Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JG: Instability: Interfacial and Thin Films III |
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Chair: Omar Matar, Imperial College London Room: Salt Palace Convention Center 250 A |
Monday, November 19, 2007 3:35PM - 3:48PM |
JG.00001: Hydrodynamics and heat transfer of thin films on inclined structured plates Karsten Loeffler, Hongyi Yu, Tatiana Gambaryan-Roisman, Peter Stephan Thin liquid films flowing down vertical and inclined plates are widely used in industrial applications, e.g. in falling film evaporators for concentrating of sugar solutions. Falling films exhibit very complex wavy patterns, which depend on various parameters. Using structured, in particular, grooved plates is a promising way to enhance the heat transfer rate in thin film evaporators. The influence of the plate topography on the wave motion is still not completely understood. In the present work the evolution of the water film thickness on smooth and structured (longitudinal and sinusoidal grooves and herringbone structures) plates has been experimentally investigated for different inclination angles, Reynolds numbers and at various distances from the inlet. A confocal chromatic sensoring technique was used to measure the film dynamics. Additionally, the temperature distribution at the heated wall has been measured with thermocouples and the liquid-gas interface has been observed with infrared thermography for different heat fluxes. The heat flux has been gradually increased until film rupture occurred. The effect of the wall topography on the film stability has been quantified. It has been found that the wall topography significantly affects the wave pattern, the heat transport and the film stability. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JG.00002: Flow of an infinite fluid strip down an inclined plane: Contact line stability Juan M. Gomba, Javier Diez, Roberto Gratton, Alejandro G. Gonz\'{a}lez, Lou Kondic We present a computational study on the flow of a fluid strip down an inclined plane. Unlike the commonly considered case of constant film thickness far behind the contact line, this flow involves a finite cross section and therefore it does not admit a traveling wave solution; instead, the base flow is time- dependent. Consequently, the equations that governs the evolution of both the base state and of the perturbation must be solved simultaneously. The computations show that, imposed perturbations travel with the same velocity as the leading contact line. The spectral analysis of the modes evolution shows that their growth rates are time-dependent. The wavelength of the mode with maximum amplitude decreases with time until it reaches an asymptotic value, $\lambda_{max}$. We explore the dependence of $\lambda_{max}$ on the cross sectional fluid area, $A$, and on the inclination angle of the plane, $\alpha$. For the considered small $A$, corresponding to small Bond numbers, we find that the dependence of $\lambda_{max}$ on $A$ is in good agreement with experimental data (Gomba et al, Phys. Rev. E 71, 016304, 2005). This dependence differs from the one observed for films characterized by much larger cross sectional areas and Bond numbers. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JG.00003: On barodiffusion in thin binary falling fluid films Zachary Borden, Herve Grandjean, A.E. Hosoi, L. Kondic, B.S. Tilley We examine interfacial dynamics of an isothermal, binary liquid thin film flowing down an inclined plane. The two fluids are incompressible with different bulk densities. Using a water-glycerol mixture, transient interfacial depressions, or ``dimples,'' are observed. These depressions appear only for a range of water concentrations from 30\% to 70\% by volume, and the frequency of their appearance is inversely proportional to the characteristic film thickness. To understand the origin of these dimples, we propose a barodiffusive model of quasi-incompressible components. The coupled set of evolution equations describes the interfacial shape and the local mass concentration of one component. The model incorporates the effects of inertia, solutalcapillarity, surface tension, and barodiffusion. We find that interfacial gradients cause a slight component segregation leading to Marangoni-driven instabilities. Comparison of this model to experimental data is presented. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JG.00004: Stretching of viscous sheets including axial and transverse viscosity variations Benoit Scheid, Sara Quiligotti, Binh Tran, Rene Gy, Howard Stone We study the stretching of a Newtonian liquid sheet under the influence of strong viscosity variations. Such a flow is encountered in film casting processes where viscosity variations are usually induced by temperature gradients, not only along the stretching coordinate but also across the film thickness. We therefore derive a generalized extensional flow model accounting for an arbitrary two-dimensional distribution of the viscosity in the sheet. Stationary solutions and their stability (usually referred to as draw resonance) are then investigated for various situations. In the case of in-plane viscosity variations only, the system is more unstable (stable) if the viscosity increases (decreases) in the flow direction. In the case of transverse viscosity variations only, the system is more unstable (stable) if the viscosity is constant on one surface and larger (smaller) on the other surface. When the two destabilizing situations are combined, it is found that the critical draw ratio can be significantly below 20.18, i.e. the value for constant viscosity. Draw resonance instability is therefore shown here to be very sensitive to the two-dimensional viscosity distribution in the film. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JG.00005: Ultrasound Measurement of Dynamic Film Thickness in Condensing and Evaporating Films Jeramy Kimball, Michael Bailey, James Hermanson, Jeffrey Allen The stability and heat transfer characteristics of a cyclically condensing and evaporating n-pentane film were studied experimentally. The films were on a flat, horizontal, downward-facing copper plate. Film thickness was determined by an ultrasound technique capable of measuring film thicknesses as low as 15 microns. Surface heat flux was determined from the time rate of change of the film thickness. Spatially averaged heat flux was also measured using an embedded heat flux sensor and surface conditions inferred by a computational inverse method. The film was imaged using a double-pass shadowgraph system. Film thickness and heat flux appear to increase most rapidly during the initial formation of a thin film of condensate, as well as at the appearance of the Rayleigh--Taylor instability and pendant drop formation during a pressure ramp-up. Hysteresis was observed in the film thickness and heat flux over each pressure variation cycle, with different behavior apparent during condensation than during evaporation. