Liquid Film Flow Research Articles

Time-varying stretching velocity analysis for an unsteady flow of Williamson fluid by Hermite wavelet

This study investigates unsteady velocity Uw=ξx/t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${U}_{w}=\\xi x/t$$\\end{document} for a Williamson nanofluid film flowing over a moving surface. This work can be used to outline the effects of an applied angled magnetic-field on liquid film flow, which occurs in numerous real-world solicitations such as coating industries for wire or sheet, labs, painting, and several others. Analyzing williamson nanoliquid film flow over a stretching sheet is the main aim of this investigation. The leading Navier–Stokes models are reduced to third-order nonlinear ODE through similarity transformations that are then undertaken using the Hermite wavelet method (HWM). Both 2-dimensional and axisymmetric film flow circumstances have been analyzed. The moving surface parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document} is said to have a limited range for which the solution exists. Specifically, ξ≤-1/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi \\le -1/4$$\\end{document} for axisymmetric flow and ξ≥-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi \\ge -1/2$$\\end{document} for two-dimensional flow. Before decreasing to the boundary condition, the velocity climbs until it reaches its maximum. By taking into account the stretching (ξ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi >0$$\\end{document}) and shrinking (ξ<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi <0$$\\end{document}) wall conditions, streamlines are also examined for axisymmetric and 2-dimensional flow patterns.

Modeling the stability of thin liquid film flows on a uniformly heated slippery inclined substrate: A realistic approach

We investigate the stability of gravity-driven, Newtonian, thin liquid film falling down a uniformly heated slippery rigid inclined wall. The authors of previous research works considered specified temperature (ST) boundary condition to study the effects of slip length. However, the ST boundary condition does not include the effects of heat fluxes at wall–air and wall–liquid interfaces and so fails to incorporate the real situation. Consequently, we consider heat flux/mixed-type boundary condition as the thermal boundary condition on the rigid plate. This boundary condition involves the heat flux from the rigid plate to the surrounding liquid and the heat losses from the wall to the ambient air. Using long-wave expansion method, we construct a highly nonlinear evolution equation in terms of the film thickness at any instant. Using normal mode approach, the linear study reveals the stabilizing (destabilizing) behavior of the wall film Biot number (dimensionless slip length). It is found that the destabilizing tendency of the slip length is more in the absence of thermocapillary stress. The linear study reveals that the destabilizing role of MB may be controlled to some extent by increasing the wall film Biot number Bw. Using asymptotic expansions of the flow variables in terms of the small wave number k, the Orr–Sommerfeld boundary value problem gives an onset of instability in terms of critical Reynolds number. It slightly differs from that of the same as obtained by Benney's long-wave expansion method, due to the consideration of small free surface Biot number [B=O(ϵ)]. For arbitrary wave numbers, using Chebyshev spectral collocation method, the effect of Marangoni number (Ma), slip length (δ), and wall film Biot number (Bw) on the H, S, P, and shear modes of instability are discussed in detail. Near the threshold, both Ma and δ show the destabilizing effect on H mode of instability, whereas Bw gives the stabilizing effect. Interestingly, their roles on H mode of instability becomes diametrically opposite far from the onset of instability. For S mode, both Ma and Bw display the destabilizing effect, whereas δ plays the dual role. For P mode, both Ma and δ show the destabilizing effect, whereas Bw plays the stabilizing role. The slip length (δ) plays the stabilizing role, in the case of shear mode. In the absence of thermocapillary effect, the vorticity balance at the liquid–air interface explains that the amplitude of the vorticity perturbation amplifies the surface deformation due to the presence of inertia and the slip length. In the absence of the slip length, a weakly nonlinear study transforms the evolution equation to the famous Kuramoto–Sivashinsky (KS) equation.

