Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session EQ: Instability: Interfacial and Thin-Film III |
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Chair: Lucien Brush, University of Washington Room: 200E |
Sunday, November 22, 2009 4:15PM - 4:28PM |
EQ.00001: Study of Pattern Evolution in Nanoscale Viscous Films Subject to Pillar Instability by Thermocapillary Stresses Sandra Troian, Mathias Dietzel Nanofilms of molten polymer subject to a large transverse thermal gradient are known to undergo instability to arrays of elongated pillars separated by a few microns. The simplicity with which such large area patterns can be formed offers a new type of resistless, non-contact lithography in which pillar spacing and amplitude can be controlled by plate separation distance, initial film thickness and thermal gradient. Here, we investigate the evolution of pillar formation from the linear to non-linear regime by examining an unexplored limit of Benard instability accessible to films of nanoscale dimensions. Given the small plate spacings used in experiment, we examine the influence of initial conditions on the wave number selection process. For intermediate values of plate separation, the pillar spacing is well predicted by linear stability analysis and unaffected by the type of initial disturbance applied. For larger plate separation, the pillar arrays evolve toward hexagonal symmetry while subsequent depletion of fluid in the interstitial regions leads to formation of subharmonic protrusions. These bifurcations are suggestive of cascade processes observed in other thin film evolution equations. [Preview Abstract] |
Sunday, November 22, 2009 4:28PM - 4:41PM |
EQ.00002: Influence of Temperature Dependent Viscosity on the Evolution of Pillar Instabilities in Polymer Nanofilms Mathias Dietzel, Sandra Troian We have previously shown that evolution of periodic elongated pillar arrays in nanoscale polymer films subject to a significant transverse thermal gradient represents an extreme limit of Benard-instability. Such ultrathin films allow access to a regime in which destabilizing thermocapillary forces outweigh stabilization by capillary and gravitational forces by many orders of magnitude. In prior work, the melt viscosity was assumed constant. Here we explore the influence of increasing viscosity as the nanopillars evolve to approach a cooler target. A comparison of models incorporating either a linear or exponential variation of viscosity with temperature with previous results reveals that the pillar spacing obtained from linear stability analysis is only marginally affected. Full numerical simulations beyond the linear regime, however, indicate a more noticeable influence on pillar shape and even more so, pillar growth times. The influence of thermal viscous effects on this moving boundary problem is therefore critical to estimates of processing times for technological applications. [Preview Abstract] |
Sunday, November 22, 2009 4:41PM - 4:54PM |
EQ.00003: Effect of insoluble surfactant on the evolution of electrified falling films B. Uma, R. Usha Nonlinear stability of a thin liquid film down an inclined plane when the film surface is contaminated with an insoluble surfactant and the film is subjected to an electric field has been analyzed. The evolution equation of the electrified contaminated film has been derived using long-wave perturbations. Linear stability analysis of the electrified contaminated film reveals that the effect of electric Weber number and Marangoni number is to destabilize the film flow system. The nonlinear evolution of the film thickness is found by numerically solving the coupled non-linear evolution equation for the film thickness and the surfactant concentration in a periodic domain. Evolution profiles of the thin film thickness and the surfactant concentration down an inclined plane are plotted for the different values of parameter governing the flow. [Preview Abstract] |
Sunday, November 22, 2009 4:54PM - 5:07PM |
EQ.00004: Convective Structure and Heat Transfer of Liquid Films Evaporating into a Pure Vapor Environment J.T. Kimball, J.C. Hermanson, J.S. Allen The stability, convective structure and heat transfer of upward facing, evaporating, thin liquid films were studied experimentally. Dichloromethane, n-pentane, and methanol films initially 5 mm to 50 $\mu $m thick were subjected to constant or impulsive superheat levels. The films resided on a temperature controlled, gold-plated copper plate in a closed, degassed test chamber. The dynamic film thickness was measured at multiple discrete points using ultrasound and instability wavelength and convective structure information was obtained by schlieren imaging. For films below the transition Rayleigh number there is little convective heat transfer present within the film. In films above this transition, the Nusselt number increases with increasing Rayleigh number. The transition in the heat flux occurs over a wide range of Marangoni numbers. Transient experiments reveal an initial rise in heat flux due to evaporation, followed by a decrease and then increase at the onset of convective motion. [Preview Abstract] |
Sunday, November 22, 2009 5:07PM - 5:20PM |
EQ.00005: Rupture of the interface between two fluids in presence of surface agents Matthieu Roche, Mounir Aytouna, Daniel Bonn, Hamid Kellay Rupture of interfaces between two fluids is ubiquitous in everyday life. It is well established that this process is driven by three stresses: capillarity, viscosity and inertia. The effects of viscosity and inertia have been widely studied, whereas capillary effects have attracted less attention. We present results concerning the rupture of an interface in the presence of surface agents. Ruptures in the presence of a surfactant (SDS) and in the presence of a mixture of surfactant (SDS) and polymers (PVA) have been studied. In both cases, surface agents are diluted in the outer fluid. All experiments have been carried out using a microfluidic flow-focusing device. In the former case, the thinning dynamics of the neck behind the droplet exhibits two modes of thinning, depending on the external flow rates, and the surfactant concentration. These modes can be related to dynamic surface tension phenomena. In the latter case, the thinning slows down exponentially in the late instants. Structures analogue to beads-on-a-string also develop. This is very similar to what is reported for the breakup of polymeric jets, though polymers are outside the jet in our case. [Preview Abstract] |
