Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session EF: Film Instabilities |
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Chair: Omar K. Matar, Imperial College London Room: 003B |
Sunday, November 23, 2008 4:10PM - 4:23PM |
EF.00001: Nonlinear stability analysis of a thin-melt film on its crystalline phase Lucien Brush, Stephen Davis, Michael Beerman The instability of an ultra-thin, metallic melt film, situated between its non-premelting crystalline phase and a gas phase, is studied using bifurcation analysis near the instability threshold. The threshold is finite wave number due to competition between a stabilizing thermal gradient and gas-melt capillary forces and the destabilizing attractive van der Waals forces. At fixed mode-number the amplitudes of the two interfaces obey coupled nonlinear evolution equations that admit standing and traveling waves all of which bifurcate subcritically. The additional effects of repulsive intermolecular interactions and crystal-melt surface tension on the nature of the bifurcation are presented. [Preview Abstract] |
Sunday, November 23, 2008 4:23PM - 4:36PM |
EF.00002: Mechanism Leading to Formation of Periodic Nanopillar Arrays in Confined Ultrathin Polymer Films Sandra Troian, Mathias Dietzel Previous groups have reported the spontaneous formation of periodic nanopillar arrays in ultrathin polymer films (order 100 nm in thickness) confined inbetween two flat smooth substrates and subject to an ultrahigh transverse thermal gradient (order $10^6-10^7$ $^{\circ}$K/cm). Crucial to these experiments is the presence of an overlying nanofilm of a second fluid to preserve a deformable interface at the polymer-fluid boundary. The formation of structures resembling stripes, columns or spirals has been attributed to a normal interfacial radiation pressure arising from phonon-like reflections at the interface separating media with different acoustic impedance. A linear stability analysis of a thin bilayer film within the lubrication approximation shows that tangential thermocapillary stresses at the free interface can well explain the phenomena observed. Predictions of the most unstable wavelength as a function of the plate spacing, thermal gradient, and material parameters provide a good fit to the experimental data. This instability can be classified as a long wavelength B\'{e}nard instability studied a decade ago by VanHook \textit{et al}. The parameter range in current experiments, however, as characterized by the ratio of thermocapillary to capillary to gravitational forces, falls beyond the range studied previously. [Preview Abstract] |
Sunday, November 23, 2008 4:36PM - 4:49PM |
EF.00003: AC electrohydrodynamic instabilities in thin liquid films Scott Roberts, Satish Kumar When DC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. We examine the possibility of using AC electric fields to exert further control over the size and shape of the pillars. For perfect dielectric films, linear stability analysis shows that the influence of an AC field can be understood by considering an effective DC field. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and it reveals that high frequencies may be used to inhibit the accumulation of interfacial free charge, leading to a lowering of growth rates and wavenumbers. Nonlinear simulations confirm the results of the linear stability analysis while also uncovering additional mechanisms for tuning overall pillar height and width through adjustment of the magnitude and frequency of the AC field. The results presented here may of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics. [Preview Abstract] |
Sunday, November 23, 2008 4:49PM - 5:02PM |
EF.00004: Instability of Free Films with Plateau Borders Anthony Anderson, Lucien Brush, Stephen Davis A surfactant-free foam of low liquid fraction coarsens by the rupture of the free films separating adjacent gas bubbles. One can find asymptotic solutions for the film and Plateau borders (Brush, L.~N.~\& Davis, S.~H., \emph{J.~Fluid Mech.}, \textbf{534}, 2005, 227-236). Using this time-dependent, flowing, non-planar solution as a basic state, we examine the linearized instability numerically. The numerical method utilizes grid generation to facilitate a finite difference calculation of the linear stability problem. [Preview Abstract] |
Sunday, November 23, 2008 5:02PM - 5:15PM |
EF.00005: Dynamics and line tension in thin nematic films Ulysse Delabre, Celine Richard, Anne-Marie Cazabat Line tension is important in phase transitions for monolayer systems and in biophysics. Nevertheless, experimental studies about hydrodynamics with line tension are still lacking compared to surface tension ones. We consider here a thin nematic film deposited at the air/water interface with hybrid anchoring conditions. This situation is very special because instability patterns exist and the nematic film coexists with a trilayer structure which leads to a line tension between the nematic and the trilayer. We made some dynamic measurements of line tension by analyzing the relaxation of two domains after coalescence. We propose here a comparison between dynamic and static measurements. We then study the early stage of coalescence between two nematic domains with high speed camera. We will explain why this ``true'' 2D case of coalescence is different from the usual 2D case with surface tension. [Preview Abstract] |
Sunday, November 23, 2008 5:15PM - 5:28PM |
