Session A9: Instability: Interfacial and Thin-Film I

Simultaneous measurement of a thickness and wave velocity of a liquid film flow, by using a single-tip optical fiber probe

We developed a new measurement technique for a liquid film flow, using a single-tip optical fiber probe (S-TOP). The measurement method for a liquid-film thickness is as follows; the S-TOP with a tapered tip was installed parallel to the main stream, and detected a wavy surface; after processing the probe signals, liquid phase fractions were calculated in every installed position of the S-TOP. Moreover, we calibrated the experimental results via our original 3D-ray-tracing numerical-simulation. Analyzing the simulated signals, we found the relationship among the liquid phase fractions, the installed positions and the wave heights. Wave velocities were accurately measured through our original micro-fabricated S-TOP that has two optical-sensors. The experimental and numerical analyses were executed in order to deeply understand the complex signals of the S-TOP. Finally, the simultaneous measurement technique of the thickness and wave velocity was demonstrated. When the liquid phase fraction was 0.52, the installed-position equals the average film thickness. The wave velocity was measured based on the event time of each sensor touching the film surface. A difference in the results of the velocity between the S-TOP and the visualization was less than 10 percent.   

Nonlinear interfacial dynamics in stratified multilayer channel flows

Viscous immiscible pressure-driven multilayer flows in channels are investigated using a combination of modelling, analysis and computations. Three stratified layers with two internal interfaces are considered and long wave theory is used to derive a coupled system of Benney-type equations containing a small parameter that cannot be scaled out. A consistent system of coupled weakly nonlinear equations is developed and two canonical cases are identified in the absence and presence of inertia, respectively. The system supports instabilities not found in single long-wave equations including, transitional instabilities due to a change of type of the nonlinearities from hyperbolic to elliptic, kinematic resonance instabilities, and long-wave instabilities induced by an interaction between nonlinearity and surface tension. In contrast to two-layer systems instabilities leading to nonlinear traveling waves are possible even at zero Reynolds number. When inertia is present the systems become general coupled Kuramoto-Sivashinsky type equations. Numerical experiments produce dynamics including traveling, time-periodic traveling, and chaotic waves. It is also possible to regularise chaotic dynamics into traveling waves by enhancing the inertialess instabilities through the advective terms.   

Instabilities and nonlinear waves in two-layer film flowing down a vertical plane

The two-layer falling film flowing down a vertical plane is considered. The approximate long-wave model is investigated and the integral method is applied on this model. The linear stability of the steady flow is analyzed by the numerical method. To calculate the steady-traveling nonlinear waves we reformulate the problem as the dynamical system and find the bifurcating solutions. Examples of solutions at real-life values of the similarity parameters for a two-layer film are shown.   

Coherent structures in non-local active-dissipative equations

We investigate a non-local weakly nonlinear equation arising in the modeling of wave dynamics on electrified falling films. The equation is a generalized Kuramoto-Sivashinsky (gKS) equation with a non-local term representing the imposed electric field. As for the case of the usual gKS equation, we find that sufficiently strong dispersion arrests the spatio-temporal chaos and the solutions evolve into arrays of pulses, each one of which resembles an infinite-domain pulse. Such pulses interact with each other and may form bound states. The Shilnikov-type approach for analyzing bound states is not applicable to non-local equations. We therefore develop an accurate weakly interaction theory for the pulses that allows us to analyze the attraction and repulsion of the pulses and the existence of bound states. The non-locality of the equation results in the fact that the infinite-domain pulse has algebraically decaying tails (in contrast to exponentially decaying tails for the local equation), which has strong effect on the interaction of the pulses. We compare the interaction theory with numerical simulations of the full equation and find very good agreement.   

