of a non-isothermal film, the theoretical model is developed taking into account the thermocapillary force. Within the framework of the spatial approach, a linear analysis of the stability of the heated film relative to perturbations in the spanwise direction to the flow is performed for the first time. A spatial growth rate of these perturbations down-stream is obtained. Analysis of experimental data for different liquids and different Reynolds numbers has shown that the distance between the rivulets corresponds well to the wavelength of most amplified perturbation. The stationary rivulet structure in the film is simulated by numerical method for two types of heating conditions implemented in our previous experiments: with constant wall temperature and heat flux on the wall. Calculations show, that on a heater with constant temperature of a wall the developed rivulet structure has a quasistationary character and very slightly changes downstream. The development of rivulets on a heater with a constant heat flux on the wall has been calculated for the first time. The good agreement between calculations and our experimental data is found for both types of heating conditions implemented in the experiments.

Cleaning of toothpaste from vessel walls by impinging liquid jets and their falling films: Quantitative modelling of soaking effects

The cleaning of thin toothpaste soiling layers from vertical glass surfaces by horizontal impinging water jets and the falling films created by the draining liquid were studied. The effect of soaking time on the rheological properties of the soil material, the force required to remove it, and the cleaning behaviour were determined. The adhesive removal model reported by Wilson et al. (2014, Chem. Eng. Sci., Vol. 109, 183–195) and Bhagat et al. (2017, Food Bioprod. Proc., Vol. 102, 31–54) gave a good description of the cleaning behaviour, including the shape of the cleaning front generated by jets from static and moving nozzles. This model was also applied to removal by the falling liquid film: when soaking kinetics are taken into consideration, it gives a good description of this process as well. This is the first study considering the effect of soil soaking on cleaning by water jets and falling films.

Application of Photocatalytic Falling Film Reactor to Elucidate the Degradation Pathways of Pharmaceutical Diclofenac and Ibuprofen in Aqueous Solutions

Diclofenac (DCF) and ibuprofen (IBP) are common pharmaceutical residues that have been detected in the aquatic system. Their presence in the aquatic environment has become an emerging contaminant problem, which has implications for public health. The degradation pathway and identification of transformation products of pharmaceutical residues are crucial to elucidate the environmental fate of photocatalytic decomposition of these pollutants in aqueous media. The degradation process might lead to creation of other possible emerging contaminates. In this study, the degradation of DCF and IBP in aqueous solutions was investigated. To this end, coated TiO2 on a Pilkington Active glass was used as a photocatalyst under UVA illumination, in a planar falling film reactor. Pilkington ActivTM glass was used as a photocatalyst and a falling liquid film generator. Degradation kinetics of both pharmaceuticals followed a pseudo-first-order model. The transformation products of both diclofenac and ibuprofen during the degradation process were detected and identified with gas chromatography–mass spectrometry (GC–MS) and ion chromatography. The results showed that the mineralization rate of both pharmaceuticals through photocatalysis was very low. Low chain carboxylic acids, such as formic, acetic, oxalic, malonic, and succinic acids were the main by-products. A pathway of DCF and IBP degradation was proposed.

Evaluation of heat irreversibility in couple stress falling liquid films along heated inclined substrate

In the present work, the analysis of entropy generation in a gravity-aided thin couple stress liquid film in an inclined heated substrate is investigated. The thin substrate layer is assumed to be porous and governed by Darcy law. Exact solutions of the dimensionless field equations are obtained and used to determine the rate of entropy is produced along the inclined plate. Velocity, temperature, entropy generation and Bejan profiles are presented for different parameter cases. The result of the analysis revealed the significance of both slip and porous permeability parameters on entropy generation rate and the effects of both modified Navier slip and porous permeability parameters on the entropy generation rate turns out to be large at the free surface of the porous substrate and must be controlled for sustainable and efficient production.

