Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L20: Interfacial/Thin Film Instability V 
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Chair: Andrew Belmonte, Pennsylvania State University Room: 323 
Monday, November 21, 2011 3:35PM  3:48PM 
L20.00001: Linear Instability, SelfSimilarity and Nonlinear Growth in Ultrathin Wetting Films Driven by Thermocapillary Flow Ryan Denlinger, Sandra Troian Nanoscale viscous films subject to very large thermocapillary stresses are susceptible to a linear instability resembling nanopillar arrays. The interstitial regions, which provide the fluid needed to grow these structures, are observed to undergo rapid depletion down to tens of nanometers in thickness. Previous analyses have neglected the role of van der Waals forces in these systems [1]. A linear stability analysis of ultrathin films in which the disjoining pressure is comparable to thermocapillary and capillary forces confirms that wetting van der Waals forces generate larger interpillar spacings. More importantly, however, growth beyond the linear regime is characterized by an ultra flat depletion zone. Using a combination of analytic work and finite element simulations, we have identified a selfsimilar regime in which finiteamplitude disturbances to this zone produce a significant nonlinear response. The resulting waveform shape is indicative of a secondary growth process leading to nanopillar formation. We discuss the behavior of three distinct growth regimes characterizing initial pillar growth, depletion zone formation, and secondary pillar growth. [1] M. Dietzel and S. M. Troian, Phys. Rev. Lett. 103, 074501 (2009); J. Appl. Phys. 108, 074308 (2010) [Preview Abstract] 
Monday, November 21, 2011 3:48PM  4:01PM 
L20.00002: The onset of Marangoni convection for evaporating liquids with spherical interfaces and finite boundaries Brendan MacDonald, Charles Ward We examine the stability of evaporating liquids with spherical interfaces bounded at one value of the polar angle for all azimuthal angles. A linear stability analysis is performed and the results are used to explain why a system with water evaporating from a funnel constructed of PMMA undergoes stable quiescent evaporation but a system with a funnel constructed of stainless steel experiences a transition from a quiescent state to a state with Marangoni convection. We develop the expression for a new stability parameter that provides a quantitative prediction of the transition to Marangoni convection, and find the predictions to be consistent with experiments. [Preview Abstract] 
Monday, November 21, 2011 4:01PM  4:14PM 
L20.00003: Coherence Resonance Behavior in Thermocapillary Lithography Nan Liu, Sandra Troian Interest in alternative means of nanofilm lithographic patterning has focused attention on a number of thin film hydrodynamic instabilities which can spontaneously generate periodic arrays of 3D protrusions. The interface evolution equation, which results from a competition between stabilizing capillary forces and destabilizing external driving forces, are well described by a nonlinear, fourth order PDE rather sensitive to initial and boundary conditions. Even small levels of noise result in arrays prone to variations in array pitch and array height at levels currently unacceptable for commercial applications. In this talk, we focus on thin film patterning by thermocapillary forces. We demonstrate how an adjacent cooled template with a small sinusoidally roughened surface presented to the free surface of a molten nanofilm can be used to trigger very rapid and uniform array growth with a pitch even smaller than predicted by linear stability analysis. This behavior is reminiscent of coherence resonance phenomena in which a small amount of external noise can trigger resonant uniform growth. We quantify the behavior of waveforms generated in this way by a combination of weakly nonlinear analysis and finite element simulations. [Preview Abstract] 
Monday, November 21, 2011 4:14PM  4:27PM 
L20.00004: Film falling on a porous substrate Arghya Samanta, Christian RuyerQuil, Beno\^It Goyeau Consider a two dimensional viscous incompressible liquid film falling on a saturated porous inclined plane. The interface between the liquid and porous medium is modeled using a onedomain approach for which the permeability and porosity varies continuously. A twoequation model is derived in terms of the flow rate $q(x,t)$ and total height $H(x,t)$ within the framework of boundary layer approximations using weighted residual techniques. Coefficients of the model are expressed in terms of combinations of the integrals of the base flow $f$ and weight function $w$ that are determined numerically to ensure consistency of the approach at first order in the film parameter. The influence of properties of the homogeneous porous substrate on the wave dynamics is investigated by constructing the nonlinear traveling wave solutions. [Preview Abstract] 
Monday, November 21, 2011 4:27PM  4:40PM 
