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 BQ: Instability: Interfacial and Thin-Film II |
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Chair: Satish Kumar, University of Minnesota Room: 200E |
Sunday, November 22, 2009 10:30AM - 10:43AM |
BQ.00001: Suppressing van der Waals rupture of thin films by imposed shear flow Michael Davis, Stephen Davis It is known that thin viscous films subject to attractive van der Waals forces will rupture in finite time due to a long-wave instability. We have studied the effects of applying a shear stress to the free surface of a film on a substrate, and found that it stabilizes perturbations in the direction of shear flow, thereby retarding rupture, or even suppressing rupture entirely for shear stress above a critical value. Perturbations orthogonal to the shear flow are not stabilized, and therefore a unidirectional shear will not prevent rupture in a three- dimensional viscous film. However, it may be possible to stabilize the film in all directions through the application of a rotating shear stress. [Preview Abstract] |
Sunday, November 22, 2009 10:43AM - 10:56AM |
BQ.00002: ABSTRACT WITHDRAWN |
Sunday, November 22, 2009 10:56AM - 11:09AM |
BQ.00003: Shear-induced suppression of rupture in two-layer thin liquid films Sreeram K. Kalpathy, Lorraine F. Francis, Satish Kumar The effect of shear on the rupture of two stratified thin liquid films confined between parallel plates and subject to van der Waals forces is examined in this work. Lubrication theory is applied to derive a one-dimensional nonlinear evolution equation for the height of the liquid-liquid interface. Linear stability analysis reveals that the real part of the growth rate and the wavelength of the fastest growing interfacial disturbance are unaffected by shear. However, the growth rate has an imaginary part which is non-zero in the presence of shear, indicating the existence of traveling waves. Nonlinear simulations of the interface behavior on homogeneous surfaces show that shear delays interfacial rupture, and suppression of rupture occurs beyond a critical shear rate. Propagation of traveling waves along the interface, and subsequent weakening of van-der-Waals-driven dewetting, is found to be the cause of the rupture delay. Analysis of flow on chemically heterogeneous surfaces also suggests a delay in interfacial rupture in the presence of shear. The problem studied here can serve as an idealized model for the lithographic printing process, and the results suggest that in the regime of shear rates relevant to printing, mechanisms of emulsification of one liquid into the other can be understood without incorporating shear. However, shear could be relevant in other physical systems such as microfluidic flows. [Preview Abstract] |
Sunday, November 22, 2009 11:09AM - 11:22AM |
BQ.00004: Spontaneous rupture of thinning liquid films with Plateau borders Anthony Anderson, Lucien Brush, Stephen Davis Spontaneous film rupture from van der Waals instability is investigated in 2D. A thin liquid film between adjacent bubbles in a foam has finite length, curved boundaries (Plateau borders), and a drainage flow from capillary suction that causes thinning. A full linear stability analysis of this thinning film shows that rupture occurs once the film has thinned to \emph{tens} of nanometers. Whereas, in an unbounded, quiescent, flat free film, rupture occurs when the thickness is \emph{hundreds} of nanometers. Finite length, Plateau borders and flow are all found to contribute to the stabilization. The drainage flow leads to several distinct qualitative features as well. In particular, unstable disturbances are advected by the flow to the edges of the thin film. As a result, the edges of the film close to the Plateau borders are more susceptible to rupture that the center of the film. [Preview Abstract] |
Sunday, November 22, 2009 11:22AM - 11:35AM |
BQ.00005: Plateau border adjustment in non-equilibrium foams Michael Gratton, Stephen H. Davis For foams without surfactants, changes occur in the Plateau border regions at the corner of nearly-polygonal bubbles three orders of magnitude faster than the thinning of lamellas. We describe the relaxation of an asymmetric Plateau border to symmetry in a two dimensional foam and compare the results to the Stoker-Hosoi hyperbolic coordinate theory for arid foams. These results are used to write a lumped-element model to describe the moderate timescale evolution of a foam, away from the time of lamella rupture, but slower than the timescale of local Plateau border adjustment. [Preview Abstract] |
Sunday, November 22, 2009 11:35AM - 11:48AM |
BQ.00006: Dynamics of thin annular films with electrokinetic effects Devin Conroy, Richard Craster, Demetrios Papageorgiou, Omar Matar The evolution of an electrolyte in a uniform cylindrical tube in the presence of an applied electric field is investigated. A thread of a perfectly conducting fluid occupies the core of the tube. We derive an evolution equation for the interfacial position in the limit where the annular film is thin. This equation accounts for electrostatic and electrokinetic effects, and is characterised by an electric capillary number, a dimensionless Debye length and a ratio of interface to wall electrostatic potentials. We explore the effect of electrokinetics on the interfacial dynamics using a linear stability analysis and transient numerical simulations. The electrokinetics are shown to either stabilise or destabilise the film and, in the former case, causes the film to rupture in finite time. In this case, the time to touch down scales as time to the one-third and the final film shape undergoes either a ring or line-like rupture. [Preview Abstract] |