EF.00006: Impact of a vibration on the behavior of a dewetting thin film Aleksey Alabuzhev, Sergey Shklyaev, Mikhail Khenner It is well known that volatile van der Waals thin films often dewet from a substrate and rupture. Thus is it important to identify and study physical mechanisms that can suppress dewetting instability. We have found that vibration of the substrate, which has been studied previously in the context of thick films, can provide desired stabilization. The large differences in characteristic length and time scales make possible the application of the time-averaging methods from the dynamical systems theory for the analysis of film dynamics. Using these methods, we obtained the nonlinear amplitude equation for the film thickness. We show that horizontal vibration produces a finite impact on the dynamics of the film when the amplitude the vibration is of the order of the film thickness. When vibration is vertical, its amplitude must be larger than the film thickness. Stabilization of the film is possible only in the latter case. [Preview Abstract] |
Sunday, November 23, 2008 5:28PM - 5:41PM |
EF.00007: Regular non-coarsening surface patterns on evaporating heated films Michael Bestehorn, Merkt Domnic We study a thin liquid film with a free surface on a uniformly heated substrate. The film is heated from the gas side. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase, regular long-scale surface patterns in the form of long-wave hexagons or stripes having a well defined lateral length scale can be observed [1]. This is in sharp contrast to the case without evaporation where coarsening or rupture to larger and larger patterns is seen in the long time limit. In this way, evaporation could be used for regular structuring of the film surface. Finally we show how other stability mechanisms can be included, e.g. the Marangoni effect or Van der Waals forces in ultra thin films. In this way, a much richer pattern dynamics is expected, showing also squares, stripes and hexagons. and transitions among them. \\[3ex] [1] M. Bestehorn, D. Merkt, Phys. Rev. Lett. {\bf 97}, 127802 (2006) [Preview Abstract] |
Sunday, November 23, 2008 5:41PM - 5:54PM |
EF.00008: Distinguishing viscosity and surface friction in quasi-2D flows Paul W. Fontana, Edward Titmus In many experimental and natural quasi-two-dimensional (Q-2D) flows the effects of internal viscosity and surface friction are significant but difficult to distinguish. We demonstrate precise, independent measurements of both kinematic viscosity and coefficient of external drag in a Q-2D experiment using soap films in a circular Couette cell configuration, using a combination of vortex decay rates and steady-state shear lengths. Dynamics at scales shorter (longer) than the shear length are dominated by internal viscosity (surface friction). The technique can be generalized to other flow configurations and promises to aid in the quantitative analysis of many Q-2D experiments. Currently the measurements are being used to make quantitative tests of the theoretical stability threshold in 2D vortex arrays. [Preview Abstract] |
Sunday, November 23, 2008 5:54PM - 6:07PM |
EF.00009: Planar extensional motion of an inertially-driven liquid sheet Linda Smolka, Thomas Witelski We examine the planar extensional motion of a liquid sheet driven by inertia and derive a time-dependent exact solution of the free surface problem for the Navier-Stokes equations. The linear stability of the exact solution to 1- and 2-D symmetric perturbations is examined in the inviscid and viscous limits within the framework of the slender body equations. Both transient growth and long-time asymptotic stability are considered. For 1-D perturbations in the axial direction, viscous and inviscid sheets are asymptotically marginally stable, though depending on the Reynolds and Weber numbers transient growth can have an important effect. For 1-D perturbations in the transverse direction, inviscid sheets are asymptotically unstable to perturbations of all wavelengths. For 2-D perturbations, inviscid sheets are unstable to perturbations of all wavelengths with the transient dynamics controlled by axial perturbations and the long-time dynamics controlled by transverse perturbations. The asymptotic stability of viscous sheets to 1-D transverse perturbations and to 2-D perturbations depends on the capillary number Ca; in both cases, the sheet is unstable to longwave transverse perturbations for any finite Ca. [Preview Abstract] |
Sunday, November 23, 2008 6:07PM - 6:20PM |
EF.00010: Lateral shaping and stability of a stretching viscous sheet Benoit Scheid, Sara Quiligotti, Binh Tran, Howard Stone We investigate the changes of shape of a stretching viscous sheet by controlling the forcing at the lateral edges, which we refer to as lateral shaping. We propose a one-dimensional model to study the dynamics of the viscous sheet and systematically address stability with respect to draw resonance. Two class of lateral forcing are considered: (i) For the case that the tension at the edges is specified, we show that a pure outward normal tension $S_{\rm n}$ is usually unfavorable to the draw resonance instability as compared to the case of stress-free lateral boundaries. Alternatively, a pure streamwise tangential tension $S_{\rm t}$ is stabilizing. (ii) For the case that the lateral velocity at the edges is specified, we show that the stability properties are problem specific but can be rationalized based on the induced tension components ($S_{\rm n}$, $S_{\rm t}$). [Preview Abstract] |
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