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 NF: Interfacial and Thin Film Instabilities V |
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Chair: Lucien Brush, University of Washington Room: Hilton Chicago Continental C |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NF.00001: The effect of surface properties on film rupture: roughness, slip, and disjoining pressure. Vladimir Ajaev Models of rupture in thin liquid films are usually developed under the assumption that the surface of the solid substrate is flat, chemically homogeneous, and that the no-slip condition is satisfied at the solid-liquid interface. Given that the rupturing film thickness is often in the sub-micron range, non-uniformities in surface properties, e.g. due to roughness or trapped nanoscale bubbles, can have a significant effect on the process. This is also confirmed by experimental data. We identify three independent mechanisms affecting the rupture dynamics: topographic features of the surface, variations in the slip length, and changes in the parameters that define the disjoining pressure. All mechanisms are included in a lubrication-type model which allows us to compute rupture time as a function of surface properties. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NF.00002: Linear and nonlinear analyses of convective instabilities in evaporating liquid layers Pierre Dauby, Mireille Dondlinger, Jonathan Margerit, Pierre Colinet The present work consists in a theoretical study of Rayleigh- B\'{e}nard-Marangoni instabilities in an evaporating horizontal liquid layer which is surmounted by a mixture of its vapour and an inert gas. The fluid and the gas mixture form a 2-layer system but simplified models can be built to analyse the behaviour of the system. In particular, a 1-layer model can be deduced by introducing a generalized Biot number. In the so- called 1.5-layer approximation, the behaviour of the gas is simplified by only keeping the linear equation of vapour diffusion. In the linear study of thermoconvective instabilities, both simplified models are shown to be in good agreement with the complete 2-layer system. For the non linear approach, only the simplified models are considered. A Galerkin– Eckhaus method is used to deduce amplitude equations for the weakly nonlinear analysis of the problem. The stability domains for the rolls, squares and hexagonal patterns emerging above threshold are determined. Both water and ethanol are used as fluids, while the inert gas is assumed to be air. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NF.00003: Enhanced Faraday pattern stability with three-frequency driving Yu Ding, Paul Umbanhowar We report experimental measurements of enhanced stability of 12-fold quasi-patterns and type-I super-lattice patterns with the addition of a third driving frequency. With two-frequency driving in the ratios 4:5 and 6:7, 12-fold quasi-patterns and type-I super-lattice patterns are observed respectively for a range of relative phases and amplitudes. Addition of a third frequency at twice the difference frequency, i.e. 4:5:2 and 6:7:2, shifts the region of pattern stability closer to onset. Our results are in qualitative agreement with a recent theoretical analysis based on three wave resonance. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NF.00004: Flow induced instability of fluid flowing through an elastic crack Shreyas Mandre, Neil Balmforth, Alison Rust Fluid-structure interaction has received a lot of attention from engineers and scientists alike due to its practical significance. In this talk, we will present analysis of a specific example of such an interaction; that of flow through a narrow crack in an elastic material. This study was motivated by its potential application to a kind of seismic signal recorded by geologists called volcanic tremor. This tremor is believed to be caused by magma or magmatic fluids flowing through narrow channels in rocks. In the analysis the elastic material is assumed to be very stiff so that the mathematical model can be thought of as a perturbation of having a rigid wall. However, rather than looking at how the fluid modes are perturbed in the presence of a stiff wall, we concentrated on how the flow modifies the elastic oscillations of the surrounding medium. Towards the end we will discuss the results and their geological relevence. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NF.00005: Electrohydrodynamic Instability of the Interface between Two Fluids in Channel Flow Ozgur Ozen, Nadine Aubry, Peter Petropoulos, Demetrius Papageorgiou The stability of two-fluid flow in a channel is of importance in the design of microfluidic systems. Due to the low Reynolds numbers, it is relatively difficult to attain mixing in micro-channels. Recent studies using miscible fluids have shown that applying electric fields enhances mixing over a short distance in short times. However, in a large class of applications, the fluids in contact are not miscible, and the interfacial tension stabilizes the interface, an effect absent in the physics of miscible fluids. We have carried out the linear stability analysis of the two-fluid flow in a channel subject to an electric field normal to the interface between the fluids using the Chebyshev Spectral tau method. Moreover, we have derived a coupled system of evolution equations for the interface position and the charge density at the interface. We will present the numerical results of the long wave analysis and discuss the effect of different physical parameters on the electrohydrodynamic instability of the interface. A comparison between the theoretical results and experiments will be given. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NF.00006: A Nonlinear Study of Electric Field Induced Pattern Formation in Thin Liquid Films Emily Tian Modern lithographic technologies rely on creating patterns in thin films. Among the methods of achieving particular morphologies is the application of electric fields. In this talk, the morphology of the interface of a thin liquid film confined between two electrodes separated by an air gap is investigated by means of a weakly nonlinear stability analysis. In the long-wavelength limit, an interface evolution equation is derived which incorporates the effects of electrical stress and surface tension. The thickness ratio of the air gap to the liquid crucially determines pattern formation, which here consists of liquid columns and holes. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NF.00007: Shock Solutions for Particle-Laden Thin Films Benjamin Cook, Andrea Bertozzi This is an analysis of the lubrication equations derived by Zhou, Dupuy, Bertozzi, and Hosoi (PRL 2005) for a thin film containg sedimenting particles. The equations take the form of a pair of conservation laws regularized by a fourth-order nonlinear surface tension term. Guided by the experimental observation of a thick, particle-rich ridge near the contact line, we seek a solution to the Riemann problem consisting of two shocks. For some left (upstream) and right (precursor) states we find such a solution, and when it exists it agrees excellently with numerical solutions of the PDE system. However due to bifurcations in the Hugoniot locus a shock solution sometimes does not exist, and there appears to be no Riemann solution in this case. Numerical solutions using a diffusive scheme suggest the solution may involve a singular shock in which fluid and sediment accumulate at the contact line. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NF.00008: Morphology of a Solidifying Thin Film Michael Beerman, Lucien Brush A pair of coupled non-linear partial differential equations is derived using lubrication theory, governing the morphology of a pure, thin, liquid film, bounded by its solid phase and passive gas phase. Both the no-slip solid-liquid (SL) and the free liquid-gas (LG) interfaces are deformable. In the isothermal case with a rigid SL interface, this system reduces to that studied by Williams and Davis (1982). Linear analysis of a uniform film reveals stationary and oscillatory instabilities which depend on capillary, latent heat, van der Waals, Marangoni, heat transfer and volume change effects. Numerical solutions of the fully non-linear system provide film evolution and rupture times. It is found that for a variety of linearly unstable initial conditions, as the film thins and nears rupture, the SL interface retreats by melting away from the tip region of the encroaching LG interface. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NF.00009: Sharp Interface Numerical Simulations of Interactions of Growing Dendrites with Solid Particles Yi Yang, J.W. Garvin, H.S. Udaykumar Dendrite-particle interaction is important to processes such as metal-matrix composites (MMCs) manufacturing. Numerical simulation of particle-dendrite interaction is carried out using a sharp interface level-set based numerical method which affords easy interface tracking. A local mesh refinement technique is also developed to further facilitate the close observation of the evolving dendrite before and after contact with the particle. The simulation of the interaction between a particle and a dendrite grown from pure material shows that for a particle to melt thermal conductivity ratio $\lambda =\frac{k_p }{k_l }<1$ (typical for MMCs), the dendrite does not approach the particle close enough to activate particle pushing. Instead, the dendrite chooses to go around the particle and eventually the particle is engulfed by sidebranches. Thus the entrapment mode is the likely outcome. The simulation of interaction of a particle with a dendrite grown from a binary alloy is also carried out. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NF.00010: The Static Stability of Supported Capillary Pipes at Zero Bond Number Jorge A. Bernate, David B. Thiessen, Philip L. Marston At low Bond numbers it is possible to have long liquid columns whose free surface is stabilized by a solid support structure. The supports considered in this work are a single wire helix and a polygonal array of parallel wires. These supported capillary structures are here referred to as supported capillary pipes (SCPs). The static stability at zero Bond number is determined from the equilibrium branch structure following Lowry and Steen [Proc. R. Soc. London Ser. A {\bf 449}, 411 (1995)] and compared with experimental measurements obtained in a Plateau Tank. Stability envelopes for different wire radii and contact angles will be presented, and different factors leading to instability will be discussed. A steady capillary-driven flow with large free surface area can be established that could have applications to two-phase fluid contacting. The maximum stable steady-state flow rate that can be achieved is dictated by the stable range of Laplace pressures the interface can sustain. [Supported by NASA] [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NF.00011: Grain--boundary grooving driven by surface melting Robert Style, Grae Worster At temperatures close to the bulk freezing point, many materials form surface melted films when exposed to air or vapour. Flow in these films provides a mechanism for mass transport driven by temperature and curvature effects. Lubrication theory is used to provide a system of equations modelling this flow and an explicit transport coefficient $B$ is derived for flow in a surface melted film. The transport coefficient is found to depend on temperature and diverges as the bulk melting temperature is approached. The equations are applied to the case of a grain--boundary groove, and it is shown that Mullins's classical equation describing grooving driven by gradients in surface curvature is produced asymptotically. It is found that the contact angle at the groove root is modified over a thin boundary layer by a factor depending on the ratio of surface tensions. [Preview Abstract] |
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