Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session AF: Interfacial and Thin Film Instabilities I |
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Chair: Satish Kumar, University of Minnesota Room: Hilton Chicago Continental C |
Sunday, November 20, 2005 8:00AM - 8:13AM |
AF.00001: Fingering phenomena at high surfactant concentrations Omar K. Matar, Richard Craster, Barry Edmonstone The spreading of a soluble surfactant droplet on a pre-existing thin liquid layer is considered at concentrations beyond the critical micelle concentration (CMC). Lubrication theory is used to derive a coupled system of four two-dimensional nonlinear evolution equations for the film thickness, monomer interface and bulk concentrations and micellar concentration. These equations are closed by a nonlinear surfactant equation of state. Our numerical results for the base state indicate that increasing the mass of surfactant deposited leads to the development of a protuberance that appears at the edge of the drop. For a sufficiently large mass, this feature separates from the drop to form a distinct secondary front that lies behind a leading front, which usually accompanies the spreading process. The results of our transient growth analysis and transient numerical simulations indicate that these features are vulnerable to transverse perturbations leading to the formation of fingers. The results obtained in the present work appear to capture phenomena recently observed experimentally. [Preview Abstract] |
Sunday, November 20, 2005 8:13AM - 8:26AM |
AF.00002: Singular shapes of sliding drops: How to avoid wetting Jacco Snoeijer, Emmanuelle Rio, Nolwenn LeGrand, Laurent Limat A droplet flowing down a window displays fascinating behaviors, involving bifurcations between singular shapes, drop emission and coalescence, which have only recently been characterized experimentally. In this talk we show how these singular shapes emerge in order to avoid a `forced' wetting transition: it is the only way for capillary forces to overcome the increasing viscous forces. We analyze the three-dimensional flow in the vicinity of the `corner' at the rear of the drop, by exploring similarity solutions of the lubrication equations. These predict a self-similar structure of the velocity field that does not depend on the distance to the corner tip, a property that has been verified by Particle Image Velocimetry. We also describe the small-scale regularization of the corner singularity, and a detailed comparison to experiments provides tentative new information on the physics near the contact line. [Preview Abstract] |
Sunday, November 20, 2005 8:26AM - 8:39AM |
AF.00003: Forced dewetting on porous media Olivier Devauchelle, Christophe Josserand, Stephane Zaleski We study the dewetting of a porous plate withdrawn from a bath of fluid. The microscopic contact angle is fixed to zero and the flow is assumed to be parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in the phase space by means of numerical integration. We show the existence of a critical value of the capillary number $\eta U / \gamma$, above which no stationary contact line can exist. An analytical model, based on asymptotic matching is developped, that reproduces the dependance of the critical capillary number on the angle of the plate with respect to the horizontal for large control parameters ($3/2$ power law). Comparison with recent experiments on granular beds are discussed. [Preview Abstract] |
Sunday, November 20, 2005 8:39AM - 8:52AM |
AF.00004: Marangoni Driven thin film flow in the presence of non-uniform precursors Anand Jayaraman, Shomeek Mukhopadhyay, Tom Witelski , Robert Behringer It is well known that a moving contact line on a dry surface is incompatible with the no slip boundary condition and we need a thin precursor layer to relieve the stress singularity . The presence of a precursor layer has been verified in some of the recent experiments and in this study we look at the effect of a thin film driven by Marangoni forces when the precursor layer is varied transverse to the flow direction. We deposit a step like precursor layer and follow the film dynamics interferometrically. Numerical results and analytic arguments are presented which show the evolution of a characteristic dip like structure and the fact that the asymptotic thickness is independent of the far field precursor layer. The velocity is strongly effected by the structured precursor layer. This work was supported by NSF Career Grant 0239125. [Preview Abstract] |
Sunday, November 20, 2005 8:52AM - 9:05AM |
