Film Flow Research Articles

Nonlinear waves in a sheared liquid film on a horizontal plane at small Reynolds numbers

The nonlinear waves in a sheared liquid film on a horizontal plate at small Reynolds numbers are examined by theoretical and numerical approaches. The analysis employs the long-wave approximation along with finite difference schemes. The results show that the surface tension can suppress disturbances and prevent the occurrence of singularities. While the film flow is driven by the shear stress on the interface, its instability highly depends on the magnitude and direction of gravity. Specifically, when the direction of gravity is opposite to the wall-normal direction, perturbations are stabilized by gravity. In contrast, when these two directions are the same, the gravitational force is destabilizing, and stationary travelling waves can exist if a balance is reached between the effects of gravity and surface tension. For the steady solitary waves, there are quasi-periodic oscillations occurring between two stationary points, indicating the presence of heteroclinic trajectories. For periodic waves, the evolutions are sensitive to several parameters and initial disturbances, while one steady-state wave exhibits a sine function-like behaviour.

Capillary filling dynamics in closed-end carbon nanotubes-Defying the classical Lucas-Washburn paradigm.

The emergence of two-dimensional (2D) materials such as carbon nanotubes (CNTs) offers the possibility of exploring new regimes of capillarity and wetting that remained inaccessible with traditional microfluidic and nanofluidic substrates. Here, we bring out the non-intuitive capillary filling regimes in closed-end CNTs using molecular-level investigations. Contrary to the existing understanding of the advancing liquid meniscus getting retarded by the viscous resistance offered by an entrapped vapor phase in a three-dimensional capillary, here the liquid meniscus is shown to accelerate toward the later stages of the dynamic wetting, which is attributed to the modified surface friction due to a 2D interface. This apparently counterintuitive observation is qualitatively linked to the local pressure fluctuations across the meniscus caused by the spontaneous bombardment of the entrapped vapor molecules, which may ramify into hitherto unexplored phenomena of a shape-reversed meniscus advancing in the 2-D pore. We further develop a simple analytical model to represent the essential physics of the resulting capillary filling dynamics, featuring significant deviations from the classical Lucas-Washburn paradigm. These results may turn out to be imperative in realizing new regimes of capillarity in 2D materials in multifarious applications, ranging from energy storage and water filtration to thin film flows in integrated electronics and photonic devices.

Flow behavior and heat transfer characteristics of liquid film on vertical hot surface by inclined jet impingement

In this study, the flow behavior and heat transfer characteristics of the liquid film on the hot wall by inclined jet impingement are experimentally studied in detail. The effects of jet parameters, such as jet inclination angle, impingement distance, jet Reynolds number (Rej), and nozzle diameter are explored. The liquid film flow is visualized using a high-speed camera, and the surface temperature and heat flux are obtained by solving the inverse heat conduction problem. The results indicate that the liquid film shape is strongly affected by jet inclination angle but is almost unaffected by other parameters. As the inclination angle increases, the liquid film shape changes from elliptical to fusiform. In addition, the onset, enhancement, and disappearance of boiling cause the expansion and contraction of liquid film. The splashing rate is barely affected by jet parameters and remains within the range of 80–95 % under all conditions. The propagation of wetting fronts exhibits anisotropy. Except for the impingement distance, the position of wetting fronts along y-axis direction displays a high dependence on all parameters. The Rej and nozzle diameter have a significant effect on the heat flux at the impingement point and parallel flow zone, while the jet inclination angle and impingement distance only effect the impingement point. The visualization image proves that the droplet impingement pattern is the main reason for the increase in heat flux at higher impingement distances. Optimizing jet parameters can promote the wall to enter the rapid cooling stage in advance and increase maximum heat flux, thereby improving the maximum cooling capacity of the jet. Finally, an empirical equation is proposed to predict the maximum Nusselt number.

Characterization of liquid-thickness distribution in micropores on elastic surface under sliding and pressurizing conditions.

