Dynamics Of Thin Liquid Films Research Articles

Swirling Capillary Instability of Rivlin–Ericksen Liquid with Heat Transfer and Axial Electric Field

The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion.

Nanoscale Investigation into Dynamics of Thin Liquid Films during Bouncing and Attachment of Rising Air Bubbles on Hydrophilic and Hydrophobic Surfaces.

Investigations on bouncing and attachment of free-rising air bubbles on hydrophobic surfaces have been limited to side-view, high-speed photography of the bubble-plate attachment process. In this work, an investigation of the dynamics as well as stability of thin liquid films (TLFs) between free-rising air bubbles and quartz surfaces was performed using a newly developed multiple-wavelength synchronized reflection interferometry microscopy (SRIM) technique. The effect of surface hydrophobicity on both the stability and critical rupture thickness of TLFs was investigated. Results showed that the TLF ruptured at a critical rupture thickness of 100-1000 nm or beyond during bubble's impact on hydrophobic quartz surfaces. The critical rupture thicknesses varied depending on the surface hydrophobicity as well as surface asperity. A higher surface hydrophobicity, in general, contributed to a higher critical rupture thickness. In addition, the effect of n-octanol on the stability of the TLFs was investigated. Results showed that film stability increased with increasing the concentration of n-octanol, which was accompanied by a significant decrease in the critical rupture thickness. The present result illustrates, for the first time, the dynamics of TLFs on hydrophobic surfaces under a dynamic condition compared with previous studies under a quasi-equilibrium condition. The information revealed from the present work has a significant implication to many industrial applications, including froth flotation and other biological and semiconductor applications.

Breakup of Thin Liquid Films: From Stochastic to Deterministic.

The thinning and rupture of thin liquid films is a ubiquitous process, controlling the lifetime of bubbles, antibubbles, and droplets. A better understanding of rupture is important for controlling and modeling the stability of multiphase products. Yet literature reports that film breakup can be either stochastic or deterministic. Here, we employ a modified thin film balance to vary the ratio of hydrodynamic to capillary stresses and its role on the dynamics of thin liquid films of polymer solutions with adequate viscosities. Varying the pressure drop across planar films allows us to control the ratio of the two competing timescales, i.e., a controlled hydrodynamic drainage time and a timescale related to fluctuations. The thickness fluctuations are visualized and quantified, and their characteristics are for the first time directly measured experimentally for varying strengths of the flow inside the film. We show how the criteria for rupture depend on the hydrodynamic conditions, changing from stochastic to deterministic as the hydrodynamic forces inside the film damp the fluctuations.

Nonlinear dynamics of thin liquid films subjected to mixed-frequency electrical field

The nonlinear dynamics of the interface between both perfect and leaky dielectric liquid films, interposed between two parallel electrodes, are investigated under the effect of mixed-frequency electric fields. A coupled system of evolution equations is derived in dimensionless form, by employing the long-wave approximation. The linear stability analysis is implemented in accordance with the characteristics of each specific case, namely, the constant (DC) and the altering (AC) fields. In particular, the response of the system to the multi-mode AC electrical field is analyzed. Assisted by the conclusions of the theoretical investigation, the initial-boundary-value problem associated with the coupled system of evolution equations is solved numerically for several parameter sets. The system behavior is studied by monitoring the evolution process and by examining the steady/quasi-steady pillar formations in the nonlinear regime. The possibility to generate interface profiles of diverse topological forms, to manipulate their features, and to control the time dependent progress and the film rupture by imposing different combinations of frequencies and/or amplitudes of the corresponding mode is confirmed.

Dynamics of thin liquid films on vertical cylindrical fibres

Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.

Modeling coating flow and surfactant dynamics inside the alveolar compartment

We derive a new model for the coating flow inside the alveolar compartment, taking into account pulmonary surfactant production and recycling by Type 2 cells as well as its degradation. As the thickness of alveolar coating is much smaller than the average radius of the alveoli, we employ the classical lubrication approximation to describe the thin liquid film dynamics in the presence of pulmonary surfactant, which is a surface tension reducing agent and thus prevents the lungs from collapse. In the lubrication limit, we derive a degenerate system of two coupled parabolic partial differential equations that describe the time evolution of the thickness of the coating film inside the alveoli together with that of the surfactant concentration at the interface. We present numerical simulations using parameter values consistent with experimental measurements.