Study on the effect of wall roughness on the flow characteristics of liquid film in airflow

During the flight, water flows under the action of shear force to form the overflow liquid film and freezes to form overflow ice. Overflow ice will change the aerodynamic shape of the aircraft and affect the safety and stability. In this paper, the three-dimensional structure of the liquid film in airflow was measured transiently with the digital image projection technology. The effects of different flat wall roughnesses, airflow velocities, and liquid film flow rates on the flow characteristics of the liquid film were analyzed. The experimental results show that the lower the wall roughness, the more pronounced the liquid film contraction toward the central axis. When the liquid flow rate drops to 0.228 l/min, the continuous liquid film transforms into rivulets on the surface of a large contact angle or low roughness. The average thickness of the liquid film on the flat is greater than that on the rough flat at low airflow velocity and low liquid flow rate, but smaller than that on the rough flat at high airflow velocity and high liquid flow rate. The wave near the inlet has an obvious acceleration process, and after reaching the peak speed, it gradually decreases and stabilizes near a certain value. The smoother the surface, the faster the acceleration of the wave at the inlet, and the greater the final stable wave speed.

A graph-based approach for modeling the soil–water retention curve of granular soils across the entire suction range

This study investigates experimentally the water retention behavior of granular soils from saturation to oven-dry state. The soil–water retention curve (SWRC) tests were conducted on a well-graded sand with clay using tensiometer and chilled-mirror hygrometer techniques. The soil samples were statically compacted at various water contents to different initial densities. The results showed that individual linear segments in the log–log graph could characterize the desorption process of capillary and adsorption water. A novel water retention model in a simple mathematical form was developed by conceptualizing the total water content as the sum of the suction-dependent capillary and adsorption components. The model parameters possess an unambiguous physical meaning. They can be easily calibrated based on the graphical properties of the test data using simple linear regression, which is a significant advantage over conventional SWRC models. The model was validated using the water retention data of the tested soil in this study and the available data of granular soils in the literature. The reproduced curves agree well with the experimental results. This study also analyzed the influence of compaction water content, initial density, and clay content on the capillary and adsorption components of the water retention curve. Additionally, the proposed framework provides a quick approximation method for the adsorption capacity, which plays an essential role in assessing the effective stress and the simulation of liquid film flow in unsaturated granular soils.

Water vapour permeability of inorganic construction materials

Water vapour permeability (WVP) data on brick, stone, plaster and cement-based materials from some seventy publications are reviewed and assessed. Almost all sources use standard cup-test methods or close variants. Comparisons of WVP values from different sources on similar materials confirm that reproducibility between different laboratories is poor. Some deficiencies of cup-test methods are discussed, including uncertainties arising from the use of saturated-salt humidistats and desiccants. There is evidence that the water vapour resistance factor decreases as volume-fraction porosity increases, and data support a simple porosity–tortuosity relation. Data also show that the resistance factor decreases with increasing mean relative humidity across the test specimen, with the wet-cup value consistently lower than the dry-cup values for a given material. The contribution of liquid film flow to mass transfer is discussed. It is shown how film thickness and film-flow permeability may be estimated from the water-vapour sorption isotherm; and a related regression equation is developed It is concluded that available data are inadequate to establish the fundamental physics of WVP; vapour-only permeability data for engineering purposes should be obtained in dry-cup tests at low humidity; and research studies should aim to integrate the WVP into the framework of unsaturated flow theory.

Physical Reservoir Computing Enabled by Solitary Waves and Biologically Inspired Nonlinear Transformation of Input Data

Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper, we experimentally validated a physical RC system that substitutes the effect of randomness that underpins the operation of the traditional RC algorithm for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the ‘next-generation’ improvement of the traditional RC algorithm.