To improve the performance of studless tires on ice surfaces, the mechanism of liquid film removal must be elucidated. In this study, an experimental system is developed to simulate the running conditions of a studless tire, and the microscopic liquid film flow generated between the rubber surface and glass is observed to evaluate the liquid thickness distribution. Liquid film removal by micropores on foamed rubber samples is investigated by visualizing the liquid thickness in the micropores. The proposed system enables variations in the pressure and sliding velocity between the rubber and glass. The liquid thickness in the micropores is measured using laser-induced fluorescence, and the effects of pressure and sliding velocity on the thickness are examined. Water penetrates the micropores on the rubber sample surface, and different liquid thicknesses are obtained for each pore. The amount of liquid penetrating the pores is affected to a greater extent by the sliding velocity than by the pressure. Therefore, liquid penetration is more strongly influenced by the hydrodynamic effect of the increasing inertia of the liquid under high sliding velocities than by the elastic deformation of the pore.

A general model for spin coating on a non-axisymmetric curved substrate

We derive a generalised asymptotic model for the flow of a thin fluid film over an arbitrarily parameterised non-axisymmetric curved substrate surface based on the lubrication approximation. In addition to surface tension, gravity and centrifugal force, our model incorporates the effects of the Coriolis force and disjoining pressure, together with a non-uniform initial condition, which have not been widely considered in existing literature. We use this model to investigate the impact of the Coriolis force and fingering instability on the spreading of a non-axisymmetric spin-coated film at a range of substrate angular velocities, first on a flat substrate, and then on parabolic cylinder- and saddle-shaped curved substrates. We show that, on flat substrates, the Coriolis force has a negligible impact at low angular velocities, and at high angular velocities results in a small deflection of fingers formed at the contact line against the direction of substrate rotation. On curved substrates, we demonstrate that, as the angular velocity is increased, spin-coated films transition from being dominated by gravitational drainage with no fingering to spreading and fingering in the direction with the greatest component of centrifugal force tangent to the substrate surface. For both curved substrates and all angular velocities considered, we show that the film thickness and total wetted substrate area remain similar over time to those on a flat substrate, with the key difference being the shape of the spreading droplet.

Oscillatory squeeze flow through an Oldroyd-B fluid-saturated porous layer

This study deals with the analytical investigation of oscillatory squeeze film flow through a Brinkman viscoelastic Oldroyd-B fluid-saturated porous layer subject to two vertically harmonically oscillatory disks. The validity of the present proposed analytical solutions is first demonstrated for the Newtonian fluids when both Λ1 and Λ2 tend to zero by comparison with the previous literature. Results demonstrate that an increase in the elasticity parameter Λ1 correlates with a rise in axial velocities, indicating that the relaxation time Λ1 facilitates enhanced squeeze flow. In the case of squeeze film flow in porous layers, low oscillating frequencies exert minimal effects on axial velocities, independent of variations in the viscoelasticity parameter Λ1. However, at higher oscillating frequencies, axial velocities escalate with increasing the viscoelasticity parameter Λ1. Furthermore, the retardation time Λ2 of the viscoelastic fluid shows no significant effect on the axial velocity, regardless of oscillating frequency changes in both pure fluids and porous layers.

Visualization Study on Oil Return Characteristics of Vapor Compression Heat Pump System

Vapor compression heat pump technology is a widely utilized method for energy conversion. Lubricating oil plays a crucial role in the heat pump system cycle by effectively reducing wear on the compressor’s moving parts and preventing refrigerant leakage. However, it can also create an oil film in the heat exchange equipment, which increases thermal resistance and diminishes heat transfer efficiency. This study utilizes a vapor compression heat pump system test bench to investigate factors influencing the system’s oil circulation rate, the two-phase flow patterns of refrigerant and lubricating oil, and the impact of oil circulation on system performance. The findings reveal that as the compressor speed increases, the oil circulation rate initially decreases before increasing again. Additionally, a decrease in the evaporator’s heat load leads to a reduction in oil circulation at high temperatures, while it increases at low temperatures. Furthermore, increasing the opening of the electronic expansion valve results in a gradual decrease in the oil circulation rate, whereas an increase in the refrigerant charge correlates with a rise in the oil circulation rate. The oil return flow pattern can primarily be categorized into three states: slow oil return, oil film flow, and high-speed oil return. These patterns are closely related to the degree of superheat, with lower superheat levels intensifying oil return.