Switching the Roles of Wettability-based Patterns Through Solutal Marangoni Effect

Controlling the dynamics of thin liquid films on solid surfaces is illustrated by a combination of substrate patterning and solutal Marangoni effect. A solid surface, patterned based on wettability differences, can trigger film instability due to wettability gradient-driven flows. Additionally, if insoluble surfactants are introduced at the liquid film surface, the surfactant transport can cause surface-tension gradients across the film, and a solutal Marangoni flow results. By using suitable non-uniform initial surfactant concentration distributions, the rate and direction of Marangoni flow can be manipulated to compete with the wettability gradient-driven flows. It is found that film dewetting can be reversed in selected problem parameter space. Dewetting can be engendered on more wettable patches of the bounding solid, with a consequent accumulation of the liquid on less wettable regions. The importance of length scales of the less and more wettable patches on switching the roles of wetting behaviour is also investigated.

Dynamics of thin liquid films flowing down the uniformly heated/cooled cylinder with wall slippage

Coating liquid films on cylinders occurs widely in nature, material sciences, and industrial processes. A typical example is the fabrication of thin solid films, which could be achieved by drawing the heated cylinder from the liquid pool and followed by a drying process. However, in some cases, the surface of the coated cylinder is actually not smooth and exhibits hydrophobicity where the slip effect may come into play. Therefore, in this paper, we study the dynamics of thin liquid films flowing down the uniformly heated or cooled cylinder in the presence of wall slippage. The thermocapillary and slip effects on the thin film flows are examined by a thin film model. Linear stability analysis (LSA) indicates that when the cylinder is heated, thermocapillary effect enhances the Rayleigh-Plateau instability, while when the cylinder is cooled, thermocapillary effect suppresses this instability. However, we find that wall slippage always promotes the capillary instability, and when M1+2β1+3β<-13, where M and β are the reduced Marangoni number and dimensionless slip length, the system are always linearly stable. The linear wave speed given by cL=1+2β, is promoted by the wall slippage but independent of the thermocapillary effect. In addition, nonlinear traveling-wave study shows that the size and moving speed of the sliding droplets are promoted for a heated cylinder and reduced for a cooled cylinder, respectively. The size and moving speed of the sliding droplets are enhanced by wall slippage. Finally, direct numerical simulations (DNS) of the full thin film model clearly demonstrate the role of thermocapillary and slip effects, agreeing well with the linear stability analysis and the nonlinear traveling-wave solutions. Our results offer insight into the influence of wall slippage on the dynamics of thin film flows coating on cylinders in non-isothermal environments.

Effects of Nozzle Geometry on the Fluid Dynamics of Thin Liquid Films Flowing down Vertical Strings in the Rayleigh-Plateau Regime.

Thin-liquid films flowing down vertical strings undergo instability, creating wavy film profiles and traveling beads. Previous studies assumed that the liquid film thickness and velocity profiles within the healing length from a nozzle were specified by the Nusselt solution, independent of the nozzle geometry. As a result, the influence of the nozzle diameter on the flow characteristics, such as the liquid bead size, spacing, and traveling speed, was largely overlooked. We report an experimental and numerical simulation study on liquid-film flows in the Rayleigh-Plateau regime while systematically varying the nozzle diameter from 0.5 to 3.2 mm at different mass flow rates (0.02, 0.04, 0.06, and 0.08 g/s). We find that the nozzle diameter does have a strong influence on the flow regime and the flow characteristics. We identify the thickness of a nearly flat portion of a liquid film that precedes the onset of instability, which we term the preinstability thickness, as a critical flow parameter that governs the size, spacing, and frequency of liquid beads that develop downstream. By defining the liquid film aspect ratio α in terms of the preinstability thickness, we capture a flow transition from the Rayleigh-Plateau (RP) instability regime to the isolated droplet regime. Improved understanding of the flow regimes and characteristics assists in the systematic design and optimization of a wide variety of processes and devices, including fiber coating and direct contact heat and mass exchangers.

