Linear and nonlinear Marangoni stability of a thin liquid film coating the inside or the outside of a cylinder with slip in the absence of gravity

The nonlinear sideband thermocapillary instability of a thin liquid film coating the inside of a heated cylinder in the absence of gravity is investigated. It is shown that for a newtonian fluid and under the approximation of small wavenumber and large radius of the cylinder, the axial and all azimuthal modes with wavenumber kmax > 0 have the same linear maximum growth rate, in the same way as in a previous papers for flow outside the cylinder. Here, this indeterminacy of the linear problem is resolved nonlinearly looking for the parameters’ range where the axial mode prevails and where it is unstable against the first azimuthal mode of thermocapillary instability.

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

Drainage kinetics, thickness, and stability of water-in-oil thin liquid emulsion films obtained from asphaltenes, heavy oil (bitumen), and deasphalted heavy oil (maltenes) diluted in toluene are studied. The results show that asphaltenes stabilize thin organic liquid films at much lower concentrations than maltenes and bitumen. The drainage of thin organic liquid films containing asphaltenes is significantly slower than the drainage of the films containing maltenes and bitumen. The films stabilized by asphaltenes are much thicker (40-90 nm) than those stabilized by maltenes (∼10 nm). Such significant variation in the film properties points to different stabilization mechanisms of thin organic liquid films. Apparent aging effects, including gradual increase of film thickness, rigidity of oil/water interface, and formation of submicrometer size aggregates, were observed for thin organic liquid films containing asphaltenes. No aging effects were observed for films containing maltenes and bitumen in toluene. The increasing stability and lower drainage dynamics of asphaltene-containing thin liquid films are attributed to specific ability of asphaltenes to self-assemble and form 3D network in the film. The characteristic length of stable films is well beyond the size of single asphaltene molecules, nanoaggregates, or even clusters of nanoaggregates reported in the literature. Buildup of such 3D structure modifies the rheological properties of the liquid film to be non-Newtonian with yield stress (gel like). Formation of such network structure appears to be responsible for the slower drainage of thin asphaltenes in toluene liquid films. The yield stress of liquid film as small as ∼10(-2) Pa is sufficient to stop the drainage before the film reaches the critical thickness at which film rupture occurs.

On evaporation of thin liquid films subjected to ultrasonic substrate vibration

This work analyzes the linear stability of a thin second-grade liquid film flowing over a stretching sheet. The one-dimensional thin liquid film model of second-grade fluid based on long-wave theory is considered for this analysis. Taking into account the sinusoidal perturbation process, we carried out the linear stability analysis and obtained the linear growth rate, which defines the stability and instability of the fluid flow. Simulation results show the stabilizing effect on the flow for higher values of the second-grade non-Newtonian parameter, Froude number and the surface tension parameter. Furthermore, it is essential to note that the impact of the Froude number on the stability at high values of the second-grade parameter is very relevant. At the same time, at small parameter values of second grade, it has a feeble effect.

Improvements in the theoretical model and computational procedure for the prediction of film height and heat transfer coefficient of the free surface flow of a radially spreading thin liquid film adjacent to aflat horizontal surface of finite extent are presented. Flows in the presence and absence of gravity are considered. Theoretical results are compared to available experimental data with good agreement. In the presence of gravity, a hydraulic jump is present, isolating the flow into two regimes: supercritical upstream from the jump and subcritical downstream. In this situation, the effects of surface tension are important near the outer edge of the disk where the fluid experiences free fall. A region of flow separation is present just downstream of the jump. In the absence of gravity, no hydraulic jump or separated flow region is present. The variation of the heat transfer coefficient for flows in the presence and absence of gravity is also presented.

Two-dimensional base state solutions for rimming flows and their stability analysis to small axial perturbations are analyzed numerically. A thin liquid film which is uniformly covered with an insoluble surfactant flows inside a counterclockwise rotating horizontal cylinder. In the present work, a mathematical model is obtained which consists of coupled thin film thickness and surfactant concentration evolution equations. The governing equations are obtained by simplifying the momentum and species transport equations using the thin-film approximation. The model equations include the effect of gravity, viscosity, capillarity, inertia, and Marangoni stress. The concentration gradients generated due to flow result in the surface tension gradient that generates the Marangoni stress near the interface region. The oscillations in the flow due to inertia are damped out by the Marangoni stress. It is observed that the Marangoni stress has stabilizing effect, whereas inertia and surface tension enhance the instability growth rate. In the presence of low diffusion of the surfactant or large value of the Péclet number, the Marangoni stress becomes more effective. The analytically obtained eigenvalues match well with the numerically computed eigenvalues in the absence of gravity.

Stability of emulsions, deemulsification of microemulsions by coalescing the dispersed phase using chemical additives or external forces, and stability of thin liquid films are of paramount importance in a wide array of industrial applications. Fundamental to all these processes is a clear understanding of the role of different physical and chemical factors on the stability of a thin film formed by one fluid phase in another. Several experimental techniques are currently available to explore the thermodynamic properties and stability of thin films, such as, micropipettes and thin film cells employing a porous plate, all of which provide a platform for following a thin film in a macroscopic sense. Setting up these experimental techniques to quantitatively and reproducibly measure thin film behaviour requires considerable time and dexterity. A novel microfluidic chip has been developed to study the break up of oily thin films in aqueous media under the influence of an externally applied electrical field. The basic concept involves two crossing micro channels etched into the surface of a glass substrate. Carefully designing the intersection of the two perpendicular channels can lead to formation of a film at the intersection. One channel would be filled with oil and the second channel, divided to half by oil channel, would deliver two water droplets toward the oil channel from both sides. Once the thin liquid film is created, an electrical potential difference can be applied across the channel. The electrical stresses developed at the interfaces of the two fluids forming the film will lead to a collapse of the film beyond a certain threshold voltage. The break up of the film was performed using a ramped DC potential, and a series of capacitance measurements determined the variation of the capacitance of the film with regards to the film thickness. This new microfluidics chip shows promise as a low cost, reproducible, microscale measurement tool to study the thermodynamic behaviour and stability of thin liquid films.