Sunday, November 22, 2009 11:48AM - 12:01PM |
BQ.00007: Deformation of fluid free surfaces driven by high frequency vibration Ming Tan, James Friend, Omar Matar, Leslie Yeo Formation of surface waves on a free surface of a thin fluid layer driven by high frequency (f $\approx$ 20 MHz) surface acoustic waves (SAWs) is investigated, both numerically and experimentally. The SAWs are transmitted along a surface of a piezoelectric substrate vibrating at nanometer displacement amplitudes $\xi$. Through a perturbation expansion, the governing equations of fluid motion are decomposed into those describing a first-order acoustic field and second-order acoustic streaming. Numerical solution of these equations and use of Fourier transforms allow the fundamental and harmonic frequencies of the surface deformation to be identified. For low excitation amplitudes ($\xi$ $\sim$ 1 nm), the frequency of the perturbed free surface is approximately equal to the SAW excitation frequency. However, as the amplitude increases ($\xi$ $>$ 1 nm), the dominant resonant frequency of the fluid free surface shifts to the low frequency range (f $\sim$ 1 MHz), suggesting that, in this regime, the free surface deformation is controlled by acoustic streaming. The numerical results for $\xi$ $\sim$ 1 nm qualitatively agree with experimental laser Doppler Vibrometry measurements. [Preview Abstract] |
Sunday, November 22, 2009 12:01PM - 12:14PM |
BQ.00008: Instability of Viscoelastic Thin Films, and Applications Scott Norris, Michael Aziz, Michael Brenner An ion beam bombarding a solid surface has been long been known to produce an instability leading to a modulated surface (with ripples or dots); though the basic mechanisms for this instability remain under considerable debate. During our investigation of this problem, we have been led to a basic problem in thin film fluid mechanics: the instability of a viscoelastic thin film that is under compressive stress. This applies to the ion bombarded problem because there is evidence that the ion beam fluidizes a thin viscoelastic layer, and that this layer is then stressed by the ion beam. By varying the ratio of the shear modulus to the viscosity, we analyze this problem and connect the known limits of a stressed elastic solid film or a surface-tension driven lubrication flow. In particular, we identify the presence or absence of a surface instability as a function of these two parameters. We discuss the application of this model to the surface layer of an ion-sputtered target; and also discuss its potential application to the wrinkling instability of a growing biofilm attached to a substrate. [Preview Abstract] |
Sunday, November 22, 2009 12:14PM - 12:27PM |
BQ.00009: Electrohydrodynamic instabilities in thin bilayer liquid films Scott Roberts, Satish Kumar When DC or AC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. We examine how the presence of a second liquid interface influences pillar dynamics and morphologies. For perfect dielectric films, linear stability analysis of a lubrication-approximation-based model shows that the root mean square voltage governs the pillar behavior. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and reveals that the accumulation of free charge at each interface depends on the conductivities in the adjoining phases and that high frequencies of the AC electric field may be used to control this accumulation at each interface independently. Nonlinear 1-D and 2-D simulations confirm the results of the linear stability analysis and reveal the final pillar morphology. The results presented here may of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics. [Preview Abstract] |
Sunday, November 22, 2009 12:27PM - 12:40PM |
BQ.00010: Wetting dynamics of thin liquid films and drops under Marangoni and centrifugal forces Shomeek Mukhopadhyay, Robert Behringer We present results from ongoing experimental studies on thin liquid drops and thin-films under the combined action of centrifugal forces due to rotation and radial Marangoni forces by using a temperature gradient. For thick rotating film in the absence of a temperature gradient, when an initially thick layer of fluid is spun to angular velocities where the classical Newtonian solution is negative, the fluid never dewets for the case of a completely wetting fluid, but leaves a microscopic uniform wet layer in the center. Similar experiments with a radially inward temperature gradient reveal the evolution of a radial height profile given by h(r) = A(t)r $\alpha$, where A(t) decays logarithmically with time, and $\alpha$ = 0.8. In the case where there is no rotation, small centrally placed drops show novel retraction behavior under a sufficiently strong temperature gradient. This work includes collaboration with Lou Kondic (NJIT), Nebojsa Murisic (UCLA) and Rich Mclaughlin (UNC-Chapel Hill). [Preview Abstract] |
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