AF.00005: Time evolution of transients in a thin liquid film Jennifer Rieser, Roman Grigoriev, Michael Schatz We present experimental and theoretical results on transient behavior in the driven spreading of a thin liquid film on a solid substrate. Both gravitationally-driven and surface-tension- driven films are considered. Perturbations with well-defined spatial and temporal characteristics are applied via distributed optical heating of the film prior to instability onset; the corresponding perturbation-induced variations in film thickness are characterized by interferometry and fluorescence imaging. The subsequent evolution of rivulets arising from contact line instability is measured using image time series. Comparison of the initial disturbance to the final disturbance enables quantitative measurement of transient amplification rates; these rates are compared to the predictions of generalized stability theory that accounts both for the initial conditions of the experiments (i.e., the specific structure of the imposed perturbations) and for the non-normal character of the linear operator that governs the evolution of small disturbances. [Preview Abstract] |
Sunday, November 20, 2005 9:05AM - 9:18AM |
AF.00006: Liquid Film Dynamics in the Presence of Surface Heterogeneity Yongli Zhao, Jeffrey Marshall A study is reported of the instability and growth of fingers on liquid films driven over heterogeneous surfaces. Computations are performed using a variation of the precursor-film model, in which a disjoining pressure term controls variation in static contact angle associated with surface heterogeneity. The formulation yields results approaching predictions of the Tanner-Hoffman-Voinov dynamic contact angle formula for sufficiently small values of the precursor film thickness. A modification of the disjoining pressure coefficient is introduced which yields correct variation of dynamic contact angle for finite values of the precursor film thickness. The film fingering instability is examined both for cases with random variation in static contact angle and for cases with ordered strips of different static contact angle. For the cases with random static contact angle variation, the surface heterogeneity is characterized by the correlation length and variance of the static contact angle variation from its mean value. Several different types of nonlinear phenomena, including subcritical instability and lock-on, are observed for the case with streamwise strips of varying contact angle. [Preview Abstract] |
Sunday, November 20, 2005 9:18AM - 9:31AM |
AF.00007: Competitive Displacement of Thin Liquid Films on Chemically Patterned Substrates Richard D. Lenz, Satish Kumar The displacement of one liquid film by another on a chemically patterned substrate is a process potentially important to lithographic printing and microfluidic flows. In order to gain a fundamental understanding of the film rupture associated with this process, the lubrication approximation is applied to obtain a one-dimensional nonlinear evolution equation for the position of the liquid-liquid interface. Chemical patterning of the substrate is incorporated through the use of a spatially varying van der Waals potential. Both linear stability analysis and numerical simulations are performed to study the behavior of the evolution equation over a wide range of parameters. When one liquid film rests on a substrate containing a chemical pattern that it does not preferentially wet, an overlying liquid film which does wet that pattern can displace the film adjacent to the substrate and cause it to rupture. The location and speed of the rupture are found to depend on a competition between the width of the chemical pattern and the wavelength of the most dangerous mode associated with a chemically homogeneous substrate. The results also show that rupture can occur in multiple places almost simultaneously, which suggests a possible mechanism for emulsification of one of the liquids into the other. [Preview Abstract] |
Sunday, November 20, 2005 9:31AM - 9:44AM |
AF.00008: Flow and Stability of Evaporating Rivulets on Surfaces with Topography Tatiana Gambaryan-Roisman, Peter Stephan Surfaces with topography promote rivulet flow patterns, which are characterized by a high cumulative length of contact lines. This property is very advantageous for evaporators and cooling devices, since the local evaporation rate in the vicinity of contact lines (micro region evaporation) is extremely high. The liquid flow in rivulets is subject to different kinds of instabilities, including the kinematic instability and the capillary instability. The instabilities may lead to the development of wavy flow patterns and to film rupture. The effect of the micro region evaporation on the rivulet stability has never been investigated. We develop a model describing the hydrodynamics and heat and mass transfer in flowing rivulets on surfaces with topography under the action of gravity, surface tension, thermocapillarity and the phase change. The contact line behaviour is modelled using the disjoining potential. The perfectly wetting case is described using the usual $h^{-3}$ potential. The partially wetting case is modelled using the integrated Lennard-Jones potential. The developed model is used for investigating the effects of the surface topography, gravity, thermocapillarity and the micro region evaporation on the rivulet stability. [Preview Abstract] |