Interplay of fluid rheology and micro-patterning toward modulating draining characteristics on an inclined substrate

We investigate a gravity-driven thin film flow of a non-Newtonian liquid over an inclined micro-patterned surface. We demonstrate the effect of micro-patterning on the film draining rate and the velocity profile by varying the relative slit width (Tr) and the length of the periodic irregularities (L). We unveil the interplay of the substrate structure and the fluid rheology by modeling the non-Newtonian thin film using the Carreau model, and the rheology of the film is varied for different values of power index n. Through numerical simulations, we delineate the effects of inertia, viscous, and capillary forces on the physics of thin film flow. We report a significant augmentation of flow velocity for both shear-thinning and shear-thickening fluids as a result of substrate micro-patterning, with the relative slit width playing a dominant role while the length of the periodic irregularities has only a minor influence on drainage characteristics. However, when the sole effect of fluid rheology is considered, flow velocity enhances for pseudoplastic fluid and decreases for dilatant fluid in comparison to Newtonian fluid. We examine the combined effect of rheology and substrate topography, revealing the dominating influence of micro-patterning at high slit-widths, while the fluid rheology has a greater role to play at lower slit-widths. We also demonstrate that the susceptibility of flow physics on varying rheology or topography is greatest for low viscosity liquids. Finally, we mark different regimes where the augmentation of average velocity and surface velocity are individually achieved. Hence, we propose a suitable combination of substrate structure and fluid rheology to engineer a flow characteristic. Based on the suitability for various applications, we provide the key to simultaneously optimizing the fluid rheology and substrate micro-patterning for precise engineering and controlling the draining characteristics of a thin film.

Numerical investigation on heat transfer enhancement of spray cooling by surface structure optimization

A numerical model of spray cooling for enhanced surfaces in the non-boiling regime is created with deionized water as cooling medium. This model is validated by contrasting the simulated data with the corresponding experimental data, and the relative deviation is within 12 %. Compared with a smooth surface, the area of the enhanced surface is expanded, the cooling performance is significantly improved, but the surface temperature distribution is less uniform. Compared to the straight groove surface with the same area, the heat flux of the radial groove surface is higher because its surface structure is more conducive to the spreading and leaving of the liquid film. Studies of the effects of the structure parameters (groove width and groove number) of the radial groove surface on the heat transfer show that there is an optimal groove width (0.2 mm) and groove number (45) for the strongest cooling capacity, and both the velocity and thickness of the liquid film are significant factors in cooling performance. The faster the liquid film velocity, the thinner the liquid film and, thus, the better the heat transfer. Motivated by these findings, three novel enhanced surfaces are machined to increase liquid film fluidity and heat transfer area even further. The cooling performance of the three novel enhanced surfaces is further improved, and the slope groove surface acquires the strongest cooling capacity due to the acceleration of liquid film flow by gravity, although its heat transfer area is not the largest. Research on all enhanced surfaces indicates that thinner liquid film and faster liquid film flow should be the primary design goals of the enhanced surface, followed by an increase in heat transfer area.

Erratum: “Interplay between salt precipitation, corner liquid film flow, and gas-liquid displacement during evaporation in microfluidic pore networks” [J. Appl. Phys. 133, 074701 (2023)

Erratum: “Interplay between salt precipitation, corner liquid film flow, and gas-liquid displacement during evaporation in microfluidic pore networks” [J. Appl. Phys. 133, 074701 (2023)

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.

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 of flow pattern transition criterion and heat transfer characteristics in vertical rectangular narrow channel for steam heating

This study clarifies the heat transfer characteristics of flow boiling in a narrow vertical rectangular channel at each stage and optimizes the performance of a heat exchanger. The flow pattern and local heat transfer characteristics in a narrow vertical rectangular channel of steam heating with dimensions of 1400 × 250 × 2.75 mm (l × w × s) were experimentally investigated using deionized water as the working medium. Based on the visualization data, the mechanical model and empirical formulas in previous literature, a preliminary derivation of the flow pattern transition criterion for steam heating in a vertical rectangular narrow channel was obtained. The effects of the inlet temperature, mass flux, and heating power on the local heat transfer characteristics were analyzed in conjunction with the flow patterns. Based on the parametric analysis of the experimental data, a new flow boiling heat transfer correlation formula was obtained and applied to the experimental conditions. The results showed that an increase in the inlet temperature had a positive effect on the nucleate boiling section, whereas the effect on the local heat transfer coefficient was minimal after entering the churn flow phases. The increase in mass flux decreased the local heat transfer coefficient in the nuclear state boiling stage and enhanced the local heat transfer coefficient in the evaporation zone of the liquid film flow. The peak of the local heat transfer coefficient tended to shift to the left as the heating power increased. The proposed heat transfer correlation equation could well predict the local heat transfer coefficient of flow boiling in a vertical rectangular narrow channel heated by steam under these experimental conditions.