Dynamics of a thin liquid film under shearing force and thermal influences

Study of liquid film dynamics promotes understanding the critical heat flux (CHF) of boiling heat transfer, which occurs as the liquid layers (micro-layer and macro-layer) near the heater wall lose their integrity. Since the measurement at micro-scale is a challenge, and further complicated by the chaotic nature of the boiling process, profound knowledge on the thin liquid film dynamics is not well documented in the existing literature. In the present paper, we employ a confocal optical sensor system to study the dynamics and the integrity of a thin liquid film sheared by the co-flowing air from above and heated from below in a horizontal aluminum channel. The results indicate that the entrainment governs the liquid film thinning process under adiabatic or lower heat flux conditions, whereas the evaporation becomes more pronounced in a higher heat flux system. The detailed evolution of liquid film is discussed. Based on our experimental observations, the critical film thickness of an integral film is related to the condition of the heating surface and the heat flux. For a specific surface, the critical film thickness remains constant under a defined heat flux and increases with the increasing heat flux. A spectrum analysis is also implemented to analyze the film instability. It is concluded that the heat flux is the dominant factor to govern the film instability compared with the effect of differential velocities of gas and liquid flow.

Numerical simulation of non-isothermal thin liquid film flow on inclined plane using an implicit finite difference scheme

The classical problem of the stability and dynamics of thin liquid films on solid surfaces has been studied extensively. Particularly, thin liquid films subjected to various physico-chemical effects such as thermocapillarity, solutal-Marangoni and evaporative instabilities at the film surface has been the focus of research for more than two decades. Various flow configurations of thin film such as thin film on plane, inclined, and wavy surfaces has been the subject of recent investigations. An inclined film compared to a horizontal film, also experiences the gravity force which may significantly influence the nonlinear dynamics of the film coupled with other forces. In this research, we attempt to study the stability and dynamics of thin liquid films subjected to thermocapillarity and evaporative instabilities at the free surface besides instability owing to ubiquitous van der Waals attraction, using numerical simulations. For a Newtonian liquid, flow in thin liquid film on a planar support and bounded by a passive gas, is represented by Navier-Stokes equation, equation of continuity and appropriate boundary conditions. The external effects are incorporated in the body force term of the Navier-Stokes equation. These governing equations are simplified using the so called long-wave approximation to arrive at a nonlinear partial differential equation, henceforth called equation of evolution (EOE), which describes the time evolution of the interfacial instability in the film caused by internal and/or external effects. Efficient numerical method is required for the solution of the equation of evolution (EOE) in order to comprehend the nonlinear dynamics of the thin film. Here we present the results of our numerical simulation using Crank-Nicholson implicit finite difference scheme applied to the thin film model incorporating instabilities owing to gravity, evaporation and thermo-capillarity. Comparison of our results with those obtained from Spectral method, show remarkable agreement for most of the cases investigated.

Numerical simulation of non-isothermal thin liquid film flow on inclined plane using an implicit finite difference scheme

The classical problem of the stability and dynamics of thin liquid films on solid surfaces has been studied extensively. Particularly, thin liquid films subjected to various physico-chemical effects such as thermocapillarity, solutal-Marangoni and evaporative instabilities at the film surface has been the focus of research for more than two decades. Various flow configurations of thin film such as thin film on plane, inclined, and wavy surfaces has been the subject of recent investigations. An inclined film compared to a horizontal film, also experiences the gravity force which may significantly influence the nonlinear dynamics of the film coupled with other forces. In this research, we attempt to study the stability and dynamics of thin liquid films subjected to thermocapillarity and evaporative instabilities at the free surface besides instability owing to ubiquitous van der Waals attraction, using numerical simulations. For a Newtonian liquid, flow in thin liquid film on a planar support and bounded by a passive gas, is represented by Navier-Stokes equation, equation of continuity and appropriate boundary conditions. The external effects are incorporated in the body force term of the Navier-Stokes equation. These governing equations are simplified using the so called long-wave approximation to arrive at a nonlinear partial differential equation, henceforth called equation of evolution (EOE), which describes the time evolution of the interfacial instability in the film caused by internal and/or external effects. Efficient numerical method is required for the solution of the equation of evolution (EOE) in order to comprehend the nonlinear dynamics of the thin film. Here we present the results of our numerical simulation using Crank-Nicholson implicit finite difference scheme applied to the thin film model incorporating instabilities owing to gravity, evaporation and thermo-capillarity. Comparison of our results with those obtained from Spectral method, show remarkable agreement for most of the cases investigated.