EFFECT OF EXTERNAL HARMONIC VIBRATION ON THE FORMATION OF SOLITARY WAVES IN FALLING TWO-LAYER LIQUID FILMS

Abstract We study the influence of a low-frequency harmonic vibration on the formation of the two-dimensional rolling solitary waves in vertically co-flowing two-layer liquid films. The system consists of two adjacent layers of immiscible fluids with the first layer being sandwiched between a vertical solid plate and the second fluid layer. The solid plate oscillates harmonically in the horizontal direction inducing Faraday waves at the liquid–liquid and liquid–air interfaces. We use a reduced hydrodynamic model derived from the Navier–Stokes equations in the long-wave approximation. Linear stability of the base flow in a flat two-layer film is determined semi-analytically using Floquet theory. We consider sub-millimetre-thick films and focus on the competition between the long-wavelength gravity-driven and finite wavelength Faraday instabilities. In the linear regime, the range of unstable wave vectors associated with the gravity-driven instability broadens at low and shrinks at high vibration frequencies. In nonlinear regimes, we find multiple metastable states characterized by solitary-like travelling waves and short pulsating waves. In particular, we find the range of the vibration parameters at which the system is multistable. In this regime, depending on the initial conditions, the long-time dynamics is dominated either by the fully developed solitary-like waves or by the shorter pulsating Faraday waves.

Exploration of drag on the thin film of micropolar fluid flow within a permeable medium

Advances in thin film acquired many industrial applications because of their use in several products like electronic devices, magnetic recording media, LED, optical coating, etc. Additionally, thin film has an extensive role in the study of multiferroic materials and superlattices in quantum phenomena. Therefore, it is an urge to predict the importance of drag employing Darcy-Forchheimer on the thin film flow of micropolar liquid through an expanding plate embedding with a permeable medium. Moreover, the current model enriches by incorporating the impact of Soret because of the cross-diffusion process and the radiative heat. By using the appropriate transformed variables, the designed problem is distorted, and further, these sets of equations are handled numerically employing Runge-Kutta shooting technique. The computation is carried out by deploying in-house built-in function bvp4c in MATLAB. The significant operational behavior of the manipulated quantities is accessible graphically and deliberated in the discussion section. The important findings are elaborated as; the angular velocity distribution shows a greater deceleration for the increasing microrotation and the inertial drag effect. Further, the thermo-diffusion due to Soret also attenuates the concentration profile and the solutal thickness became thinner for the higher heavier species.

The Role of the Working Fluid and Non-Ideal Thermodynamic Effects on Performance of Gas Lubricated Bearings

Abstract Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Unsteady numerical simulations of aircraft icing based on the dynamic grid method

In this study, an unsteady numerical simulation method based on dynamic grids was established to solve unsteady aircraft icing processes. The dual-time step method was used to achieve the time advancement of the transient airflow and droplets fields. The droplets trajectory was calculated using the Euler method, which incorporates a supercooled large droplets model. The transient evolution of the water film and ice layer on the substrate surface was considered in the icing thermodynamic model. The accuracy of the unsteady method for ice-shape prediction was verified via comparison and analysis of numerical examples. Additionally, the rime and glaze ice formation processes were explored, and the coupling effects of ice horn growth and the air convective heat transfer coefficient, water collection coefficient, and water film flow on the substrate surface were studied. The ice shapes calculated by unsteady and quasi-steady methods were compared. The results indicated that the latter predicts a larger icing range than the former. Moreover, there may be more obvious distinctions between these two methods in predicting glaze ice.

Modelling Mucus Clearance in Sinuses: Thin-Film Flow Inside a Fluid-Producing Cavity Lined with an Active Surface

The paranasal sinuses are a group of hollow spaces within the human skull, surrounding the nose. They are lined with an epithelium that contains mucus-producing cells and tiny hairlike active appendages called cilia. The cilia beat constantly to sweep mucus out of the sinus into the nasal cavity, thus maintaining a clean mucus layer within the sinuses. This process, called mucociliary clearance, is essential for a healthy nasal environment and disruption in mucus clearance leads to diseases such as chronic rhinosinusitis, specifically in the maxillary sinuses, which are the largest of the paranasal sinuses. We present here a continuum mathematical model of mucociliary clearance inside the human maxillary sinus. Using a combination of analysis and computations, we study the flow of a thin fluid film inside a fluid-producing cavity lined with an active surface: fluid is continuously produced by a wall-normal flux in the cavity and then is swept out, against gravity, due to an effective tangential flow induced by the cilia. We show that a steady layer of mucus develops over the cavity surface only when the rate of ciliary clearance exceeds a threshold, which itself depends on the rate of mucus production. We then use a scaling analysis, which highlights the competition between gravitational retention and cilia-driven drainage of mucus, to rationalise our computational results. We discuss the biological relevance of our findings, noting that measurements of mucus production and clearance rates in healthy sinuses fall within our predicted regime of steady-state mucus layer development.