A robust numerical strategy for finding surface waves in flows of non-Newtonian liquids

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular characteristics. In this paper, we analyze numerically the temporal stability of films of non-Newtonian liquids falling by gravity, on the onset of instability. The liquid flows over an incline, where surface waves appear under certain conditions, and we do not fix a priori its rheological behavior. For that, we made used of the Carreau–Yasuda model without assigning specific values to its constants, and we compute general stability solutions. The numerical strategy is based on expansions of Chebyshev polynomials for discretizing the Orr–Sommerfeld equation and boundary conditions, and a Galerkin method for solving the generalized eigenvalue problem. In addition, an Inverse Iteration method was implemented to increase accuracy and improve computational time. The result is a robust and light numerical tool capable of finding the critical conditions for different types of fluids, which we use to analyze some key fluids. We show that the outputs of the general code match previous solutions obtained for specific computations. Besides increasing our knowledge on surface-wave instabilities in non-Newtonian liquids, our findings provide a new tool for obtaining comprehensive solutions on the onset of instability.

Liquid entrainment in annular gas–liquid two-phase flow: A critical assessment of experimental data and prediction methods

Annular flow is one of the most frequently observed flow patterns with gas–liquid two-phase flows in tubes or channels. In the annular flow pattern, a thin liquid film flows along the channel wall, while the gas flows in the center of the channel carrying liquid droplets in suspension. The fraction of the liquid flow rate that is transported as suspended droplets is quantified using the entrained liquid fraction (ELF), which is a key flow parameter in the analysis and modeling of annular flows. This review provides a critical assessment of ELF experimental data available in the open literature and of ELF prediction methods proposed to date. The experimental data assessment is carried out by means of a large ELF data bank collected from the literature (4175 data points from 53 literature studies; 10 fluids combinations; operating pressures from atmospheric to 20 MPa; experiments carried out with adiabatic, evaporating, and condensing flows through circular tubes, and non-circular channels with diameters from 3.02 to 155.7 mm), which is critically analyzed devoting special attention to important aspects not adequately addressed in previous studies, such as a cross-comparison between different ELF measuring techniques, and the analysis of flow development and gravity effects. The assessment of the ELF prediction methods focuses on 15 widely quoted methods, which are critically analyzed and whose prediction performance is evaluated against the measured data. The curated ELF experimental data bank is provided in full and usable form. Research gaps for further investigations are identified and discussed.

A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.

Mass Transfer Enhancement in Liquid–Liquid Extraction with Discrete Liquid Film Flow

Mass Transfer Enhancement in Liquid–Liquid Extraction with Discrete Liquid Film Flow

Modeling and Analysis of Metal Liquid Film Flow Characteristics during Centrifugal Spray Forming

Liquid films are an important part of liquid metal granulation in the process of centrifugal spray forming. The size of the granulated particles has an important influence on the density, grain size and microstructure uniformity of the deposited blanks. The particle size is closely related to the flow characteristics of liquid films. Therefore, enhancing our understanding of the flow characteristics of liquid films can provide guidance for forming blanks. In this study, force analysis of a liquid film on the surface of a high-speed rotating centrifugal disc used in centrifugal spray-forming technology was carried out using D’Alembert’s principle and Newton’s law of viscosity. Then, combined with the principle of mass conservation, a theoretical model of the smooth flow of the liquid metal film was established. The experimental values obtained by Leshev were compared with our values to verify the correctness and accuracy of the model. Through the model, the influencing factors of the liquid film flow were obtained, such as the centrifugal disc speed, centrifugal disc radius, inlet volume flow rate and kinematic viscosity. Taking A390 aluminum alloy as the research object, the influence of the process parameters on the thickness, velocity and trajectory of the liquid film was revealed theoretically, and the relationship between the process parameters and the trajectory length and liquid film thickness was clarified. Modeling and analysis can not only help us to understand the flow of a liquid film, but also help us to predict the relevant parameters, which is convenient for the accurate and rapid regulation of the process to obtain the desired flow parameters. Therefore, the research content of this paper is of great significance for the preparation of billets with a uniform microstructure and excellent mechanical properties.

