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 NG: Instability: Interfacial and Thin Films V |
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Chair: Reza Sadr, Georgia Institute of Technology Room: Salt Palace Convention Center 250 A |
Tuesday, November 20, 2007 11:35AM - 11:48AM |
NG.00001: Thickening Effect of Surfactants in the Dragout Coating Problem Gelu Pasa, Prabir Daripa We study the dip coating flow on a flat plate which is being withdrawn from a liquid bath. This problem was considered in the seminal paper of Landau and Levich (1942). A similar problem, concerning the motion of long bubbles in capillary tubes was considered by Bretherton (1961). In both problems, it is important to study the effects produced by interfacial surfactant. Bretherton reported that the thickness of the film left behind the moving front could be increased by the presence of surfactant. The same result was obtained in several papers using numerical methods. In the present paper, we consider the drag-out problem with a small variation of an insoluble surfactant. We obtain a formula for an upper bound in terms of the Marangoni and Capillary number. The main result is following: the upper bound is less in the ``clean'' case (without surfactant) consistent with previous numerical results. We use the lubrication approximation and the ``flux'' method. A perturbation analysis of the equations of fluid flow is performed to obtain the result. [Preview Abstract] |
Tuesday, November 20, 2007 11:48AM - 12:01PM |
NG.00002: Nonlinear evolution and traveling waves of sheared-film flows with insoluble surfactant Alexander Frenkel, David Halpern We study traveling wave solutions which bifurcate from a plane- Couette film flow with an insoluble surfactant. The flat interface with a non-zero shear becomes unstable when the disturbance wavelength exceeds a marginal value. (This theoretically predicted instability was recently confirmed in experiments by Stocker and Bush (JFM vol. 583, 2007).) Traveling wave equilibria bifurcate from the flat film flow as the spatial period increases from the marginal-stability value. The disturbances are governed by a system of PDEs for the film thickness and the surfactant concentration which is controlled by a single parameter $C$. The Hopf bifurcation to traveling waves is supercritical for $C< C_s$ and subcritical for $C> C_s$, where $C_s \approx 0.29$. For the subcritical cases, there are two values of equilibrium amplitude for a range of $C$ near $C_s$, but the traveling-wave with the smaller amplitude is unstable as a periodic orbit of the associated dynamical system whose independent variable is the spatial coordinate. Numerical simulations of time-dependent evolution equations show that the saturation of the disturbances is invariably large amplitude. This suggests that, in general, for flowing film instabilities of the Kuramoto-Sivashinsky type that have zero wavenumber at criticality, the saturated disturbance amplitudes do not always have to decrease to zero as the control parameter approaches its critical value. [Preview Abstract] |
Tuesday, November 20, 2007 12:01PM - 12:14PM |
NG.00003: Interfacial Instabilities Due to Evaporation and Convection: Nonlinear Analysis. Weidong Guo, Ranga Narayanan Evaporative and convective instabilities in two phase systems arise in a variety of industrial processes, such as drying of films and in coating technology. Past theories assume either a passive vapor layer or unbounded geometries. We have investigated the evaporative convection by taking into account the fluid dynamics of both liquid and vapor phases as well as rigid side wall conditions. The base state is one of zero evaporation flux and two cases are considered; one where the upper wall and lower walls allow mass flux and another where the top and bottom walls are made impermeable. The onset and post onset regions are studied. The nature of the bifurcation as well as the change in mass and heat flux in the nonlinear regime are determined. [Preview Abstract] |
Tuesday, November 20, 2007 12:14PM - 12:27PM |
NG.00004: Influence of phase change on non-equilibrium contact lines Pierre Colinet, Alexey Rednikov, Severine Rossomme Despite their crucial importance in the fields of microfluidics and in heat transfer technologies, contact lines are not yet completely understood from the modeling point of view, in particular when involving heat and fluid flows coupled by means of evaporation/condensation processes. In this presentation, such non-equilibrium contact lines are analyzed theoretically, using a lubrication-type equation incorporating relevant micro-scale effects, i.e. kinetic resistance to phase change, disjoining pressure and influence of interfacial curvature. In addition, the effect of an inert gas is also addressed. It is shown that steady contact line shapes can be accurately described by an analytical solution based on matched asymptotic expansions in a certain meaningful limit. For moving contact lines, the dependence of the apparent contact angle upon the contact line velocity is also investigated, and compared to numerical simulations of the evolution equation, for droplet-like solutions. Finally, the relevance of our results for the macroscopic modeling of heat transfer processes such as boiling, is also discussed. [Preview Abstract] |
Tuesday, November 20, 2007 12:27PM - 12:40PM |
