Falling Liquid Film Research Articles

Instability of odd viscosity falling liquid films with insoluble surfactants

Instability of odd viscosity falling liquid films with insoluble surfactants

Linear Quadratic Regulation Control for Falling Liquid Films

Linear Quadratic Regulation Control for Falling Liquid Films

Numerical modeling of a confined falling liquid film sheared by a gas flow in a plate heat exchanger of an NH3/H20 absorption chiller

In recent years, the demand for cooling has seen a substantial increase, primarily due to rising summertime temperatures. Conventional mechanical compression air conditioners have played a predominant role in fulfilling this demand, albeit at the cost of significant electricity consumption. In response, absorption chillers have emerged as an eco-friendly alternative, powered by sustainable heat sources like solar energy or industrial waste heat. The present work is conducted within the framework of developing compact absorption chillers incorporating plate heat exchangers. It builds upon prior research by improving an existing numerical model for falling film plate heat exchangers within an NH3/H2O absorption chiller. This former numerical model evaluates the coupled heat and mass transfer between the liquid film and the vapor flow while excluding hydrodynamic interactions at the liquid-vapor interface. The current investigation aims to address compactness and cost-efficiency limitations in absorption chillers. The consequences of operation within confined spaces were numerically evaluated. An innovative analytical model was developed to quantify the influence of the interactions at the liquid-vapor interface. Shear stress and interfacial perturbations were considered compared to the classical Nusselt model, enabling the evaluation of the changes in the average film thickness and the flooding phenomenon. This analytical model was then added to the previously developed heat and mass transfer model. The numerical model was applied to both the desorber and absorber units. The results show that increased confinement has minimal effects on the transfer coefficients. Additionally, an approach is suggested for estimating flooding in confined spaces and the results are compared with various correlations available in the literature.

Probing time-resolved plasma-driven solution electrochemistry in a falling liquid film plasma reactor: Identification of HO2- as a plasma-derived reducing agent.

Many applications involving plasma-liquid interactions depend on the reactive processes occurring at the plasma-liquid interface. We report on a falling liquid film plasma reactor allowing for in situ optical absorption measurements of the time-dependence of the ferricyanide/ferrocyanide redox reactivity, complemented with ex situ measurement of the decomposition of formate. We found excellent agreement between the measured decomposition percentages and the diffusion-limited decomposition of formate by interfacial plasma-enabled reactions, except at high pH in thin liquid films, indicating the involvement of previously unexplored plasma-induced liquid phase chemistry enabled by long-lived reactive species. We also determined that high pH facilitates a reduction-favoring environment in ferricyanide/ferrocyanide redox solutions. In situ conversion measurements of a 1:1 ferricyanide/ferrocyanide redox mixture exceed the measured ex situ conversion and show that conversion of a 1:1 ferricyanide/ferrocyanide mixture is strongly dependent on film thickness. We identified three dominant processes: reduction faster than ms time scales for film thicknesses >100 µm, •OH-driven oxidation on time scales of <10ms, and reduction on 15ms time scales for film thickness <100 µm. We attribute the slow reduction and larger formate decomposition at high pH to HO2- formed from plasma-produced H2O2 enabled by the high pH at the plasma-liquid interface as confirmed experimentally and by computed reaction rates of HO2- with ferricyanide. Overall, this work demonstrates the utility of liquid film reactors in enabling the discovery of new plasma-interfacial chemistry and the utility of atmospheric plasmas for electrodeless electrochemistry.

Effect of a static magnetic field on the falling-film evaporation on a vertical plate evaporator by mixed convection

The application of a magnetic field to a falling-film evaporation system can have several effects. The magnetic field can alter the liquid film's flow behavior and modify the system's heat transfer characteristics. The numerical study of falling film evaporation by mixed convection on a vertical channel under a static magnetic field has been investigated. The vertical channel is composed of two parallel plates. The right plate is dry and isothermal, while the left plate is wetted by a falling liquid film and exposed to a static, uniform heat flux from the outside. Water film makes up the liquid, while dry air and water vapor make up the gas mixture. The results relate to the effects of the magnetic field on heat and mass transfer and on liquid film evaporation. The results demonstrate that the static magnetic field has a weak effect on heat and mass transfer and water film evaporation. In fact, it is shown that an increase in the static magnetic field weakly enhances heat and mass transfer as well as liquid film evaporation.

