Falling Liquid Film Research Articles

Flow structure in the three dimensional waves on the surface of the vertically falling liquid films

Results of simultaneous liquid velocity and film thickness fields measurements in the three dimensional waves are presented. The three dimensional waves formed as a result of decay of the forced two dimensional waves were studied. Liquid velocity fields were reconstructed at different distance from the film surface with reference to the specific area of the wave. It was shown that flow in the three dimensional wave has complicated structure with existence of areas with backflow and transverse flows of opposite directions. Main areas of transverse flows existence are lying under main humps of three dimensional waves.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper 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 the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

Characteristics of solitary waves on a falling liquid film sheared by a turbulent counter-current gas flow

We report an experimental investigation of a falling water film sheared by a turbulent counter-current air flow in an inclined rectangular channel. Film thickness and wave velocity measurements associated with visual observation are conducted to study the influence of the air flow on controlled traveling waves consisting of a large wave hump preceded by capillary ripples. First, we focus on the variation of the shape, amplitude and velocity of the waves as the gas velocity is gradually increased. We demonstrate that the amplitude of the main hump grows substantially even for moderate gas velocities, whereas modification of the wave celerity becomes significant above a specific gas velocity around 4 m/s, associated with an alteration of the capillary region. The influence of the gas flow on 3D secondary instabilities of the solitary waves detected in a previous study Kofman et al. (2014), namely rugged or scallop waves, is also investigated. We show that the capillary mode is damped while the inertial mode is enhanced by the interfacial shear. Next, the gas velocity is increased until the onset of upstream-moving patterns referred to as flooding in our experiments. At moderate inclination angles (typically < 7 ○), flooding occurs for a gas velocity around 8 m/s and is initiated at the scallop wave crests by a backward wave-breaking phenomenon preceded by the onset of ripples on the flat residual film separating two waves. At high inclination angle, a rapid development of solitons is observed as the air velocity is increased preventing the waves to turn back. Finally, at high liquid Reynolds number, sudden and intermittent events are triggered consisting of very large amplitude waves that go back upwards very fast. These “slugs” either extend over the whole width of the channel or are very localized and can thus potentially evolve towards atomization.

Novel Pemulen/Pullulan blended hydrogel containing clotrimazole-loaded cationic nanocapsules: Evaluation of mucoadhesion and vaginal permeation

In this work, hydrogels containing clotrimazole-loaded nanocapsules were developed through the innovative association of two mucoadhesive polymers: Pemulen® TR1 and Pullulan. Furthermore, the hydrogels macroscopic characteristics, pH and spreadability were evaluated. The formulations showed homogeneous appearance and pH compatible with vaginal application (around 5.0). Similar spreadability profiles were found in hydrogels containing clotrimazole-loaded nanocapsules and in the free drug as well. Hydrogels were evaluated considering their mucoadhesive potential by the falling liquid film method and the permeation/penetration capacity through cow vaginal mucosa in Franz cell. The results showed that the concentration of 3% Pullulan was important to increase the adhesive strength on the layer used (mucin gel or animal mucosa). The results of the permeation/penetration study showed that the hydrogel containing clotrimazole-loaded nanocapsules remained on the vaginal mucosa surface, what is ideal for the treatment of superficial vaginal infections. This way, the Pemulen/Pullulan blended hydrogel is a promising alternative for the treatment of vulvovaginal candidiasis.

Analytical and Numerical Solution of Conjugate Heat and Mass Transfer in Falling Film Absorption Process

Investigation of heat and mass transfer at nonisothermal absorption on the falling liquid film surrounded by pure vapour is presented. The analytical method for entrance region and numerical method for solving the problem are proposed. The analytical solution is obtained for the entry region, where temperature and concentration perturbations are near the interface. Then, the analytical solution is used as an inlet condition for further numerical solution by the finite-difference method. The key dimensionless criteria characterizing heat and mass transfer at absorption on the falling liquid film are defined.

側壁のある流路壁面を流下する液膜流れのぬれ性能に関する研究

側壁のある流路壁面を流下する液膜流れのぬれ性能に関する研究

Feasibility Test of a Liquid Film Thickness Sensor on a Flexible Printed Circuit Board Using a Three-Electrode Conductance Method.

Liquid film thickness measurements under temperature-varying conditions in a two-phase flow are of great importance to refining our understanding of two-phase flows. In order to overcome the limitations of the conventional electrical means of measuring the thickness of a liquid film, this study proposes a three-electrode conductance method, with the device fabricated on a flexible printed circuit board (FPCB). The three-electrode conductance method offers the advantage of applicability under conditions with varying temperatures in principle, while the FPCB has the advantage of usability on curved surfaces and in relatively high-temperature conditions in comparison with sensors based on a printed circuit board (PCB). Two types of prototype sensors were fabricated on an FPCB and the feasibility of both was confirmed in a calibration test conducted at different temperatures. With the calibrated sensor, liquid film thickness measurements were conducted via a falling liquid film flow experiment, and the working performance was tested.