Sunday, November 22, 2009 5:20PM - 5:33PM |
EQ.00006: Drops and waves on a viscous film coating a vertical fiber Camille Duprat, Frederique Giorgiutti-Dauphine We consider the nonlinear dynamics of a liquid viscous film flowing down a vertical fiber. The initially flat film spontaneously breaks up into a regular wavetrain due to the Rayleigh-Plateau instability. The characteristics of the fully developed structures then depend on the dominant mechanisms. When the advection of the waves by the flow dominates over the instability, we observe moderate amplitude waves that propagate without carrying mass. When surface tension is strong, the film breaks up into large amplitude drops exhibiting a recirculation region. The transition between drops and waves regimes and the corresponding structures have been characterized experimentally and numerically. When both surface tension and viscosity effects are strong, the system can be seen has a paradigm for active (unstable), dissipative and dispersive media. The particular shape of the resulting structures gives rise to complex interactions (attraction and repulsion) leading to the formation of bound states. The system then appears to select a finite number of preferred specific distances in agreement with a weak interaction theory developed by D. Tseluiko, S. Saprykin and S. Kalliadasis (Imperial College London). [Preview Abstract] |
Sunday, November 22, 2009 5:33PM - 5:46PM |
EQ.00007: Tear Film Dynamics for Blink Cycles with a Wetting Cornea and Evaporation R.J. Braun, J. Tang, L.P. Cook, D.M. Anderson We consider a lubrication model in one spatial dimension for the human tear film. The ends of the domain move to mimic the blink cycle of the eyelids; the underside of the film is wettable surface due to a conjoining pressure and evaporation occurs from the top surface of the film. The film can equilibrate at a small finite thickness where the conjoining pressure and evaporation balance. This small thickness is interpreted as a dry spot; the model can compute past dry spot formation. Results are given for the film dynamics with either pressure of flux boundary conditions on the ends of the film. The film can form dry spots for some boundary conditions of either type. The persistence of the dry spots with respect lid motion and other effects are explored. [Preview Abstract] |
Sunday, November 22, 2009 5:46PM - 5:59PM |
EQ.00008: Turbulent gas -- laminar liquid flows Dmitri Tseluiko, Serafim Kalliadasis We study two-dimensional co-current and counter-current turbulent gas-laminar liquid flows. Specifically, we consider a liquid film flowing under gravity down the lower wall of an inclined channel when a turbulent gas flows above it. The solution of the full system of equations describing the gas-liquid flow faces serious technical difficulties. However, a number of certain assumptions allow separating the gas problem and solving it independently. This permits finding perturbations to pressure and tangential stresses at the interface. We then proceed to the liquid problem and derive model equations describing the dynamics of the interface, i.e. boundary-layer equations, an integral-boundary-layer model and a long-wave model and we analyze solutions of these equations. As the simplest prototype retaining all the important physical mechanisms, we derive a weakly nonlinear model, a Kuramoto-Sivashinsky-type equation with a dispersive term and a contribution from the turbulent gas. [Preview Abstract] |
Sunday, November 22, 2009 5:59PM - 6:12PM |
EQ.00009: Spin-coating of layered liquids Alan McIntyre, Lucien Brush An axisymmetric model of the spin-coating of two immiscible, vertically stratified liquids is derived using lubrication theory. The model includes gravitational, van der Waals, capillary, viscous forces and evaporation/condensation processes. During the evolution of uniform layers, the lower layer thins monotonically and never reaches zero thickness. With evaporation the upper layer disappears in finite time. With condensation the upper layer reaches a steady-state thickness. Fully nonlinear calculations, including viscous and evaporation/condensation effects, show that disturbances of the lower layer have a greater effect on the upper layer than disturbances of the upper layer have on the lower layer. Disturbances along the upper gas-liquid free surface propagate outward more rapidly than those along the lower liquid-liquid interface. The effects of additional forces on the evolution of bilayer films during spin-coating are also presented. [Preview Abstract] |
Sunday, November 22, 2009 6:12PM - 6:25PM |
EQ.00010: Linear and nonlinear stability of floating viscous sheets Gilles Pfingstag, Arezki Boudaoud, Basile Audoly The dynamics of thin viscous sheets is relevant to industrial processes such as float glass and to natural processes such as plate tectonics. We study the behavior of a thin, Newtonian viscous sheet undergoing stretching and bending. We use asymtotic expansions to derive the equations governing the evolution of the thickness and of profile of the sheet subjected to an external force field. Two models are obtained according to the scaling of the characteristic evolution time. In this framework, we investigate the stability of a viscous sheet floating on a denser fluid [at rest], accounting for gravitation and surface tension.The various instable modes are described. A nonlinear analysis yields the long-time evolution of the sheet. We also discuss possible extensions to falling sheets or to variable viscosities. [Preview Abstract] |
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