Measurement of 3-D Characteristics of Falling Liquid Film Based on SLIF

Measurement of 3-D Characteristics of Falling Liquid Film Based on SLIF

Experiments on the onset of boiling entrainment from a falling liquid film with gas sheared flow

The process of droplet entrainment caused by nucleate boiling within a falling liquid film was visualized using a high-speed camera to investigate the mechanism and the onset conditions of the boiling entrainment. In the experiments, air was flowed along the liquid film to explore the potential effects of vapor core flow on the droplet generation process in diabatic annular two-phase flow. The two types of boiling entrainment mechanisms called the jet-type and the filament-type were observed in the present work. The jet-type boiling entrainment commenced at relatively low wall heat flux and produced small droplets. The filament-type was observed at higher wall heat flux and it produced larger droplets. Hence, the filament-type was supposed to have a greater impact on the liquid film flow rate in diabatic annular two-phase flow. The experimental data accumulated in this work were used to develop correlations for the onset conditions of the jet-type and filament-type boiling entrainments.

Study on temperature distribution of vertical liquid falling film heat transfer with Al2O3 nanofluid

This study presents a laminar smooth 2-D theoretical model of the falling liquid film using an in-house code and validated with experimental results. The numerical model considers thermophysical property enhancements with nanoparticles Al2O3 to different liquids such as water, ethylene glycol (EG), and LiBr-H2O. An experimental setup has been developed to validate the pure heat transfer process in the falling liquid film, using the measurement of the falling film interface temperature. The simulation results agreed well with the experimental results for various liquids at low flow rates. The discrepancy increases as the flow rate increases due to the limitations of the laminar smooth film model in the numerical simulation. With a volumetric concentration of ϕ=4% nanoparticle Al2O3, the heat transfer coefficient of nanofluid water, EG, LiBr-H2O increased around 15%–20% compared with the baseline fluid. A new correlation was obtained to predict the average heat transfer coefficient based on experimental data. The experimental results have an uncertainty at 9.3% for the surface temperature and 5.5% for the falling film bulk temperature. The maximum deviation between the calculated heat transfer coefficient by the model and experimental data is around 25%, at Re<1000. The average error has decreased by 23% when comparing the new correlation considering Ka and the conventional form.

Shear imposed falling liquid films on a slippery substrate with Marangoni effects: Effect of odd viscosity

We investigate the behavior of a thin fluid with disrupted time-reversal symmetry on a uniformly heated inclined surface under external shear stress using modified Navier–Stokes equations, an energy conservation equation, and incorporating a Navier slip condition. Critical conditions for instability onset are determined by a linear stability analysis within the Orr–Sommerfeld framework. We derive a first-order Benney-type evolution equation to study long-wave instabilities. We find slippery substrate, imposed shear stress along the flow direction, and Marangoni number consistently destabilize the flow, while odd viscosity and imposed counter-flow shear stabilize it. A weakly nonlinear analysis using multiple scales reveal distinct zones of instability. Marangoni number, slip length, odd viscosity, and imposed shear direction significantly impact stability and instability regions. Numerical simulations of the free surface evolution equation of a flow system under consideration provide clear evidence of the contributions of thermocapillary, slip length, odd viscosity, and imposed shear direction. Furthermore, our analysis of linear and weakly nonlinear stability, as well as our numerical simulations, exhibit remarkable consistency.

Three‐Dimensional, Molecule‐Sensitive Mapping of Structured Falling Liquid Films Using Raman Scanning

AbstractA method for molecule‐sensitive, non‐contact and marker‐free 3D mapping of vertical falling liquid films using Raman spectroscopy is presented. Technical liquid films are common in many applications in the chemical industry such as columns, evaporators, dryers and absorbers/desorbers. Measurements of an aqueous sodium sulfate film on a plain surface with a small pyramid attached to it, as well as a pillow plate are presented using a 3D surface plot. Suppressing surface gloss as well as other optical reflections from the metallic backplates is realized by using only inelastic light scattering and mathematical background correction. The results show that liquid mapping with Raman spectroscopy is possible and 3D maps can be created from different structured surfaces.

Heat Transfer in a Falling Liquid Film of Freon R21 on an Array of Horizontal Tubes with Modified MAO Coatings

Heat Transfer in a Falling Liquid Film of Freon R21 on an Array of Horizontal Tubes with Modified MAO Coatings

Hydrodynamics and instabilities of a falling liquid film with an insoluble surfactant

In this study, we investigate the linear and weakly nonlinear stability of a liquid film flowing down an inclined plane with an insoluble surfactant. First, the nonlinear evolution equations of a liquid film thickness and surfactant concentration are derived using the long-wave expansion method at a moderate Reynolds number (0 &amp;lt; Re ≤ 20). The linear stability of the flow is examined using the normal-mode method, and the linear stability criterion and critical Reynolds number Rec are obtained. The results reveal the destabilizing nature with increasing Reynolds number Re and the stabilizing nature with increasing Marangoni number M. Second, the nonlinear equations described by the complex Ginzburg–Landau equation are obtained using the multiple-scale method to investigate the weakly nonlinear stability of the system. The results show that a new linear instability region appears above the neutral stability curve caused by the solute-Marangoni effect, which develops into a supercritical stable zone under the influence of nonlinear factors. Increasing M generally improves the stability of the flow but continuing to increase M under the condition of M &amp;gt; Mc (critical Marangoni number) improves the nonlinear instability in the region and transforms part of the unconditional stability zone into a subcritical instability zone. The increase in Re extends an explosive unstable zone and reduces the threshold amplitude in the subcritical unstable zone. In contrast, the unconditional stable zone decreases and disappears after increasing Re to a specific value, which reflects the destabilizing effect of Re on the nonlinear zone of the flow.