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JG.00006: Falling films on flexible substrates Omar Matar, Richard Craster, Satish Kumar Falling films have a long history and modern advances in the theory have led to accurate modelling for flows down rigid inclines. We now consider the possible effects that can be introduced by flexible substrates. In this work, we derive Benney-like coupled equations for the film thickness and substrate deflection using long-wave theory. Weakly nonlinear equations are also derived, which, in the limit of small substrate deflections, reduce to the Kuramoto-Sivashinsky equation. We also use boundary-layer theory in conjunction with the Karman-Polhausen approximation to derive three strongly coupled evolution equations for the film thickness, substrate deflection and film volumetric flow rate. Inertial, gravtiational, capillary, viscous, substrate tension and damping effects are elucidated via numerical solutions of the above systems of equations. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JG.00007: Transient amplification and nonlinear stability of driven thin films Roman Grigoriev, Radford Mitchell Transient amplification of small disturbances (e.g., microscale surface roughness or chemical heterogeneity) has been suggested as an alternative explanation for contact line instability in thin liquid films spreading over solid substrates. Although transient growth has been observed experimentally (for thermocapillary-driven flows), reasonable theoretical understanding of this phenomenon has been achieved only in the limit of infinitesimal disturbances. Here we present the results of an analytical study of gravity-driven films which goes beyond linear stability analysis by considering the effect of nonlinearities on the asymptotic behavior of finite disturbances. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JG.00008: Transition to Absolute instability in a Liquid Sheet Nathaniel Barlow, Brian Helenbrook, Sung Lin A set of two simultaneous partial differential equations are derived which govern the spatio-temporal evolution of an initially local disturbance on a liquid sheet. Numerical solutions of these equations show how the absolute instability predicted by the spatio-temporal linear stability theory is approached when the Weber number is smaller than one. The results support the predictions of de Luca\footnote{ L. de Luca and M. Costa. J. Fluid Mech. 331, 127, 1997.} and Lin and Jiang\footnote{ S.P. Lin and W. Y. Jiang. Phys. Fluids. 15, 1745, 2003.}. They showed that the disturbance in an absolutely unstable liquid sheet grows as fast as the cubic root of time as time approaches infinity. The temporal normal mode solution of Luchini \footnote{ P. Luchini. Phys. Fluids, 16, 2154, 2004.} failed to capture this large time asymptotic behavior. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JG.00009: Coarsening of dewetting thin ?lms subject to gravity Michael Gratton, Thomas Witelski Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultra-thin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue -- the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity is expected to only have an influence on thicker films, we show that it has a significant influence on the coarsening dynamics of the problem, dramatically slowing the rate of coarsening for large drops. Small drops may be relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are different. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JG.00010: Electrified viscous thin film flow over topography Demetrios Papageorgiou, Dmitri Tseluiko, Mark Blyth, Jean-Marc Vanden-Broeck We investigate the gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field. The film is assumed to be a perfect conductor and the bounding air region above is a perfect dielectric. We study the interaction between the electric field and the topography at steady state conditions. Using a long-wave analysis we derive a nonlinear, non-local evolution equation for the thickness of the liquid film and compute steady solutions for flow into a rectangular trench and over a rectangular mound, for example. We demonstrate that the electric field can be used to reduce or completely remove the familiar ridge features seen ahead of a downward step. Boundary integral computations of the full problem are also presented and compared with the long-wave theory. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JG.00011: Stability of a Volatile Liquid Film Flowing Over a Locally-Heated Surface Naveen Tiwari, Jeffrey Davis The dynamics and linear stability of a volatile liquid film flowing over a locally-heated surface are studied using a long- wave analysis. The Marangoni stress at the heater induces a pronounced capillary ridge. A linear stability analysis of this ridge with respect to spanwise perturbations reveals that the operator of the linearized system can have both a discrete and continuous spectrum. The discrete spectrum appears above a critical value of the Marangoni number for a finite band of wavenumbers separated from zero. Above a second, larger critical value of the Marangoni number, a band of the discrete spectrum becomes unstable, corresponding to rivulet formation. For sufficiently large evaporation, a second band of unstable discrete modes appears, which is associated with an oscillatory, thermocapillary instability above the heater. The critical Marangoni number at instability has a non- monotonic dependence on the steepness of the temperature profile, and an energy analysis is used to gain insight into the instability mechanisms. Transient, non-modal amplification of over two orders of magnitude is found for films susceptible to both rivulet and thermocapillary instabilities for a narrow band of transverse wavenumbers different from those corresponding to the largest eigenvalues. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JG.00012: Dynamics and Stability of Thin Film on a porous inclined plane Usha Ranganathan, Mohammed Rizwan Sadiq The flow of a thin viscous incompressible film on a porous inclined plane is considered. The long wave theory is applied and an evolution equation for the film thickness is obtained. It is assumed that the flow through the porous medium is governed by Darcy's law. The characteristic length scale of the pore space is much smaller than the depth of the fluid layer on the inclined plane. The critical condition for the onset of instability is obtained. The results of the linear stability analysis reveal that the film flow system on a porous inclined plane is more unstable than on a rigid wall. The increase of permeability of the porous medium enhances the destabilizing effect. The existence of both supercritical stable and subcritical unstable states is established through the weakly nonlinear stability analysis. The nonlinear waves in the supercritical stable region are captured numerically. The solutions exhibit different kinds of typical waves such as nearly sinusoidal and solitary waves at long times. The shape and amplitude of such waves are strongly influenced by the permeability of the porous wall. Further the steady state solution profiles are determined for various values of the permeability parameter. [Preview Abstract] |
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