Numerical simulation on the condensation heat transfer and flow characteristics outside smooth and enhanced tubes

Most of the current studies only conducts two-dimensional simulations of condensation heat transfer and flow outside enhanced tubes, which cannot accurately reflect the flow and heat transfer characteristics of liquid film outside enhanced tubes. In order to provide theoretical support for the design optimization of enhanced tubes, this study adopts the VOF multiphase model and Lee condensation model to simulate the condensation heat transfer(HTC) of refrigerants outside smooth and enhanced tubes. The instantaneous film flow characteristics of the liquid film outside the horizontal smooth and enhanced tubes are analyzed, and the thickness of the liquid film and the relationship with the condensation heat transfer coefficient of the smooth and enhanced tubes under different working conditions are calculated. The refrigerants are compared under the same working conditions, and the results are shown: The simulation results are in good agreement with the experimental data and the Nusselt analytical solution, and the error is all within 15%; the distribution of liquid film is highly sensitive to the magnitude of local condensation heat transfer coefficients, and the condensation HTC outside the enhanced tube is approximately six times of that of smooth tube. Combining the distribution of the liquid film and the thermophysical properties of the refrigerants, it was determined that R410A has the highest HTC, while R1234yf has the lowest HTC.

Numerical simulation and experimental study of the influence of disk groove structure optimization on the air film flow field signature of an air-cushion sandwich belt conveyor

A new type of disk groove mechanism was developed and manufactured. The effects of the structural and operating factors of the disk groove on the air film loading performance were examined using single factor and orthogonal experimental methods. The results of numerical simulation and experimental studies showed that the air film loading performance correlated positively with the orifice diameter and inlet pressure, with the orifice spacing and diameter having the most significant effects, and that the belt speed boosted the air film uniformity. Meanwhile, a comparative analysis of the corresponding level values showed that an air film thickness of 0.8 mm, orifice diameter of 5 mm, orifice spacing of 30 mm, inlet pressure of 8000 Pa, and conveyor speed of 5 m/s were the optimal parameter combinations for the maximum loading capacity. To verify the accuracy of the model, a field experiment was conducted at Jiangmen Southern Conveying Machinery Engineering Co., Ltd. The air film pressure at the experimental position matched the numerical simulation results. In addition, when the number of rows was one and the air volume was 10 m3/h, the smallest value of traction resistance was obtained under minimum power consumption.

Interfacial characterization of spinning water film along a concave wall

Abstract Thin liquid film flowing down the inner concave surface of a vertical cylindrical vessel is examined. At the top of the vessel, the water is injected horizontally at high speed circumferentially along the vessel wall and flows downwards due to the action of gravity. This turbulent film flow is modeled using the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) approaches combined with the volume-of-fluid method. The results of both methods are validated with direct numerical simulation. The Favre-filtered two-phase LES, which is implemented and studied in this paper, can reasonably predict the film thickness similarly to that of the RANS approach using the elliptic blending Reynolds stress model, although it requires fine resolution in the wall region. The effect of volume flow rate on the film structure and thickness is investigated. The film thickness is shown to be nearly constant when the wall is partially wetted and changes as the cubic root of the volume flow rate when the spinning film encloses the entire circumference of the vessel.