Investigation on wave morphology and temperature distribution of falling liquid film in a vertical tube

The waves of the falling liquid film have a strong interaction with its temperature, and the flow and heat transfer mechanisms contained therein are of great significance for optimizing industrial equipment and improving energy efficiency. In this paper, the thickness and temperature field of the liquid film in a vertical tube were measured simultaneously based on planar laser-induced fluorescence (PLIF). The wave morphology, as well as the temperature distribution within the liquid film, was analyzed by high-speed imaging visualization and the film temperature extraction method, respectively. With the increase of the Reynolds number, an evolution of the wave morphology from ripples to high-frequency disturbance waves and finally to solitary waves was observed. The method of Dynamic Mode Decomposition (DMD) was developed to reconstruct the flow field and calculate the characteristic frequencies in the flow, from which the wave features under different wave morphologies were revealed. It was found that the temperature variation of the liquid film at the gas-liquid interface was accelerated by the waves from the results of the temperature distribution of the liquid film. Besides, the low-temperature micro clusters observed in the solitary waves can be considered as one mechanism of the enhancement of heat transfer in the liquid film.

Nonlinear wave attenuation in strongly confined falling liquid films sheared by a laminar counter-current gas flow

Experiments are conducted in water films falling along the bottom wall of a weakly inclined rectangular channel of height$5$mm in the presence of a laminar counter-current air flow. Boundary conditions have been specifically designed to avoid flooding at the liquid outlet, thus allowing us to focus on the wave dynamics in the core of the channel. Surface waves are excited via coherent inlet forcing before they come into contact with the air flow. The effect of the air flow on the height, shape and speed of two-dimensional travelling nonlinear waves is investigated and contrasted with experiments of Kofman, Mergui &amp; Ruyer-Quil (Intl J. Multiphase Flow, vol. 95, 2017, pp. 22–34), which were performed in a weakly confined channel. We observe a striking difference between these two cases. In our strongly confined configuration, a monotonic stabilizing effect or a non-monotonic trend (i.e. the wave height first increases and then diminishes upon increasing the gas flow rate) is observed, in contrast to the weakly confined configuration where the gas flow is always destabilizing. This stabilizing effect implies the possibility of attenuating waves via the gas flow and it confirms recent numerical results obtained by Lavalleet al.(J. Fluid Mech., vol. 919, 2021, R2) in a superconfined channel.

Numerical simulation of evaporating wavy falling liquid films in laminar gas streams

Numerical simulations are performed to investigate the interfacial heat and mass transfer from evaporating wavy falling liquid films in interaction with laminar gas streams. The OpenFOAM solver has been used to conduct the simulations where the liquid-gas interface is resolved using the Volume of Fluid method of solving for three phases, i.e., liquid, vapor, and air. The configuration considered is a falling liquid (water) film on a heated vertical plate with a confined laminar moist air (gas) flow that is either (a) co-current or (b) counter-current to the downward liquid flow. The evaporation at the liquid-gas interface is driven by the interfacial gradient of the vapor mass fraction. Interfacial waves are triggered using a monochromatic forcing disturbance that leads to sinusoidal or solitary waves forming at the liquid-gas interface under respective forcing frequencies. The numerical model is validated with the available experimental data. The results show nearly a 15% enhancement in time-averaged Sherwood number (Sh) due to film waviness (sinusoidal or solitary) at the lower volumetric gas flow rate, Qg = +50 (co-current) and Qg = −50 (counter-current). This enhancement in the Sh for both the waves further increases by 11% with Qg = +800 and 196% with Qg = −800. A closer examination of the mass transfer process over a wave demonstrates that with Qg = +50, the concentration of the gas side streamlines at the trough locations of the wave leads to higher values of Sh at these locations. However, with Qg = +800, although the overall Sh increases, vortices appear at the wave trough locations, leading to a corresponding decrease in the local Sh values. Correlations are proposed for predicting Sh under co-current and counter-current gas flow effects.