Experimental study of the falling film of liquid around a Taylor bubble

The present work reports an experimental study of the falling liquid film around single Taylor bubbles rising in vertical tubes filled with stagnant liquids by using a pulse-echo ultrasonic technique. The experiments were carried out in acrylic tubes 2.0 m long, with inner diameters of 0.019, 0.024 and 0.034 m, with five water-glycerin mixtures, corresponding to inverse viscosity number ranging from 15 to 22422. The rising bubble and the falling liquid film were measured by using ultrasonic transducers located at the one side of the tube. The velocity and profile of the Taylor bubble, and the development length and equilibrium thickness of the falling liquid film around the bubble were obtained by the ultrasonic signals processing. Based on the experimental results of the present study, several correlations available to estimate the equilibrium thicknesses of liquid films falling around Taylor bubbles were evaluated and new correlations were proposed to estimate the dimensionless equilibrium film thickness and the film development length respectively.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. Weakly nonlinear steady-state traveling solutions of the equation with wave numbers in a vicinity of neutral wave numbers are constructed analytically. The nature of the wave branching from the undisturbed solution is investigated. Steady-state traveling solutions, whose wave numbers within the instability area are far from neutral wave numbers, are found numerically.

Falling Liquid Film Evaporation in Subcooled and Saturated Water Over Horizontal Heated Tubes

ABSTRACTThis paper presents an experimental study of heat transfer and film thickness behavior in falling liquid water film evaporation technology over horizontal tubes. Liquid distribution systems have also been evaluated. The experimental setup consisted of two horizontal 0.019-m OD stainless-steel tubes, 0.194 m in length. Reynolds numbers in the 160–940 range were tested in both subcooled and saturated liquid regimes. For the liquid distribution system study, several distributor geometries were tested in order to develop the least disturbed film over the tubes. An intrusive method was used for measuring the liquid film thickness in the laminar regime and the measured values were compared with the theoretical prediction computed from the Nusselt equation. An experimental heat transfer correlation was obtained and compared with previous ones obtained by other authors. In addition, the local heat transfer coefficient was observed to be always higher at the horizontal tube top region for all operational conditions (on the order of 14 kW/m2-°C). Finally, the use of a liquid storage distribution system along with the installation of a wire mesh to obtain an uniform liquid distribution for all Reynolds numbers tested.

Effect of viscosity on thermocapillary breakdown of a falling liquid film

Thermocapillary breakdown of a liquid film flowing due to gravity over a vertical plate with a heater of 150×150 mm is studied in a wide range of liquid properties (in particular, dynamic viscosity at the initial temperature varies from 0.91·10-3 to 16.9·10-3 Pa·s) and film Reynolds number (Re = 0.15-53.5). It is found that liquid viscosity has a significant effect on the threshold heat flux corresponding to film breakdown. To take into account the effect of liquid properties, the breakdown criterion traditionally used in literature was modified. This allowed successful generalization of all data obtained.

Selection of solitary waves in vertically falling liquid films

Two-dimensional solitary waves at the surface of a film flow down a vertical plane are considered. When the system is subjected to inlet white noise, solitary waves are formed after an inception region and interact with each other. Using open-domain simulations of reduced equation models, we investigate numerically their late time process dynamics. Close to the instability threshold, the waves synchronize themselves into bound states. For higher values of the Reynolds number, the separation distance between the waves increases and the synchronization process at work is weaker. Performing statistics, we show that the mean characteristics of the waves correspond to the minimal value of the mean film thickness along the traveling-wave branch of solutions. In this regime, synchronization occurs through the waves tails which is associated with a change of scaling of the waves features. A similar behavior is observed performing simulations in periodic domains: the selected waves maximize the mean flow rate.

Mathematical Modeling of Layer Crystallization on a Cold Column with Recirculation

Falling film crystallization is a novel technique used to overcome the challenges of solid and slurry handling used for continuous manufacturing in the pharmaceutical industry. The process and its performance were demonstrated recently. In this study, a dynamic model of falling film crystallization with a recirculation loop was developed in the form of coupled partial differential equations describing the effects of mass transfer, heat transfer, impurity inclusion, and crystallization kinetics. The model described the variation of processing parameters, such as the flow rate and cooling temperature, for three different crystallization solution systems (16 cases). The experimental results confirm the predictions of the model, which will provide further insights into processes in which experimental values do not exist or are difficult to obtain, such as the axial temperature profile of the falling liquid film or the overall purity of the deposited crystal layer at different time intervals.