Sunday, November 20, 2005 9:44AM - 9:57AM |
AF.00009: Meandering instability of a rivulet on a partially wetting incline Adrian Daerr, Nolwenn Le Grand-Piteira, Laurent Limat A rivulet will not generally follow a straight path when flowing down an inclined plane. Depending on the control parameters (flowrate and inclination angle), as well as the liquid and substrate type, the straight path is unstable and after some transient dynamics the rivulet settles on a stationary sinuous path. Although this path is not perfectly reproduced in successive runs, the amplitude, wavelength and the curvature of the bends have characteristic mean values. It appears that the stationary pattern results from an equilibrium between inertial forces and hysteretic wetting effects (pinning of the contact line on the substrate). As opposed to that, we find that the instability of the straight path results from a competition between inertial forces and surface tension. We will present our experimental result and simple models for the dependencies of amplitude, wavelength and curvature on the control parameters. [Preview Abstract] |
Sunday, November 20, 2005 9:57AM - 10:10AM |
AF.00010: Dewetting of Thin Polymer Films: The Role of Nonlinear Friction Thomas Vilmin, Elie Rapha\"{e}l The study of the dewetting of very thin polymer films has recently revealed many unexpected features (\textit{e.g.} unusual rim morphologies and front velocities) which have been the focus of several theoretical models. Surprisingly, the most striking feature of all, that is a decrease of the rim width with time, have not yet been explained. In the present letter, we show how the combined effects of a non-linear friction between the film and the substrate, and the presence of residual stresses within the film, result in the presence of a maximum in the time evolution of the rim width. In addition, we show how the introduction of a non-linear friction can also simply explain the rapid decrease of the dewetting velocity with time observed experimentally. [Preview Abstract] |
Sunday, November 20, 2005 10:10AM - 10:23AM |
AF.00011: Viscoelastic Effect on the Spinodal Dewetting of a Thin Liquid Film Lin Wu We theoretically study the interfacial instability that leads to the spinodal dewetting of an initially flat and static viscoelastic film on a nonwetting surface via a linear analysis. The previously ignored non-Newtonian flow effect of the liquid film is modeled by the Jeffreys constitutive equation. The driving force for the spinodal dewetting is the conjoining pressure induced by the long range intermolecular force. Surface tension provides a stabilizing mechanism by resisting the deformation of the interface. The system is unconditionally unstable subject to disturbances with a wavelength larger than a critical value. The elasticity of the polymer is found to further destabilize the system. For polymer melt with a negligible solvent retardation effect, a resonant phenomenon appears as a result of the interaction between the two destabilizing mechanisms (the conjoining pressure and the polymer elasticity) when the Deborah number is above a critical value. The resonance introduces two most unstable wave numbers, at which the growth rate of the disturbance is unbounded. The two most unstable wave numbers bifurcate at a minimum Deborah number, below which no resonance is observed. [Preview Abstract] |
Sunday, November 20, 2005 10:23AM - 10:36AM |
AF.00012: Fingering instability of Bingham fluids Shilpa Ghadge, Neil Balmforth, Tim Myers Contact line instabilities have been extensively studied and many useful results obtained for industrial applications. Our research in this area is to explore these instabilities for non-Newtonian fluids which has wide scope in geological, biological as well as industrial areas. In this talk, we will present an analysis of fingering instability near a contact line of the thin sheet of fluid flowing down on a moderately inclined plane. This instability has been well studied for Newtonian fluids. We explore the effect of a yield strength of the fluid on this instability. We have conveniently assumed the presence of the precussor film of small thickness ahead of the fluid film to avoid some mathematical singularities. Using a lubrication-type approximation, we perform a linear stability analysis of a straight contact line. We will show comparison with some experimental results using suspensions of kaolin in silicone oil as a yield strength fluid. [Preview Abstract] |
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