Three-dimensional dynamics of thin liquid films on vertical cylinders with Marangoni effect

The effects of thermocapillary force on the three dimensional dynamics of thin liquid films flowing down a uniformly heated vertical cylinder are investigated using a thin film model. Linear and nonlinear analyses predict the existence of a non-axisymmetric mode due to the Marangoni effect. Symmetry-breaking of axisymmetric steady traveling waves is observed when the Marangoni number exceeds a critical value. Linear stability analysis demonstrates that the steady traveling wave can be unstable to azimuthal disturbances due to the Marangoni effect, leading to the formation of non-axisymmetric patterns.

Nonlinear dynamics of a thin liquid film deposited on a laterally oscillating corrugated surface in the high-frequency limit

The nonlinear dynamics of thin liquid films deposited on various periodically corrugated substrates, both left-right symmetric and asymmetric, subjected to lateral vibration in the high-frequency limit is investigated. The method used to derive the governing evolution equation is based on the long-wave approximation, multiscale time expansion, and averaging over the fast time scale. The resulting evolution equation contains the effects of gravity, capillarity, vibration, and the substrate topology. The initial-boundary-value problem associated with this evolution equation is numerically solved and the system behavior is investigated for a variety of parameter sets. Typical patterns emerging as a result of the film evolution include hump formation within the troughs of the substrate and homogenized coatings whose configuration resembles that of the substrate, as well as the possibility of film rupture. We show that the choice of the vibration parameters and the topological features of the substrate may be used for controlling the shape of the film interface as well as its properties such as the amplitude, continuity, or rupture. Together with the film profiles stationary in terms of the averaged film interface with respect to the slow time scale, time evolution of the total (comprising of the averaged and pulsating components) interfacial profiles and streamline maps is presented to illustrate the film flow. We carry out Floquet stability analysis of periodically replicated steady states for the time-independent problem, linear stability analysis based on a reduced low-order projection approximation for the time-dependent problem, and stability analysis with respect to disturbances of a larger wavelength. We have found also that in the case of two-dimensional corrugated substrates, the vast majority of two-dimensional steady-state flows in terms of the averaged film interface exhibit stability in three dimensions with respect to small perturbations in the transverse spatial direction.

A numerical reduced model for thin liquid films sheared by a gas flow

The non-linear dynamics of thin liquid films sheared by a laminar gas flow in a channel is investigated. Such a two-layer flow is driven by pressure gradient and possibly by the gravity force. We describe the liquid phase with a long-wave integral model, with the aim to save computational cost with respect to the full Direct Numerical Simulation (DNS) of the Navier–Stokes equations. We derive this long-wave model by the integration of the Navier–Stokes equations over the film thickness, and by an asymptotic expansion up to the first order in terms of a long-wave parameter. These depth-integrated (or shallow water) equations are discretized by means of an augmented system, which holds an evolution equation for the surface tension in order to avoid numerical instabilities of classical upwind and centered schemes. On the other side, we study the gas phase with compressible Navier–Stokes equations, and we discretize them by means of a low-Mach scheme, accounting also for moving meshes (ALE). In order to analyze liquid–gas interactions, we introduce then a coupling methodology between depth-integrated equations and Navier–Stokes equations. This approach represents a compromise between the two existing methods: the full DNS, and the full long-wave model applied to both phases. In order to validate this approach, we present comparisons with DNS, showing a good agreement of spatio-temporal evolutions of the film thickness and the stress field. Furthermore, interfacial shear stress and pressure gradient evolutions are shown to be in accordance with those provided by two-layer second-order low-dimensional models.

Cracks in bursting soap films

The rupture of soap films is traditionally described by a law accounting for a balance between momentum and surface tension forces, derived independently by Taylor and Culick in the 1960s. This law is highly relevant to the dynamics of thin liquid films of jets when viscous effects are negligible. However, the minute amounts of surfactant molecules present in soap films play a major role in interfacial rheology, and may result in complex behaviour. Petit et al. (J. Fluid Mech., vol. 774, 2015, R3) challenge standard thin film dynamics via intriguing experiments conducted with highly elastic surfactants. Unexpected structures reminiscent of faults are observed.