Performance improvement of a falling-film-type heat exchanger by insertion of shafts with screw blade in a heat exchanger tube

Highly-efficient heat exchange is expected for the falling-film-type heat exchanger handled in this study by utilizing a falling liquid film, etc. The heat medium is flowed inside the heat exchanger tube. In contrast, the falling film is flowed outside the heat exchanger tube, thereby exchanging heat. In the previous study, considering the basic heat transfer characteristic of the falling-film-type heat exchanger, the design equation was developed in the limited extent. In this study, focusing on the flow condition in a heat exchanger tube of the falling-film-type heat exchanger, various shafts with screw blade were inserted in a single heat exchanger tube and it was evaluated how the pitch and height of screw and the flow rate of cooling water would give an effect on the heat exchange performance. Additionally, the heat transfer coefficient and the overall heat transfer coefficient of the falling-film-type heat exchanger were logically calculated, and then a theoretical value and an experimental value were compared and evaluated. As a result, it was clarified that the heat exchange performance of the falling-film-type heat exchanger was improved by inserting the shaft with screw blade, and theoretical and experimental values were roughly matched.

Self-similarity of solitary waves on inertia-dominated falling liquid films.

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20-120 and surface tension coefficients σ=0.0512-0.072 N m(-1) on substrates with inclination angles β=19°-90°. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

Positive frictional pressure gradient in vertical gas-high viscosity oil slug flow

The present study describes the wall shear stress and the falling liquid film behavior in upward vertical slug flow of air and high viscosity oil. The frictional pressure gradient is directly related to the wall shear stress, and it is usually negative (opposite to the overall flow direction). However, in vertical slug flow, the average total wall shear stress of a slug unit may be negative (in the same direction of the overall flow), resulting in a positive frictional pressure gradient. However, this does not mean, by any way, generation of additional energy or violation of the second law of thermodynamics.The positive frictional pressure gradient phenomenon, reasons and required conditions were explained in this paper. A simplified model was developed and validated against recent experimental data of air-high viscosity oil slug flow in a 50.8mm ID vertical pipe. The oil viscosity was in the range of 127mPas to 580mPas. Positive frictional pressure gradient appears when the liquid film wall shear stress supersede the wall shear stress in the slug body. The rate of increase of both wall shear stresses (with respect to the mixture Reynolds number) depend, not only, on the mixture Reynolds number but also, highly, on the liquid viscosity.

Laplace transform solution of conjugate heat and mass transfer in falling film absorption process

In this study, the conjugate heat and mass transfer process taking place during the absorption of a refrigerant vapor into a falling liquid film is analyzed using the Laplace transform method. The Laplace transform method has been previously utilized to model the process but under a uniform velocity profile assumption. Here, a more realistic linear velocity profile is employed. The results suggest that the uniform velocity profile assumption overestimates the refrigerant concentration across the liquid film, and underestimates the temperature profile and the vapor absorption rate. Overall, the uniform velocity profile assumption can result in up to 30% error in calculating the absorption rate. Using the new model, the effect of different flow parameters on the absorption rate has been studied. The efficacy of the model is demonstrated through comparison with various experimental and numerical results reported in the literature. The analytical solution developed in the present study provides a simple, fast and accurate approach for calculating the absorption rate at different operating conditions and fluid properties.

Measurement of Interfacial Profiles of Wavy Film Flow on Inclined Wall

Falling liquid films on inclined wall present in many industrial processes such as in food processing, seawater desalination and electronic devices manufacturing industries. In order to ensure an optimal efficiency of the operation in these industries, a fundamental study on the interfacial flow profiles of the liquid film is of great importance. However, it is generally difficult to experimentally predict the interfacial profiles of liquid film flow on inclined wall due to the instable wavy flow that usually formed on the liquid film surface. In this paper, the liquid film surface velocity was measured by using a non-intrusive technique called as photochromic dye marking method. This technique utilizes the color change of liquid containing the photochromic dye when exposed to the UV light source. The movement of liquid film surface marked by the UV light was analyzed together with the wave passing over the liquid. As a result, the liquid film surface was found to slightly shrink its gradual movement when approached by the wave before gradually move again after the intersection with the wave.

Stabilising falling liquid film flows using feedback control

Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slope sufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating and heat transfer, which benefit from smooth and wavy interfaces, respectively. Here, we discuss how the dynamics of the system are altered by feedback controls based on observations of the interface height, and supplied to the system via the perpendicular injection and suction of fluid through the wall. In this study, we model the system using both Benney and weighted-residual models that account for the fluid injection through the wall. We find that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of the flow modelling. Furthermore, we show that the system can still be successfully controlled when the feedback is applied via a set of localised actuators and only a small number of system observations are available, and that this is possible using both static (where the controls are based on only the most recent set of observations) and dynamic (where the controls are based on an approximation of the system which evolves over time) control schemes. This study thus provides a solid theoretical foundation for future experimental realisations of the active feedback control of falling liquid films.

Studying Periodic Rolling Waves on the Surface of a Falling Liquid Film

In this paper the mathematical model describing the falling thin liquid film on a vertical wall is considered taking into account heat and mass transfer at the interface in the regime of periodic rolling waves. The families of exact and numerical generalized solutions, where periodic traveling waves conjugate through the strong and weak discontinuities with each other or with the residual thickness, are constructed. Evolution of exact periodic generalized solutions is studied in time.