Linear and nonlinear instability and ligament dynamics in 3D laminar two-layer liquid/liquid flows

We consider the linear and nonlinear stability of two-phase density-matched but viscosity contrasted fluids subject to laminar Poiseuille flow in a channel, paying particular attention to the formation of three-dimensional waves. The Orr--Sommerfeld--Squire analysis is used along with DNS of the 3D two-phase Navier--Stokes equations using our newly launched TPLS Solver (http://edin.ac/10cRKzS). For the parameter regimes considered, we demonstrate the existence of two distinct mechanisms whereby 3D waves enter the system, and dominate at late time. There exists a direct route, whereby 3D waves are amplified by the standard linear mechanism; for certain parameter classes, such waves grow at a rate less than but comparable to that of most-dangerous two-dimensional mode. Additionally, there is a weakly nonlinear route, whereby a purely spanwise wave couples to a streamwise mode and grows exponentially. We demonstrate these mechanisms in isolation and in concert. Consideration is also given to the ultimate state of these waves: persistent three-dimensional nonlinear waves are stretched and distorted by the base flow, thereby producing regimes of ligaments, ``sheets,'' or ``interfacial turbulence.''   

Contact line instability of gravity-driven flow of power-law fluids: Comparison of Experiments and Simulations

We previously studied the fingering instabilities of power-law fluids using linear stability analysis (LSA). We also developed a 3D FEM model to simulate a constant-volume power-law fluid flowing down an incline. In this study, we try to perform 3D simulations with constant-flux condition and perturbed contact line, and compare the results to LSA. Moreover, we develop a fluid depth measurement experiment based on fluorescence imaging for further comparison to the numerical results. Instead of using laser-induced fluorescence, we try a simple quantitative way of using LEDs, which is much less expensive. The impact of inclination angle, surface tension, and especially shear-thinning effect on contact line instabilities is investigated.   

Spin coating flow of Power law fluid: spreading and contact line intsability

A computational study of the flow of a power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of shear thinning nature on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolution of film thickness. The movement of contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin finite element method (G/FEM) based approach. The numerical results show that the spreading rate of the fluid increases with the increase in the shear-thinning character of the fluid. It is also observed that the sharpness of capillary ridge is reduced as the shear-thinning character of the fluid becomes dominant. In order to study the stability of these ridges, linear stability theory is developed for shear thinning fluid. The dispersion relationship depicting the growth rate for a given wave number have been reported and compared for different power-law fluids. It is found that the growth rate of the fingers decreases as the fluid becomes more shear-thinning in   

Engineering and control of surfactant-laden flows: experiments and MD simulations

The dynamics of surfactant-laden flows remain full of surprises. For hydrophobic substrates with a water contact angle of less than 110$^\circ$, certain types of surfactants, known as {\it superspreaders}, can lead to an increase in the spreading factor by two orders of magnitude over water droplets; spreading takes place with speeds between 1-10 mm/s. The superspreading effect occurs provided the concentration of superspreaders is above the critical wetting concentration (CWC), which, in turn, exceeds (by several times) the critical aggregation concentration. The CWC is dependent on the type of surfactant but independent of the nature of the substrate. In this study, we use a combination of molecular dynamics simulation, and direct experimentation to analyse the spreading behaviour of well-known superspreaders. We correlate this behaviour in terms of the physic-chemical properties of the surfactant (sorption kinetics, aggregation formation, and dynamic surface tension).   

New spreading law of thin film liquids controlled by gravity and vdW forces under thermal fluctuations

It has been shown that, in the regime controlled by surface tension, the spreading dynamics of a thin viscous fluid droplet changes significantly when it is subjected to thermal fluctuations. Technically, this has been accomplished through the incorporation of appropriate stochastic terms into the standard lubrication equation. In practice, it leads to a modification of the classic Tanner's law for spreading, with implications for Micro and Nanofluidic systems. We have recently found a new law of spreading for the same kind of systems, but in the gravity-dominated regime. Moreover, in the deteministic case a finite contact angle is formed when a van der Waals attractive force is introduced to the system and we show that there is a slight change in contact angle when thermal fluctuations are taken into account.