NG.00005: Heat transfer in the vicinity of a steady evaporating contact line Severine Rossomme, Benoit Scheid, Pierre Colinet The quantitative determination of overall heat transfer in the vicinity of contact lines is crucial for many heat transfer devices such as heat pipes and boilers. In this context, a long-wave evolution equation describing the evaporation of an ultra-thin film is solved, focusing on nonlinear solutions in the form of contact lines connecting a constant slope region to an adsorbed precursor film. First, the latter film is found to be stable to hydrodynamic disturbances, via linear stability analysis. Then, the main characteristics of evaporating contact lines are analyzed, with particular attention to the sharp peak of the heat flux occurring in the transition region, which results in a microscopic (though non-negligible) contribution to the overall heat transfer. The latter is then quantified as a function of the thermal conductivity of the solid, the mass transfer resistance, the interface curvature and the Van der Waals forces, including their influence on the saturation temperature. For small superheat, a useful scaling behavior is found for the apparent contact angle and for the heat flux characteristics. [Preview Abstract] |
Tuesday, November 20, 2007 12:40PM - 12:53PM |
NG.00006: Frost flowers Grae Worster, Robert Style Frost flowers are dendritic or rod-like ice crystals found on young sea ice. Given that sea ice is briny and that frost flowers grown in the laboratory had seemed to be associated with a salty slush layer on the surface, it has been thought that brine transport through the porous sea ice is a prerequisite for frost-flower formation. Additionally, reported experiments in which frost flowers were grown in the laboratory have involved an external vapour source, suggesting further that frost flowers condense from a saturated atmosphere in the same way as hoar frost. We have determined a regime diagram of external temperature and humidity showing the conditions under which an ice surface will evaporate (sublimate) or grow by condensation and the conditions under which supersaturation occurs local to the ice surface. This shows that frost flowers can grow into a relatively dry atmosphere while the underlying ice surface is evaporating and also that frost flowers can grow on a pure ice surface. We have confirmed these results with laboratory experiments and evaluated linear and nonlinear stability analyses to elucidate the initial formation of frost flowers further. [Preview Abstract] |
Tuesday, November 20, 2007 12:53PM - 1:06PM |
NG.00007: The Yih mode as a limit in diffuse interface instability: when and how? Suthee Wiri, Theo Theofanous Instability of two sparingly-miscible fluids is shown to always approach the sharp interface, Yih-mode, when both the diffuse layer thickness, $\delta $, and molecular diffusivity approach zero ($\delta \to 0,Sc\to \infty )$. The physical mechanism of this ``Yih-like'' instability is discussed, and the quantitative aspects of the approach to the sharp limit are elucidated by extensive coverage of the (dimensionless) parameter space in Poiseuille and Couette flow. The formulation of the mathematical problem differs from that of recent work in the literature in that the (viscosity) constitutive law is applied consistently to both disturbance \textit{and} base flow equations. In the numerical work we found it necessary to meet rather severe spatial resolutions, made possible by the virtual interface method, and to control round-off errors to the extent of quadruple precision. Thusly, significant discrepancies with previous work are accounted for, in the limited parameter spaced covered by these works. More importantly, extension of the parameter space, along with energy-transfer diagnostics on the solutions, allowed the relationship to Yih instability be established and understood. The results are important in setting guidelines for spatial resolution in direct numerical simulations of instability in shear flows, and in providing robust benchmarks for such numerical work. [Preview Abstract] |
Tuesday, November 20, 2007 1:06PM - 1:19PM |
NG.00008: Structure and stability of binary mixtures with free evolving surface Santiago Madruga, Uwe Thiele Thin polymer films of binary mixtures are used in technological applications as homogeneous coatings or structured functional layers. Experiments show a coupled dynamics of decomposition within the film and the dewetting of the film [1]. We propose a model of the decomposition induced profile evolution of a free surface film of a binary mixture. The model is based on model-H [2] describing the coupled transport of concentration (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) fields supplemented by boundary conditions at the substrate and the free surface. After determining homogeneous and vertically stratified base states we analyse their lateral stability [3] and show that depending on the energetical bias at the surface and the mean concentration the convective transport (i) promotes the instability and (ii) induces surface deflections for the stratified base states. \newline $[1]$ R. Yerushalmi-Rozen et al. Science. 285, 1254-1256 (1999). $[2]$ D.M. Anderson et al. Ann. Rev. Fluid Mech. 30, 139-165 (1998). $[3]$ U. Thiele, S. Madruga, and L. Frastia. Submitted to Phys. Fluids. http://arxiv.org/abs/0707.3374 [Preview Abstract] |
Tuesday, November 20, 2007 1:19PM - 1:32PM |
NG.00009: Stability of a two-layer binary fluid system with diffuse interface Alexander Nepomnyashchy, Oxana Frolovskaya, Alex Oron, Alexander Golovin The phase separation of a binary fluid can lead to creation of two horizontal fluid layers with different concentrations resting on a solid substrate and divided by a diffuse interface. In the framework of the Cahn-Hilliard equation, it is shown analytically and numerically that such a layered system is subject to a transverse instability that generates a slowly coarsening multidomain structure. The influence of gravity, solutocapillary effect at the free boundary and Korteweg stresses inside the diffuse interface on the stability is studied using the coupled system of the hydrodynamic equations and the nonlinear equation for the concentration (H-model). Parameter regions of long-wave instabilities are found. [Preview Abstract] |
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