Visualization experiment and numerical simulation on behaviors of gas-liquid falling film flow on the air-side of two-row plain finned-tube heat exchanger

The frost-free air-source heat pump (ASHP) with integrated liquid desiccant dehumidification is a more promising energy-saving alternative to the conventional ASHP unit. The performance of spray-type finned-tube heat exchanger (FTHE), as one of the key equipment of this frost-free ASHP system, is affected by a combination of various factors including wall wettability, liquid film flow pattern, liquid film thickness, velocity distribution in a liquid film, interface wave, interface velocity and so on. To provide a theoretical basis for the operation, design and optimization of high-performance spray-type FTHE, a visualization experiment system and a three-dimensional (3D) numerical model are employed to study the behaviors of counter-current gas-liquid falling film flow on the air-side of two-row plain FTHE under different parameters in the present paper. According to the experimental results, the flow pattern of liquid film on the finned-tube surface is a mixture flow composed of the rivulet flow and the thin falling film flow, demonstrating that the assumption of the uniform distribution for liquid film thickness proposed in previous studies is not completely consistent with the actual situation. Meanwhile, the numerical results indicate that the transient-average film thickness on the surface of two-row plain finned-tube is significantly 18.3% – 32.5% higher than that on the vertical plate calculated by Nusselt's model. After that, the critical gas and liquid Reynolds numbers of the flow pattern transition for the liquid film are obtained, and it is pointed out that the wall contact angle of 10° is more conducive to the formation of complete film flow on the air-side of the two-row plain FTHE within the fin pitch range of 4.8 – 6.0 mm. The changes of the falling liquid film and gas-liquid interface characteristics are fundamentally attributed to the drag effect of the interfacial shear force. Furthermore, there is a cubic curve relationship between average interface shear force and gas Reg. A quadratic curve relation exists between average wall shear stress and gas Reg. At the same time, the velocity of falling film fluid at the bottom region of laminar flow is reduced, resulting from the inhibiting effect of the interfacial shear force.

Three-Dimensional Sag Tracking in Falling Liquid Films

Coating defects often arise during application in the flash stage, which constitutes the ∼10 min interval immediately following film application when the solvent evaporates. Understanding the transient rheology and kinematics of a coating system is necessary to avoid defects such as sag, which results in undesirable appearance. A new technique named variable angle inspection microscopy (VAIM) aimed at measuring these phenomena was developed and is summarized herein. The essence of this new, non-invasive, rheological technique is the measurement of a flow field in response to a known gravitational stress. VAIM was used to measure the flow profile through a volume of a liquid thin film at an arbitrary orientation. Flow kinematics of the falling thin film was inferred from particle tracking measurements. Initial benchmarking measurements in the absence of drying tracked the velocity of silica probe particles in ∼140 μm thick films of known viscosity, much greater than water, at incline angles of 5° and 10°. Probe particles were tracked through the entire thickness of the film and at speeds as high as ∼100 μm/s. The sag flow field was well resolved in ∼10 μm thick cross sections, and in general the VAIM measurements were highly reproducible. Complementary profilometer measurements of film thinning were utilized to predict sag velocities with a known model. The model predictions showed good agreement with measurements, which validated the effectiveness of this new method in relating material properties and flow kinematics.

The Mechanism of Flow Patterns and Rivulet Instability in Gravity-Driven Film Flow on a Porous Wall with Uniform Heating

Properties of porous mediums have significant impacts on the spreading pattern of falling-film along a vertical heated wall. In this paper, we investigate the combined effect of porosity and uniform heating on the flow instability of a falling liquid film. Based on the film thickness equation derived by the long wave theory, linear stability analysis and numerical simulations are given to verify the influences of various dimensionless parameters, and the physical mechanism for the flow instability is explained. With the uniform heating, it is shown that the increasing Marangoni number and Biot number both enhance the rivulet instability because the Marangoni force becomes larger with bigger values of the two numbers. For porous properties, the existence of Darcy number causes the contact line to move faster and results in a destabilizing effect, while a bigger Beavers–Joseph coefficient causes the contact line to move slower and plays a stabilizing role. Increment of porous thickness and the thermal conductivity ratio slightly enhances or impedes the flow instability, respectively, and neither of the two parameters influences the moving speed of the contact lines.

Effect of evaporation rate for the heat and mass transfer of the laminar liquid falling film in still air

The heat and mass transfer process of the laminar falling liquid film along a vertical heated plate with constant heat flux is studied. Through thermal equilibrium analysis, the energy conservation equation is established and solved by the parametric variation method. The analytical solution considering evaporation is in good agreement with the experimental results. Based on the model, the temperature distribution of liquid film with or without evaporation is obtained. It is demonstrated that the thickness and average temperature of liquid film show decreasing and increasing trends linearly in the flow direction. Along with the increase in the evaporation rate, the average temperature decreases and the share of evaporative heat dissipation in the total heat flux increases, which demonstrates that evaporation is an important physical factor for heat dissipation when the falling liquid film flows on a hot plate.

Falling film on an anisotropic porous medium

The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.