INVESTIGATION OF THE EFFECT OF ELECTRIC FIELD ON CO2 ABSORPTION IN WATER/Fe3O4 NANOFLUID

Abstract In this study, a novel strategy for controlling the mass transfer rate in a gas-liquid system was reported and used for the industrially important system of CO2 absorption. The strategy used Fe3O4 nanoparticles in the liquid phase and also exerting an external electric field. To demonstrate this approach, a unique experimental set up was applied to form a falling liquid film, which was water, to be in contact with the gas phase, which was pure carbon dioxide. Nanofluid with concentrations less than 0.03% by volume and field intensities of 133, 200, 266 kV/m were used in this study. Experimental results showed that the external electric field was able to remarkably enhance the gas absorption rate in dilute nanofluids, while it deteriorated mass transfer in concentrated nanofluids. In order to explain the results, the viscosity of the nanofluid was also experimentally measured in the presence of the electric field.

Limiting Wave Regimes during the Spatial and Time Development of Disturbances in Falling Liquid Films

The theoretical and experimental results are compared in the classical problem on regular two-dimensional waves in heavy viscous liquid films down a vertical plane. Some similarity transformations are used to perform a comparative analysis of numerical methods to study the nonlinear waves formed in a film during the spatial and time development of disturbances in the main steady flow.

Thermocapillary instability and rivulet structure formation in uniformly heated falling liquid film

A system of equations is derived to describe the nonstationary three-dimensional flow of non-isothermal liquid film in the presence of thermocapillary effect in long-wave approximation. The developed model is applicable for moderate Reynolds numbers and does not imply an a priori temperature profile in the film. Based on the derived equations the stability of a uniformly heated vertically falling liquid film is considered relative to spanwise perturbations. The linear analysis of the flow stability is carried out, and the dispersion dependences are obtained. A numerical method is used to study the nonlinear development of instabilities in 2D and 3D statements. It is shown that in a 3D statement, a small transverse perturbation evolves into the time-independent rivulet structure. The influence of dimensionless criteria of the problem on characteristic time and spatial scales of instability development and parameters of rivulet structures has been revealed.

Suppression of the Kapitza instability in confined falling liquid films

We revisit the linear stability of a falling liquid film flowing through an inclined narrow channel in interaction with a gas phase. We focus on a particular region of parameter space, small inclination and very strong confinement, where we have found the gas to strongly stabilize the film, up to the point of fully suppressing the long-wave interfacial instability attributed to Kapitza (Zh. Eksp. Teor. Fiz., vol. 18 (1), 1948, pp. 3–28). The stabilization occurs both when the gas is merely subject to an aerostatic pressure difference, i.e. when the pressure difference balances the weight of the gas column, and when it flows counter-currently. In the latter case, the degree of stabilization increases with the gas velocity. Our investigation is based on a numerical solution of the Orr–Sommerfeld temporal linear stability problem as well as stability experiments that clearly confirm the observed effect. We quantify the degree of stabilization by comparing the linear stability threshold with its passive-gas limit, and perform a parametric study, varying the relative confinement, the Reynolds number, the inclination angle and the Kapitza number. For example, we find a 30 % reduction of the cutoff wavenumber of the instability for a water film in contact with air, flowing through a channel inclined at$3^{\circ }$and of height 2.8 times the film thickness. We also identify the critical conditions for the full suppression of the instability in terms of the governing parameters. The stabilization is caused by the strong confinement of the gas, which produces perturbations of the adverse interfacial tangential shear stress that are shifted by half a wavelength with respect to the wavy film surface. This tends to reduce flow-rate variations within the film, thus attenuating the inertia-based driving mechanism of the Kapitza instability.

Nonstationary periodic wave regimes on a falling liquid film

The theoretical and numerical study of the periodic regimes of free flowing liquid film is carried out. As a result of the theoretical analysis, a simple three-harmonic model was obtained. The obtained model allowed demonstrating the basic mechanisms of the periodic flow regime. Calculations on the full model, the Nepomnyashchy equation and three harmonic models are performed. The results of the numerical solutions of the Nepomnyashchy equation and new model qualitatively consistent with the results of the solution of the full model are presented.

