Solitary waves on falling liquid films in the inertia-dominated regime

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development

Absolute linear instability in laminar and turbulent gas/liquid two-layer channel flow

We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully-developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr--Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r=1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil/gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r=1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally-determined flow-regime map, and discuss the potential application of the present method to non-linear analyses.Comment: 33 pages, 20 figure

Complex interfacial and wetting dynamics

Consider interface evolution in bounded and unbounded settings, namely in the spreading of droplets and stratified gas-liquid flows. A typical prototype consists of the surface-tension-dominated motion of a two-dimensional droplet on a substrate. The case of chemically heterogeneous substrates was examined here. Assuming small slopes, a single evolution equation for the droplet free surface was derived from the Navier-Stokes equations, with the singularity at the contact line being alleviated using the Navier slip condition. The chemical nature of the substrate is incorporated into the system by local variations in the microscopic contact angle. By using the method of matched asymptotic expansions, the flow in the vicinity of the contact lines is matched to that in the bulk of the droplet to obtain a set of coupled ordinary differential equations for the location of the two contact points. The solutions obtained by asymptotic matching are in excellent agreement with the solutions to the full governing evolution equation. The dynamics of the droplet is examined in detail via a phase-plane analysis. A number of interesting features that are not present in homogeneous substrates are observed: multiple droplet equilibria, pinning of contact points on localised heterogeneities, unidirectional motion of droplet and the possibility of stick-slip behaviour of contact points. Unbounded gas-liquid flows are also often encountered in natural phenomena and applications. The prototypical system considered here consists of a liquid film flowing down an inclined planar substrate in the presence of a co-flowing turbulent gas. The gas and liquid problems are solved independently by making certain reasonable assumptions. The influence of gas flow on the liquid problem is analysed by developing a weighted integral-boundary-layer (WIBL) model, which is valid up to moderate Reynolds numbers. We seek solitary-wave solutions of this model using a pseudo-arclength continuation approach. As a general trend, it is found that the wave speed increases with increasing gas shear and the liquid flow rate. Further insight into the problem is provided by time-dependent computations of the WIBL model. Finally, the absolute-convective instability of a falling film that is in contact with a counter-current turbulent gas is analysed. The Orr--Sommerfeld (O-S) problem is formulated from the full governing equations and boundary conditions. The O-S problem along with low-dimensional models, namely, a long-wave and WIBL models are used to explore the linear stability of the gas-liquid system. It is found that for a fixed liquid Reynolds number, at low and high gas flow rates, the system is convectively unstable, and for a range of intermediate gas flow rates we have absolute instability. We supplemented our analysis by doing time-dependent computations of the linearised WIBL model subject to a localised initial condition which showed good agreement. The upper limit of the absolute instability regime predicted by our linear analysis is close to the flooding point obtained from the fully non-linear computations of the WIBL model.Open Acces

Level-set simulations of a 2D topological rearrangement in a bubble assembly: effects of surfactant properties

International audienceA liquid foam is a dispersion of gas bubbles in a liquid matrix containing surface active agents. Their flow involves the relative motion of bubbles, which switches neighbours during a so-called topological rearrangement of type 1 (T1). The dynamics of T1 events, as well as foam rheology, have been extensively studied, and experimental results point to the key role played by surfactants in these processes. However, the complex and multiscale nature of the system has so far impeded a complete understanding of the mechanisms at stake. In this work, we investigate numerically the effect of surfactants on the rheological response of a 2D sheared bubble cluster. To do so, a level-set method previously employed for simulating two-phase flow has been extended to include the effects of the surfactants. The dynamical processes of the surfactants-diffusion in the liquid and along the interface, adsorption/desorption at the interface-and their coupling with the flow-surfactant advection and Laplace and Marangoni stresses at the interface-are all taken into account explicitly. Through a systematic study in Biot, capillary and Péclet numbers which characterise the surfactant properties in the simulation, we find that the presence of surfactants can affect the liquid/gas hydrodynamic boundary condition (from a rigid-like situation to a mobile one), which modifies the nature of the flow in the volume from a purely extensional situation to a shear. Furthermore, the work done by surface tension (the 2D analogue of the work by pressure forces), resulting from surfactant and interface dynamics, can be interpreted as an effective dissipation, which reaches a maximum for Péclet number of order unity. Our results, obtained at high liquid fraction, should provide a reference point, to which experiments and models of T1 dynamics and foam rheology can be compared

Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film

Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactant monolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are self-similar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows

Effect of the surfactant on complex multi-phase annular flows

In the modern world, the scale of industrial production within all sectors has reached unprecedented levels due to ever-growing demand and consumption of various products. A vast majority of industrial processes exploits the benefits brought by the multiphase flows whose complex dynamics are governed by the concoction of fundamental physics. Probing the details of such flows, experimentally and/or theoretically provides an ability to develop and optimise the needs of industrial applications. Yet, this progression is gradual as it depends on the advancement of measurement technologies that enable the investigation of the complex behaviour and topologies of many different possible combinations of phases utilised in industry. Use of the novel optical diagnostic techniques coupled with bespoke capacitance probes in the present study enables us to explore uncharted territory of two-phase gas-liquid annular flows in vertically orientated pipes. In the present study, a recently developed variant of laser-induced fluorescence (LIF) technique, termed structured-planar laser-induced fluorescence (S-PLIF), is used which allows us to eliminate biases commonly encountered during film-thickness measurements of gas-liquid flows due to refraction and reflection of the light at the interface. In parallel, a bespoke capacitance probe is also employed which permits us to conduct film thickness measurements with high temporal resolution along the perimeter of the pipe. Simultaneous application of these two measurement techniques provides an opportunity to study the subtle differences found in thin annular film structures caused not only by the function of liquid and gas flow rates, but also by the surface-active agents which are widely known to cause drastic changes in flow behaviour due to surface tension gradients. The flow characteristics are studied in terms of mean film thickness, roughness, probability density functions, time-scales of the flows, and gas entrainment in the liquid film. The analysis of the data reveals important changes in the flow characteristics due to the presence of soluble surfactant. Firstly, it is observed that surfactant promotes thinning of annular films at nearly all flow conditions investigated herein, hinting at its influence on the turbulence within the bulk flow. The behaviour of interfacial waves was also found to be notably altered by the surfactant where the film roughness and the time-scale of the waves increase in gas-sheared film flows with low to moderate turbulence and low gas entrainment. This corresponds to flows not in the `regular wave' regime. A decrease in both characteristics then follows upon an increase in turbulence to a sufficiently high level of the two phases. The high gas-shear rate not only limits the highest attainable wave amplitude downstream, but also results in high agitation of air and water phases, and thus, high gas and liquid entrainment. Ultimately, this smooths the base film populated with small-amplitude waves and substantially reduces the amplitude of large interfacial waves. Generally, good agreement with relevant literature correlations is found. The estimated time-scales of the wave dynamics and Marangoni flow showed that the surfactant plays an increasingly important role on waves with lower amplitudes. The sizes of the bubbles entrained in the surfactant-free liquid film are found to exhibit log-normal distributions that become flatter with a decrease in the gas Reynolds number, while this distribution is maintained for surfactant-laden flows. On the other hand, wider distributions in the bubble sizes are found for the surfactant-laden flows at the highest gas-shear rate for all liquid Reynolds numbers. The normalised location of the bubbles (quantified as the relative entrainment depth, i.e., distance of the bubble from the local air-water film height in the wall-normal direction divided by the local film thickness) follows a Gaussian distribution, where the majority of the bubbles accumulate in the middle of the thin film. Understanding the need for further development of the multiphase flows that involves the use of surfactants, motivated us to develop a method to prepare water soluble fluorescent surfactant, which is described in the present work. Furthermore, a detailed characterisation of the fluorescent surfactant is also provided, which may encourage further experimental and modelling investigations of the relevant surfactant-laden multiphase dynamics found in small- and large-industrial scale applications.Open Acces