Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session GY: Instability: Interfacial and Thin Film IV |
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Chair: Manoranjan Mishra, Indian Institute of Technology Room: Hyatt Regency Long Beach Regency E |
Monday, November 22, 2010 8:00AM - 8:13AM |
GY.00001: An Energy Approach to Capillary-Driven Thin Film Folding Huan Li, K. Jimmy Hsia, Sascha Hilgenfeldt Capillary-driven self-assembly methods provide a promising tool to fabricate three-dimensional, micro- or millimeter scale structures. Recently, we explored the self-assembly of 3D photovoltaic devices from Si thin films through equilibrium considerations of fluid-solid interactions (Guo, et al. 2009, Li, et al. 2010). In the present study, an alternative approach, the minimization of the total free energy is employed to investigate the interactions between fluid droplet and a flexible thin film. Variation of a 2D energy functional, comprising the surface energy of the fluid and the bending energy of the thin film, yields governing equations and boundary conditions. Through direct simulations with Surface Evolver (Brakke 2008), the shape of the droplet and the thin film at the equilibrium state is obtained. A critical thin film length necessary for complete enclosure of the fluid droplet, and thus successful device self-assembly, is determined and compared with the experimental study of Guo et al. (2009). Augmenting the formalism, we obtain an upper bound of the thin film length, beyond which gravity is dominant. The current 2D study can be extended into 3D. Critical parameters obtained from these analyses can be used to guide device fabrication and manufacturing. [Preview Abstract] |
Monday, November 22, 2010 8:13AM - 8:26AM |
GY.00002: Thin films: instabilities, waves, and dewetting Te-Sheng Lin, Lou Kondic We study free surface instabilities of spreading thin films exposed to destabilizing body force (gravity) on partially wetting substrates. For completely wetting films on inverted substrates, we have uncovered rich structure of convective and absolute instabilities which evolve due to contact line presence.\footnote{T.-S. Lin, L. Kondic, Phys. Fluid 22, 052105 (2010).} In this talk, we will concentrate on partially wetting case, where additional destabilizing component of disjoining pressure may lead to significant modifications of the instabilities discovered for the complete wetting case. In particular, we consider the interplay between different destabilizing mechanisms to discuss free surface instabilities which lead to dewetting, in contrast to those which do not. We conclude by presenting preliminary results of three dimensional simulations showing the interplay between free surface and fingering type of instabilities. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GY.00003: Experimental Analysis of the Instability and Breakup of an Annular Liquid Sheet with Axial Co-flow Daniel Duke, Julio Soria, Damon Honnery A novel application of a correlation-based velocimetry technique combined with high speed imaging has been employed to measure the interfacial stability properties of a thin annular liquid sheet with dual co-flowing axial gas streams undergoing aerodynamic breakup. The measurement of instabilities in thin liquid sheets has traditionally been limited due to the challenging complexities of taking measurements in the near-nozzle region where instability amplitudes are very small. Agreement with theoretical stability analysis has also proven elusive. The application of new techniques permits quantitative velocity measurement of with significantly improved resolution, for a more detailed analysis of the instability properties. Latest results are shown for the effects of inner and outer co-flow Re, sheet thickness and liquid Re on the aerodynamically driven instabily. Improved agreement with theoretical stability analysis is also shown. Improved techniques may afford a better understanding of the complex dynamics of sheet atomisation. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GY.00004: Wavy regimes of a film flow down a slip inclined plane Arghya Samanta, Christian Ruyer-Quil, Benoit Goyeau Consider a 2D viscous incompressible liquid film flow down a slip inclined plane under the action of gravitational force. Two coupled depth averaged equations are derived in terms of the flow rate $q(x,t)$ and the film thickness $h(x,t)$ within the framework of boundary layer approximations together with weighted-residual technique. Linear stability analysis of the averaged equations show good agreement with the results of Orr-Sommerfeld analysis of linearized basic equations. At small values of Reynolds number, presence of slip length is destabilizing whereas it becomes stabilizing at moderate values of Reynolds number. This phenomena indicates the nontrivial stabilizing effect of slip length on the primary instability. In the nonlinear regime, the influence of slip length has been investigated through traveling-wave solutions of the averaged equations. Comparisons with direct numerical simulations of Navier-Stoke's equations also show good agreement. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GY.00005: Wavy regime of a viscoplastic film flow Symphony Chakraborty, Christian Ruyer-Quil, Bhabani S. Dandapat We consider a power-law fluid flowing down an inclined plane under the action of gravity. The divergence of the viscosity of a shear-thinning fluid at zero strain rate is taken care of by introducing a Newtonian plateau at small strain rate. Applying a weighted residual approach, a two-equations model is formulated in terms of two coupled evolution equations for the film thickness $h$ and the local flow rate $q$ within the framework of lubrication theory. The model accounts for the streamwise diffusion of momentum. Consistency of the model is achieved up to first order in the film parameter for inertia terms and up to second order for viscous terms. Comparison to Orr-Sommerfeld stability analysis and to DNS show convincing agreement in both linear and nonlinear regimes. In the case of shear-thinning fluids, lowering the power index has a