The formation of the waves on a thin liquid water film was analytically investigated by studying its shear mode stability. The inclined angle of the substrate is limited to 8°. The purpose of analytical solution is to determine the maximum growth rate of the generated wave as well as its corresponding wave number, which is realized by solving the Orr-Sommerfeld equations for both gas and liquid phases with the corresponding boundary conditions. The results of wave formations on a surface with a thin liquid film of de-icing are validated by previous experimental data as well as compared with Yih’s theoretical analysis [7]. Studies have also conducted on the effect of surface tension or liquid film depth on the stability of a thin liquid film flowing along a solid substrate.

Foam lamellae are the smallest structural elements in foam. Such lamellae can experimentally be studied by analysis of thin liquid films in glass cells. These thin liquid films usually have to be stabilized against rupture by surface active substances, such as proteins or low molecular weight surfactants. However, horizontal thin liquid films of pure water with a radius of 100 μm also show remarkable stability when created in closed Sheludko cells. To understand thin film stability of surfactant-free films, the drainage behavior and rupture times of films of water and NaCl solutions were determined. The drainage was modeled with an extended Derjaguin-Landau-Verwey-Overbeek (DLVO) model, which combines DLVO and hydrophobic contributions. Good correspondence between experiment and theory is observed, when hydrophobic interactions are included, with fitted values for surface potential (ψ(0,water)) of -60 ± 5 mV, hydrophobic strength (B(hb,water)) of 0.22 ± 0.02 mJ/m(2), and a range of the hydrophobic interaction (λ(hb, water)) of 15 ± 1 nm in thin liquid films. In addition, Vrij's rupture criterion was successfully applied to model the stability regions and rupture times of the films. The films of pure water are stable over long time scales (hours) and drain to a final thickness >40 nm if the concentration of electrolytes is low (resistivity 18.2 MQ). With increasing amounts of ions (NaCl) the thin films drain to <40 nm thickness and the rupture stability of the films is reduced from hours to seconds.

The three-dimensional thermocapillary instability of a fluid film coating the outside or the inside of a cylinder is investigated in the absence and in the presence of gravity. In the absence of gravity (pure thermocapillarity), it is found that it is possible to excite high azimuthal modes as the most unstable. In the presence of gravity the thermocapillary instability of a thin fluid film flowing down a vertical cylinder is investigated. It is shown that thermocapillarity also promotes the instability of high azimuthal modes, even higher than those found in the pure thermocapillary case. This is in contrast with the isothermal case where only the zeroth mode (the longitudinal one) is the most unstable and also with previous work on flow down a rotating cylinder where, in some conditions, rotation may promote the first azimuthal mode as the most unstable. Curves of criticality and those corresponding to the maximum growth rate are given for different values of the parameters.

Thin liquid films are ubiquitous in nature and have many practical applications. From biological films to the curtain coating process, thin films are present in both large and small scales. Despite their importance, understanding the stability of these films remains a significant challenge due to the fluid–fluid interface that is free to deform, affected by interfacial tension and complex rheological behavior. Instabilities in thin films are often caused by van der Waals attractions, which can lead to the rupture of the layer. To investigate the rupture dynamics, numerical methods are commonly used, such as asymptotic derivations of the lubrication theory or interface tracking methods. In this paper, we present a computational study of the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface, using the arbitrary Lagrangian–Eulerian method and the Boussinesq–Scriven constitutive law to model the rheological behavior. Our results demonstrate that the stability of thin liquid films is influenced by both surface rheology and disjoining effects and that the viscous character of the interface can delay sheet breakup, leading to more stable films.

The linear stability of a thin film of volatile liquid flowing over a surface with embedded, regularly spaced heaters is investigated. The temperature gradients at the upstream edges of the heaters induce gradients in surface tension that create a pronounced non-uniformity in the film profile due to the formation of capillary ridges. The Governing equations for the evolution of the film thickness are derived within the lubrication approximation, and three important parameters that affect the dynamics and stability of the film are identified. The computed two-dimensional, steady solutions for the local film thickness reveal that due to evaporation there is a slight change in the height of capillary ridge at subsequent heaters downstream. Using a linear stability analysis, it is shown that, as for a single heater, the film is susceptible to two types of instabilities. A rivulet instability leads to spanwise-periodic rivulets, and an oscillating thermocapillary instability leads to streamwise, time-periodic oscillations in the film thickness. The critical Marangoni number is calculated for both types of instability for a range of parameter values. The effect of the number of heaters, heater width, and gap between the heaters on the critical Marangoni number is computed and analyzed. For small evaporation rates and less volatile films, the presence of multiple heaters has almost no noticeable effect on the film stability. For larger evaporation rates and more volatile films, additional heaters decrease the Marangoni number at instability onset. The destabilizing effect of multiple heaters is sensitive to the heater geometry and spacing. Furthermore, the limitations of streamwise periodic boundary conditions for analyzing the stability of such flows are discussed. Computations on the transient and nonlinear growth of perturbations are also presented and indicate that the results of eigenanalysis are physically determinant.

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.

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.