On the non-linearity of rheological film condensation

Condensation of non-Newtonian fluids is a less explored research field but has tremendous potential in the industry. We propose a mathematical theory to model the behaviour of non-Newtonian film condensation on vertical surfaces. The simple theory can contribute to understanding the operation of many engineering appliances using motor oils, polymeric liquids, and fuels. The well-known power-law model approximates the viscosity of condensate. We vary the power-law index (n) within 0.8≤n≤1.2 to encompass the behaviour of shear-thinning, Newtonian and shear-thickening films, while the flow consistency index (μ0) remains constant throughout the study. Since the film flow is gravity-driven, stream-wise advection is expected to dominate over cross-stream advection. We, however, establish the subtle role of cross-stream advection within the thin condensate film. We have identified a thinner film, a lower condensate drainage rate and a greater average heat transfer coefficient (hm) as an influence of the cross-stream advection. An exclusion of cross-stream advection transforms temperature distribution across the film from non-linear to linear. The linear temperature distribution is unrealistic for Ja≥0.5. We illustrate approximately 5% error incurred for neglecting cross-stream advection in estimating hm at Ja=0.81 and n=0.8. The error increases with a further decrease in n values or an increase in the Ja. The exclusion of cross-stream advection affects the film-thickness and average heat transfer disproportionately in shear-thinning and shear-thickening regimes. Finally, we propose mathematical expressions to estimate heat transfer coefficient and Nusselt number, which would be helpful for field engineers.

Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number St, Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, St, De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, St, and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.

Hyperslip velocity of melting ice sliding down inclined parallel ridges

A geometric and physical model for melting ice sliding over inclined superhydrophobic (SH) surfaces with parallel ridges is presented. By analyzing the micro-shear flows of molten liquid films between the ice layer and SH surfaces, the hyperslip velocities of melting ice sliding are investigated. The stick-slip boundary condition of the SH surface is used to establish the dual-series equations analytically, and the numerical solutions are implemented by truncating Fourier series and transforming the dual-series equations into linear algebraic equations to determine the hyperslip velocities of melting ice sliding. The numerical results indicate that the non-dimensional hyperslip velocities increase nonlinearly from near 0 to approximately 1.1 for longitudinal sliding and from near 0 to approximately 0.55 for transverse sliding with an increasing air groove ratio (a). The hyperslip velocities increase with increasing δ at the beginning initially (δ < 1), after which they tend toward asymptotic solutions as δ = 1. The hyperslip velocity ratio (Wh/Uh) shows that longitudinal ridges are at least twice as effective as transverse ridges in enhancing the ice hyperslip velocity, with the velocities accounting for more than 60% of the ice sliding velocities for arbitrary θ at a = 0.95 and δ = 0.1. The relative deviations between the numerical and asymptotic solutions are less than 5% at δ = 1, with the maximum relative deviation occurring at a = 0.65 for arbitrary θ.

Coating flow of a liquid film with colloidal particles on a vertical fiber

A thin liquid film of colloidal suspension is considered which is spreading down on a vertical cylinder under the effect of gravity. A precursor film model is employed at the three-phase contact line to relieve the stress singularity. The curvature pressure leads to the formation of a capillary ridge at the contact-line. Bulk and surface colloids are assumed to be present in the liquid film. The interfacial pattern is governed by the film evolution equation, obtained by simplifying mass and momentum balance equations within the lubrication assumption, while rapid vertical diffusion is assumed for the advection–diffusion equation of the bulk concentration. Fluid viscosity and diffusivity are considered to be functions of the particle volume fraction. The effects of the bulk and surface colloids on the spreading film dynamics are systematically studied. The presence of bulk colloids leads to the thinning of the capillary ridge for smaller inlet bulk colloid concentrations. On the other hand, a larger inlet bulk concentration leads to the formation of a secondary advancing front behind the capillary ridge in the film profile. A reduced contact point velocity is observed with an increase in the upstream bulk concentration. Surface concentration is found to result in a hump-like structure behind the capillary ridge in the upstream direction due to solutal Marangoni stress. The Marangoni stress also hinders the surface-tension-driven spreading, resulting in a smaller contact line velocity. Reducing the Bond number results in unstable film profiles, which lead to a wave-like structure in the region with no bulk concentration gradients.

Evolution of supersonic cooling film flow over concave and convex surfaces with different radius curvatures

A cooling film (Mach 2.3) is injected into a supersonic wind tunnel's (Mach 3.8) flow field. As the curvature radius decreases, mixing layer destabilization is delayed on the CV (convex wall) and advanced on the CC (concave wall). When x = 20–60 mm, wall pressure is influenced by the cooling film, and when x = 100–220 mm, curvature dominates. As the curvature radius decreases, pressure on the concave wall increases more rapidly, while that on the convex wall decreases more swiftly. IP (impulse for bulk dilation) values on the CC-1500 and CV-1500 walls are approximately twice those on the CC-3000 and CV-3000 walls, respectively.