non-trivial effect on the primary instability of the film: the threshold of the instability occurs at a smaller Reynolds number but the range of instable wavenumber is also reduced. In the nonlinear regime, we have evidenced a subcritical bifurcation of the traveling-wave solutions from marginal stability conditions. [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GY.00006: Rupture of thin liquid films with Plateau borders Lucien Brush, Alan McIntyre, Steven Roper In metal foams there is fluid flow from a lamella into the Plateau borders resulting in lamellar thinning. Since surfactants are not used to slow the flow, instability of a lamella quickly leads to rupture, bubble coalescence and overall coarsening of the foam. This talk presents the results of numerical calculations of the rupture process of a lamellar film with Plateau borders in a gas-liquid metallic foam. The numerical calculations show the evolution of a lamella from the initiation of an instability up to the time just prior to rupture. Rupture times and locations are monitored as a function of the Plateau border radius of curvature. The effect of symmetry-breaking configurations in which a lamella spans two Plateau borders having different radii of curvature shows that the location of rupture can be near the thin film - Plateau border junction. Solutions at late times are compared to the similarity solutions for the case of free films without Plateau borders. [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GY.00007: An ADI Scheme for Particle-Laden Thin Film Flow in 2D Matthew Mata We derive a semi-implicit numerical scheme for a lubrication model of particle-laden thin film flow in two dimensions. The scheme relies on an ADI process to handle the higher-order and advection terms, and an iterative procedure is utilized within each time step in order to improve the quality of the solution and the size of the time step. We compare computational results to laboratory experiments involving mixtures of silicon oil and glass beads on an incline. The results of the simulation agree qualitatively with the experiment and suggest some possible improvements to the model to achieve a quantitative match. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GY.00008: Instability and rupture of thin liquid films on structured surfaces Elizaveta Gatapova, Vladimir Ajaev, Oleg Kabov We investigate stability and break-up of a thin liquid film on a solid surface under the action of disjoining pressure. The solid surface is structured by parallel grooves. Air is trapped in the grooves under the liquid film. Our mathematical model takes into account the effect of slip due to presence of menisci separating the liquid film from the air inside the grooves, the deformation of these menisci due to local variations of pressure in the liquid film, and non-uniformities of the Hamaker constant. Rupture time is found to decrease due to the presence of the grooves. It is shown that simplified descriptions of the film dynamics, e.g. using the standard formulas for effective slip, can lead to significant deviations from the behaviour seen in our simulations. A new regime of self-similar behaviour is found, which is different from the known solutions for films on flat solid substrates and free liquid films. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GY.00009: Rupture Limit of Thin Moving Films Juan C. Padrino, Daniel D. Joseph, Hyungjun Kim The rupture of a thin film in another fluid is studied including the effects of disjoining pressure. The study considers the linear stability of a moving viscous film in a motionless inviscid fluid and of a stagnant viscous film in a motionless viscous fluid. These are analyzed by means of the Navier--Stokes equations and the dissipation approximation based on potential flow. Results reveal that the dissipation method provides a good approximation for the case of a moving film, whereas its predictions are off the mark for the stagnant film case. The thickness of the gap at the trough of Kelvin-Helmholtz waves locates the formation of holes. The wavelength at final collapse is determined by the length of waves at the trough of the corrugated film. The disjoining pressure effects cause very fast break-up for very thin films. These effects influence the cutoff wavenumber. In the limit of small gaps on this corrugated film, the Reynolds and Weber numbers tend to zero with the gap size, the Ohnesorge number increases like the reciprocal of the square root and the Hamaker number like the reciprocal of the square of the gap. The motion of the film does not enter at the point of formation of holes. Moreover, for the most unstable wave, the ratio of the wavelength to film thickness is found to decrease with decreasing film thickness. [Preview Abstract] |
Monday, November 22, 2010 9:57AM - 10:10AM |
GY.00010: Interplay between phase separation and surface deformations in thin films of binary mixtures Santiago Madruga, Fathi Bribesh, Uwe Thiele Films of polymer blends are used in technological applications such as coatings or structured functional layers. The evolution of those films is involved by the coupling of phase separation within the film and surface deformations. We developed a model for films of binary mixtures [1], such as polymer blends, with free evolving surfaces. The model is based on model-H describing the coupled transport of concentration and momentum fields supplemented by boundary conditions at the substrate and free surface. We use the model to analyze the stability of vertically stratified base states of free surface films and the influence of composition in the shape of the films. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. The inclusion of convective transport leads to further destabilization as compared to the purely diffusive case [2]. In addition, we discuss the role of composition for off-critical mixtures on surface deflections. \\[4pt] [1] U. Thiele, S. Madruga, and L. Frastia. Phys. of Fluids. 19, 122106, (2007).\\[0pt] [2] S. Madruga and U. Thiele. Phys. of Fluids. 21, 062104, (2009). [Preview Abstract] |
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