Evolution of three-dimensional waves on vertically falling liquid films. Comparison between calculations and experiment

In this paper we present the results of a comparison of calculated and experimental data on the main regularities of the evolution of a three-dimensional wave on vertically falling liquid films in the range of film flow Reynolds number 5 < Re < 30. Numerical calculation based on the Shkadov model equations shows both experimentally observed scenarios of the evolution of three-dimensional waves: propagation of a single wave or wave train evolution. Comparison of the wave shape shows good qualitative agreement between experiment and calculation for both scenarios.

Experimental Investigation of Local Film Thickness and Velocity Distribution Inside Falling Liquid Films on Corrugated Structured Packings

Understanding the complex fluid dynamics of the liquid phase in structured packing is crucial for the prediction of the separation performance of packed tower and for further optimization of the packing geometry. Detailed numerical investigations are useful to study a wide range of parameters, but require high computational effort and validation is required. Therefore, in this study, experimental investigations on the gravity driven liquid film flow phenomena over corrugated structured packing geometries are presented and evaluated. Due to the fragile nature of thin liquid films, nonintrusive optical measurements where performed through the backside of transparent moldings of packing geometries, thereby reducing optical distortion. To enable the investigation of three-dimensional flow phenomena a µ-Stereoscopic Particle Image Velocimetry (µSPIV) was adapted for thin liquid films. Measurements are performed on MONTZ-Pak B1.250 macro-structure with a smooth surface or a micro-structured surface at different locations. Values of film thicknesses and velocity distributions inside the falling liquid film are discussed in detail.

Intensification of the liquid side mass transfer in double-side falling film microchannels by micro-mixing structures

The interphase mass transfer in a falling film microchannel relies on the liquid-phase mass transfer behavior. Flow in a liquid film is predominantly laminar, and the liquid mass transfer is usually controlled by molecular diffusion. Micro-mixing structures were designed and configured in a double-side falling film microchannel, and the liquid side mass transfer was enhanced by fluid mixing and surface renewal. Computational fluid dynamics approach was used to simulate the falling film flow and mass transfer behavior with and without micro-mixing structures. The impact of the micro-mixing structures on the liquid side mass transfer coefficient was systematically investigated via CO2 absorption experiments in water. The results showed that the fluid flow and mixing was improved by staggered flow mode with micro-mixing structures in the falling film microchannels. Three flow patterns are observed inside the liquid film, including direct flow, cross flow, and vortex flow when the falling liquid film crosses the micro-mixing structures. Both cross flow and vortex flow intensify the surface renewal and turbulence of the liquid film, which is the fundamental reason for the enhancement of the liquid side mass transfer. The experimental results reveal that liquid side mass transfer coefficient in double falling film microchannels with micro-mixing structures is between 3.59 × 10−5 m/s and 5.38 × 10−5 m/s, while it is between 3.35 × 10−5 m/s and 4.82 × 10−5 m/s without micro-mixing structures. The liquid side mass transfer coefficient is increased 7–14% by the configuration of micro-mixing structures. Therefore, a double-side falling film microcontactor with micro-mixing structures not only reduces the contactor size, but also effectively enhances the interphase mass transfer behavior.

Investigation on heat transfer characteristics of falling liquid film by planar laser-induced fluorescence

Falling liquid film evaporation is widely used in many industrial applications due to its efficient heat transfer characteristics. In this paper, a quantitative thermometry technique based on planar laser-induced fluorescence (PLIF) was applied to analyze the heat transfer characteristics of falling liquid film with high spatiotemporal resolution. The optimal gray values extraction method was proposed for the calibration of temperature-fluorescence intensity. The quantitative calculation of convective heat transfer coefficient and Nusselt number were conducted based on the liquid film temperature field distribution which was measured by PLIF and the trends of them were shown in different range of temperature and Reynolds number. Finally, the heat transfer correlation was proposed and the heat transfer characteristics of falling liquid film was analyzed. The quantitative correlations analysis shows that most of the correlations are more suitable for the liquid film with low Prandtl number, and the Nusselt number tends to decrease when the temperature of the liquid film increases at the constant flow rate.