Opening and retraction of particulate soap films

We study for the first time the bursting dynamics of thin liquid films laden with hydrophobic micronic particles either with free or constrained edges. We highlight that the particles can arrange in bilayer or monolayer configurations and explore a range of particles coverage from zero to random close packing. When the particles bridge the two interfaces (monolayer configuration) of free-edge films, the hole opens intermittently. For the other cases, we observe constant retraction velocities, modeled by balancing liquid and particles inertia against surface tension as in Taylor-Culick theory. But, this approach is only valid up to a critical value of particles coverage due to the interplay between the interfaces and the friction between particles.

Measurement of Interactions between Solid Particles, Liquid Droplets, and/or Gas Bubbles in a Liquid using an Integrated Thin Film Drainage Apparatus

A novel device was designed to measure drainage dynamics of thin liquid films confined between a solid particle, an immiscible liquid droplet, and/or gas bubble. Equipped with a bimorph force sensor, a computer-interfaced video capture, and a data acquisition system, the newly designed integrated thin film drainage apparatus (ITFDA) allows for the direct and simultaneous measurements of force barrier, true film drainage time, and bubble/droplet deformation under a well-controlled external force, receding and advancing contact angles, capillary force, and adhesion (detachment) force between an air bubble or oil droplet and a solid, a liquid, or an air bubble in an immiscible liquid. Using the diaphragm of a high-frequency speaker as the drive mechanism for the air bubble or oil droplet attached to a capillary tube, this newly designed device is capable of measuring forces over a wide range of hydrodynamic conditions, including bubble approach and retract velocities up to 50 mm/s and displacement range up to 1 mm. The results showed that the ITFDA was capable of measuring hydrodynamic resistance, film drainage time, and other important physical parameters between air bubbles and solid particles in aqueous solutions. As an example of illustrating the versatility, the ITFDA was also applied to other important systems such as interactions between air bubble and oil droplet, two air bubbles, and two oil droplets in an aqueous solution.

Nonlinear dynamics of thin liquid films consisting of two miscible components

Recently, we systematically derived a system of two coupled conservation equations governing a thin liquid layer with a deformable surface composed of two completely miscible components [Phys. Fluids 22, 104102 (2010)]. One equation describes the location of the free surface and the second one the evolution of the mean concentration. This lubrication model was investigated previously in linearized form. The study is now extended to the fully nonlinear case of thin liquid films of a binary mixture (in one and two horizontal spatial dimensions) with and without heat transport. For an initially flat and motionless film heated from below, we analyze the component separation induced by the Soret effect. Nonlinear simulations show that the Soret effect can cause a multitude of interesting behaviors, such as oscillatory patterns and solitonlike structures (localized traveling drops or holes). A stronger component separation induced by stronger Soret effects favors faster-moving localized structures. For isothermal systems, we study the fusion and the mixing of two thin liquid films of different but perfectly miscible liquids. Marangoni-driven forces can cause delayed coalescence, ripple formation, and fingering patterns at the borderline between the two liquid layers. A systematic analysis for ripple pattern formation and finger instabilities at different diffusion constants shows that these phenomena appear more pronounced for lower diffusion in the system.

Slippage and nanorheology of thin liquid polymer films

Thin liquid films on surfaces are part of our everyday life; they serve, e.g., as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of many studies in recent decades. In recent years, the dynamics of thin liquid films has come into focus since results on the reduction of the glass transition temperature raised new questions on the behavior of especially polymeric liquids in confined geometries. The new focus was fired by theoretical models that proposed significant implication of the boundary condition at the solid/liquid interface on the dynamics of dewetting and the form of a liquid front. Our study reflects these recent developments and adds new experimental data to corroborate the theoretical models. To probe the solid/liquid boundary condition experimentally, different methods are possible, each bearing advantages and disadvantages, which will be discussed. Studying liquid flow on a variety of different substrates entails a view on the direct implications of the substrate. The experimental focus of this study is the variation of the polymer chain length; the results demonstrate that inter-chain entanglements and in particular their density close to the interface, originating from non-bulk conformations, govern the liquid slip of a polymer.