L20.00005: How does a soap film burst during generation? Emmanuelle Rio, Laurie Saulnier, Frederic Restagno, Dominique Langevin Foams are dispersions of bubbles in a liquid matrix in the presence of stabilizing surfactants. Even if foams are ubiquitous, the ability of a solution to create a certain foam quantity is still not fully understood. As a first step, we choose to work on a simplified system and studied the stability of a soap film during its generation. We have built an experiment, in which we determine simultaneously the velocity of a frame pulled out of a soapy solution and the entire shape of the liquid film. We found that the film is made of two parts: the bottom part is of uniform and stationary thickness, well described by the classical Frankel's law; in the top part, the film drains until a black film appears near the frame upper boundary frame, and then bursts. In this study, we characterize both part of the films and show that the Frankel law breaks down at high capillary number due to surfactants confinement. We also explain why films pulled at high velocity have a shorter lifetime than those pulled at low velocity. [Preview Abstract] 
Monday, November 21, 2011 4:40PM  4:53PM 
L20.00006: Modeling of the stability of freefalling liquid curtain flow Fortunato De Rosa, Gennaro Coppola, Luigi de Luca The physical mechanisms leading to the disintegration of a gravitational (non parallel) twodimensional plane liquid curtain (sheet), occurring at low fluid flow rates, are not yet fully known. The problem is reconsidered here through the development of an unsteady inviscid mathematical model where the dependent variables are expressed by means of polynomial expansions in terms of powers of the local lateral distance from the centerline position. Surface tension effects are included, and the ambient pressure field may be either applied or induced by the compliant free interface. The linearization around the base flow allows the separation of sinuous and varicose responses. The global linear stability of such a model is analyzed by inspecting both modal and nonmodal amplifications of disturbances energy. An equation of energy budget is also derived, which is used to estimate the contribution of the various physical effects evaluated via direct numerical simulations of the governing system of equations. [Preview Abstract] 
Monday, November 21, 2011 4:53PM  5:06PM 
L20.00007: Layer formation in particleladen freefilms Lucien Brush, Steven Roper Solutions to a model of a particleladen freefilm that includes structural oscillatory forces in addition to van der Waals forces are presented. Examination of steady solutions to the equations reveals layer and bulge solutions. Fully nonlinear timedependent numerical calculations reveal that at fixed concentration a uniform film evolves into a multilayered film, the heights of which are given by the common tangent construction applied to the particlefilm interaction free energy. If the interaction free energy curvature is negative there is no barrier to the formation of a layered film from the uniform film, whereas if the interaction free energy curvature is positive the uniform layer is metastable. This behavior is analogous to spinodal decomposition and nucleation and growth mechanisms observed in classical first order phase transformations. Phase diagrams for layer transitions are also presented and discussed. [Preview Abstract] 
Monday, November 21, 2011 5:06PM  5:19PM 
L20.00008: Interfacial instabilities of reactive fingering Andong He, Andrew Belmonte We consider viscous flows in a HeleShaw cell in which two immiscible fluids chemically react and form a complex substance at the interface. The interface is modeled as an elastic membrane whose bending rigidity depends on the local curvature. A dispersion relation is derived using the energy variation method. Several types of instabilities are categorized and how various physical parameters affect the stability is investigated. Our model is able to explain the anomalous fingering instability from experimental observations reported by other authors. [Preview Abstract] 

L20.00009: ABSTRACT WITHDRAWN 
Monday, November 21, 2011 5:32PM  5:45PM 
L20.00010: Thin film rupture on flat and structured surfaces with surface charge densities Christiaan Ketelaar, Vladimir Ajaev We perform a linear and nonlinear stability analysis to determine the conditions at which a thin film of viscous liquid containing a small concentration of ions will rupture for different surface charge densities at the solidliquid and gasliquid interfaces. The rupture is driven by the combined action of the electrostatic component of the disjoining pressure and van der Waals forces. The evolution of the interface shape is described using the system of lubricationtype equations. By considering a small perturbation to the constant steadystate solution, we obtain the growth rate of the instability and find a wave number range where the perturbation decays. The nonlinear stability analysis is performed by solving the interface shape equation numerically for a range of parameters corresponding to different values of the initial film thickness, Debye length, and surface charge densities. We then discuss applications of the same mathematical framework to analyze film rupture on charged structured surfaces. [Preview Abstract] 
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