Instability of Liquid Film with Odd Viscosity over a Non-Uniformly Heated and Corrugated Substrate.

The effect of odd viscosity on the instability of liquid film along a wavy inclined bottom with linear temperature variation is investigated. By utilizing the long-wave approximation, the non-linear evolution equation of the free surface is derived. By applying the normal mode method, the linear instability of thin film flow is investigated. With the help of multi-scale analysis methods, the weakly non-linear instability of thin film flow is also investigated. The results reveal that the Marangoni effect caused by non-uniform temperature distribution promotes the instability of the liquid film, while the odd viscosity has a stabilizing effect. In addition, for a positive local inclination angle θ, an increase in bottom steepness ζ inhibits the instability of the liquid film flow. In contrast, with a negative local inclination angle θ, increased bottom steepness ζ promotes the instability of the liquid film flow. The results of the temporal linear instability analysis and the weakly non-linear instability analysis have been substantiated through numerical simulations of the non-linear evolution equations.

A numerical study on fluid flow and heat transfer characteristics of oily wastewater falling film outside an elliptical tube

Falling film heat exchangers have recently been widespread as a heat transfer technique for oily wastewater. Researching the characteristics of fluid mechanism for heat transmission is crucial. In this research, numerical models are applied to simulate the heat transmission and flow of falling film outside ellipse tube. In order to emulate fluid flow and heat transmission, the oily wastewater falling film is analyzed utilizing the VOF approach under circumstances of constant thermal flow. On the flow properties and heat transfer coefficient distribution of liquid film, the impacts of the input height, contact angle, liquid film flow rate, and oil content are examined. These computational outcomes are attained: (1) More so than film thickness, according to the simulation results, increasing liquid film flow significantly affects velocity;(2) One of the main causes of how oil concentration affects heat transmission is the complex disturbance process of liquid film and the force change around tube structure;(3) Around 40°, inlet height has the greatest impact on local heat transfer coefficient;(4) The overall heat transmission will deteriorate due to the hydrophobic impact brought on by increased contact angle.

Transient cooling experiment of laminar jet impacting on cylinder

Liquid jet impact cooling is found in many industrial applications. In transient process of liquid jet impacting on surface, there are correlations among liquid film flow, heat transfer regime and surface temperature when phase transition is involved. Aiming at application scenarios of laminar jet impacting on cylindrical cooling targets, an experiment of laminar jet impacting on cylinder was performed to investigate transient cooling characteristics featured by temperature dropping curves. Liquid film evolutions were acquired by high-speed camera, while surface temperatures were monitored by thermocouples, and effects of jet outlet velocity u (outlet Reynolds number Re) and impact height H were explored. Results reveal that, transient process of jet impact is categorized into non-wetted (film boiling, duration of τ1), developing wetted (mainly transition boiling and nucleate boiling, duration of τ2) and fully wetted stages (mainly non-phase transition convection). Among them, τ1 and τ2 are decreased with rising of Re. Jet exhibits steady, perturbed and fractured states at different H. When u = 0.44 m/s (Re = 680), for steady state jet, τ1 decreases from 119 s to 103 s, while variation of τ2 is insignificant as H increases from 27 mm to 37 mm. When jet is unstable (H = 42–47 mm), τ1 drops remarkably while τ2 rises with increasing H. Effect of H on temperature dropping curves is weakened with increasing Re. Unlike cases of liquid impacting on flat surface, there are clear distinctions in durations of each transient stage, and there is a secondary inflection point for surface temperature variation in present experiment due to secondary mixing of liquid film.