Session HY: Instability: Interfacial and Thin Film V

Marangoni-B\'enard instability in microgravity: PTV-analysis of the velocimetry data generated during the BAMBI - FOTON-M2 experiment

The BAMBI (Bifurcation Anomalies in Marangoni-B\'enard Instabilities) experiment has been successfully flown onboard the FOTON-M2 satellite in June 2005. During the 4 days available for the experiment, a 5mm-thick 200 cSt silicone oil layer in a 10x10cm$^2$ wide container, and in contact with a similarly-sized helium gas layer was heated from ``below'' and cooled from ``above.'' By varying the heating power applied at each experimental step, a range of temperature differences across the liquid and gas layers was scanned and the onset and evolution of the Marangoni-B\'enard instability typical for this type of configuration was examined. The used optical diagnostics were Infrared Thermography of the liquid/gas interface, PTV (multiple views and heights in the liquid layer), Wollaston Interferometry and Electronic Speckle Pattern Interferometry. The present contribution focuses on the velocity results obtained by PTV in the interface plane, and discusses them in relation both with infrared images, and with theory/numerics.   

Experimental analysis of evaporation-driven B\'{e}nard instabilities

We study experimentally the spontaneous patterns induced by evaporation of a pure liquid layer into dry air. The liquid/vapour interface temperature is lower than the substrate temperature because of the energy consumption for the phase change. This temperature difference across the liquid layer generates surface-tension-driven convection and/or buoyancy-driven convection in the liquid, depending on the layer thickness. In practice, the volatile liquid is placed in a circular dish placed in dry air under ambient conditions. During the evaporation process, the convective patterns are observed using an optical Z-type Schlieren set-up. The evaporation rate and the layer thickness are estimated from liquid weight measurements using a precision balance. Several liquids and dish diameters/heights have been tested. As could be expected, the evaporation rate remains almost constant during time, while different convective patterns are observed when the layer thickness decreases. Their phenomenology and transitions are analysed, in relation with existing theoretical models.   

Suppressing van der Waals driven rupture through shear

A thin viscous film on a substrate is susceptible to rupture instabilities driven by van der Waals attractions. When a sufficiently large shear is applied to the free surface, the rupture instability is suppressed in two dimensions for sufficiently large shear magnitude and replaced by a permanent finite amplitude travelling wave with speed approximately equal to the speed of the surface. For small amplitudes, the wave is governed by the Kuramoto-Sivashinsky equation. If three- dimensional disturbances are allowed, the shear is decoupled from perpendicular disturbances to the flow, and line rupture would occur. In this case, replacing the unidirectional shear with a rotating shear can suppress rupture for suitable choices of shear magnitude and angular velocity.   

Experimental Confirmation of Pillar Array Formation in Polymer Nanofilms by Thermocapillary Instability

During the past decade, three mechanisms have been proposed to explain the spontaneous formation of periodic fluid elongations in polymer nanofilms confined to closely spaced parallel substrates held at different temperatures. Models suggest linear instability due either to variation in surface charge density at the air/polymer interface, variation in acoustic phonon pressure within the film, or variation in thermocapillary stress along the air/polymer interface. Comparison of theory to experiment requires that the film structuring process be observed at early times in accordance with the assumptions of linear stability analysis. To date, however, all experimental investigations of the most unstable wavelength have been conducted in the solidified state and long after the original molten structures had contacted and reorganized along the cooler substrate. For the first time, we present experimental measurements based on direct observation of in-situ nanopillar growth. Investigation of the fastest growing wavelength as a function of substrate separation distance, temperature difference and initial film thickness indicates excellent agreement with predictions of the thermocapillary model. These studies also make evident how film depletion and contact may have skewed values of the wavelength previously reported in the literature.   

Viscous dispersion effects on bound-state formation in falling liquid films

We examine the influence of viscous dispersion on the interaction of two-dimensional solitary pulses in falling liquid films at moderate Reynolds number. We make use of an averaged model that includes second-order viscous effects in the long-wave expansion. These effects play a dispersive role affecting primarily the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a coherent-structures theory that assumes weak interaction between the pulses, we are able to theoretically predict the pulse-separation distances for which bound states are formed. It is shown that viscous dispersion significantly affects the distances at which bound states are observed. In all cases, there is very good agreement between the theory and computations of the fully nonlinear system.   