Wetting Behavior of Falling Liquid Film Flowing on a Plate with a Side Wall

The wettability of liquid film flowing on an inclined plate is extremely deteriorated if there is a vertical wall on the channel side. In this study, an experimental study was conducted to investigate the influence of the side wall on the dryout of liquid film flow. The film surface forms a meniscus having a minimum film thickness near the side wall. The thin film thickness causes the dryout of film flow at lower flow rate. To avoid the appearance of the minimum thickness, the test channels of SUS-304 plate having circular side walls with various curvature radii RS were manufactured and the surface profiles of liquid film were measured experimentally for three kinds of test liquids. The meniscus profile was flattened at appropriate radius of curvature, i.e., RS.~6 mm for θR=20～30°(θR : receding contact angle) in this experiment. The critical Weber number at which dryout disappears is lowered remarkably and is recovered to the value those experienced for the flat plate without side walls.

Solitary waves on falling liquid films in the inertia-dominated regime

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

Evaporative Heat Transfer Characteristics of a Novel Continuous, Multi-Staged Evaporator/Distiller with Unsteady Falling Liquid Film Flow

Evaporative Heat Transfer Characteristics of a Novel Continuous, Multi-Staged Evaporator/Distiller with Unsteady Falling Liquid Film Flow

Dynamics of falling films on the outside of a vertical rotating cylinder: waves, rivulets and dripping transitions

Falling liquid films on the underside of a plate or on the outside of a rotating cylinder are subject to a destabilizing body force. The evolution of the film topology is determined by interactions between the Kapitza and the Rayleigh–Taylor instability, leading to complex patterning of the film surface and eventually fluid detachment from the substrate. This study experimentally investigates the evolution of the surface topology for a film on the outside of a vertical rotating cylinder of large radius. Shear at the liquid/air interface is suppressed through an outer, co-rotating cylinder. The film evolution is captured through high speed visualization in dependence of the control parameters, namely Reynolds number and rotation frequency. An increasing influence of the Rayleigh–Taylor instability for an increasing destabilizing body force (increasing rotational speed of the cylinder) is most notably observed in the form of a decreasing inception length of rivulet structures dominating the film topology. Wavelength as well as inception length of rivulets match the predictions from linear stability analysis of the classical Rayleigh–Taylor problem. In this context, experimental and supporting numerical results suggest that the emergence of rivulets occurs for any non-zero value of the destabilizing body force after a given evolution length that decreases with increasing body force. Fluid detachment from the substrate is found to be intimately related to the existence of rivulet structures. In dependence of the control parameters, detaching droplets are either observed as a result of interactions of solitary pulses of varying phase speed on rivulets, directly after destabilization of two-dimensional waves into rivulets or immediately at the fluid inlet. By comparison to the convective/absolute instability transition predicted by linear stability analysis of an integral boundary layer formulation of the problem in question, it is shown that the prediction of a predominant dripping mechanism lies beyond the scope of linear analysis.

Modeling nonlinear wave regimes in a falling liquid film entrained by a gas flow

The article studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers, the problem is reduced to solving a nonlinear integro-differential equation for the film thickness deviation from the undisturbed level. The nature of branching of wave modes of the unperturbed flow with a flat interface has been investigated. The steady-state traveling solutions with wave numbers that are far enough from the neutral ones, have been numerically found. Using methods of stability theory, the analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that, similarly to the case of the falling film, this model equation has solutions in the form of solitons-humps.