Fingering instability down the outside of a vertical cylinder

We present an experimental and numerical study of the dynamics of a gravity-driven contact line of a thin viscous film traveling down the outside of a vertical cylinder of radius $R$. In all of our experiments with cylinder radii ranging between 0.159 and 3.81~cm, the contact line becomes unstable to a fingering pattern. Observations are compared to inclined plane experiments in order to understand the influence curvature plays on the fingering pattern. Using lubrication theory, we derive a model for the film height that includes gravitational and surface tension effects and examine the structure and linear stability of the contact line using traveling wave solutions. For $Bo \ge O(10^1),$ our model predicts curvature's influence is negligibly weak as the shape and stability of the contact line converge to the behavior one observes for a vertical plane. For $Bo \ge 1.3,$ the most unstable and cutoff wave modes and maximum growth rate scale like $Bo^{0.45},$ indicating instability of the contact line increases as gravitational effects increase or, for a specific fluid, as cylinder radius increases. The linear stability of the contact line changes at the critical value $ Bo_c = 0.56;$ above $Bo_c$ the contact line is unstable and below $Bo_c$ it is stable to fingering. We find excellent agreement between the number of fingers that form along the contact line and the range of wavelengths measured in experiments and the range of unstable modes and wavelengths predicted by our model.   

Transverse Fracture Bands during Rapid Peeling of Adhesive Tape

The typical roll of {\it Scotch} tape consists of sticky acrylic adhesive attached to an acetate film, with a total thickness of 58 $\mu$m. When this adhesive tape is peeled from a solid surface, the detachment occurs with a well-known stick- slip mechanism accompanied by a characteristic ripping sound. Here we present direct ultra-high-speed video imaging of the detachment zone when Scotch tape is peeled off at high speed from a solid glass surface. The tape is manually pulled from the surface at very large velocities between 4 - 14 m/s and is viewed through the substrate, with a long-distance microscope. The video imaging at 1 million fps reveals a highly regular substructure of transverse fractures, which appear during the slip phase. The typical 4 mm-long slip region has a regular substructure of transverse 220 $\mu$m wide slip bands, which fracture sideways at speeds over 300 m/s. Our imaging can observe the growth and relaxation of cavitation bubbles within the adhesive layer. The fracture tip emits waves, which travel up the detached section of the tape at $\sim 100$ m/s. We believe this promotes the sound, so characteristic of this phenomenon.   

Influence of Inertia, Gravity and Thermal Conditions on the Draw Resonance

The instability known as the ``draw resonance'' is studied for a Newtonian viscous flow. Both eigenvalue analysis and transient solutions are used to study the instability. The effects of inertia, gravity and the thermal conditions on stability are explored. The thermal conditions are studied as a combination of global and local heating/cooling conditions. While monotonous global cooling along the draw always gives critical draw ratios less than that of the isothermal case (i.e. Dr* = 20.218 for isothermal), critical draw ratios larger than 20.218 can be obtained by local heating effects superposed onto the global cooling. The global heating is stabilizing and very large critical draw ratios are obtained when the intensity of this global heating is large.   

Gravity-driven propagation of thin non-isoviscous rivulets on vertical and inclined planes

Many practical problems require the spreading of a liquid on a solid. In the glass industry, flows of molten glass on a vertical or inclined, in respect to the vertical, solid refractory surface are parts of several important applications. In present paper, propagation of a thin and relatively narrow rivulet on vertical and inclined solid planar surface is considered within a mathematical frame of general lubrication theory, using a commercially available PDE solver. In contrast to most of previous studies, the addressed flows are gravity driven, and the coefficient in front of the surface tension term in the dimensionless equations (the inverse Bond number) is small and does not exceed 10$^{-5}$. It has been found that the flow pattern strongly depends on the inclination angle. For example, the contact line of rivulets propagating on vertical and negatively inclined plates becomes unstable, sending ahead one or several smaller forerunner rivulets (fingers) having a higher amplitude and moving faster than the main rivulet. This instability is similar to fingering instability of infinite films on solid surfaces, but the pattern of the flow is symmetric in respect to the middle line of the rivulet rather than a periodic. In the case of the gradient of viscosity applied in the cross-direction to the main flow, the symmetry breaks and motion of both main rivulet and forerunners is diverted in the direction of areas with lower viscosity.   

Effect of Variable Viscosity on Stabilization in Hele-Shaw Flows

Current work is in progress on numerical investigation of the effect of variable viscosity profiles of internal layers on the stabilization of multi-layer Hele-Shaw flows. Our findings will be presented and compared, to the extent possible, with theoretical results available. Effect of diffusion on this stabilization may also be presented. This talk is partially based on an going work with Xueru Ding.