Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session AG: Drops I |
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Chair: Osman Basaran, Purdue University Room: 101A |
Sunday, November 23, 2008 8:00AM - 8:13AM |
AG.00001: A Mesh-Dependent Model For Applying Dynamic Contact Angles To VOF Simulations St\'{e}phane Zaleski, Shahriar Afkhami, Markus Bussmann Typical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this study presents examples of that variation, when applying both no-slip and Navier-slip boundary conditions. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. This scaling relationship is then used as a means to evaluate the contact angle boundary condition as a function of the apparent contact angle, $\theta_{app}$, the capillary number, $\mathbf{Ca}$, and the mesh size, that yields mesh-independent solutions of dynamic contact line phenomena. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers. [Preview Abstract] |
Sunday, November 23, 2008 8:13AM - 8:26AM |
AG.00002: VOF-Based Height Function Method for 3D Calculation of Contact Line Phenomena Shahriar Afkhami A rigorous methodology is presented for applying a contact angle as a contact line boundary condition within a 3D VOF-based flow algorithm. Based on the recently-developed height function methodology, an approach for modeling contact lines is presented that yields accurate interface normals and curvatures from volume fractions and allows the rigorous representation of surface tension forces at contact lines, values that converge with spatial refinement. Although VOF methods have been used before to model phenomena that includes contact lines, the implementation details have rarely been presented. Here a detailed implementation is presented, that includes algorithms for identifying so-called ``contact line'' and ``adjacent'' cells, as well as for calculating normals and curvatures in these cells. The efficacy of this approach is demonstrated via examples of both static and dynamic contact line phenomena. The model is shown to accurately predict steady state configurations defined by the imposed contact angles, from initial conditions far from equilibrium. [Preview Abstract] |
Sunday, November 23, 2008 8:26AM - 8:39AM |
AG.00003: The crown splash Robert Deegan, Philippe Brunet, Jens Eggers The impact of a drop onto a liquid layer and the subsequent splash has important implications for diverse physical processes such as air-sea gas transfer, cooling, and combustion. In the {\it crown splash} parameter regime, the splash pattern is highly regular. We focus on this case as a model for the mechanism that leads to secondary droplets, and thus explain the drop size distribution resulting from the splash. We show that the mean number of secondary droplets is determined by the most unstable wavelength of the Rayleigh-Plateau instability. Variations from this mean are governed by the width of the spectrum. Our results for the crown splash will provide the basis for understanding more complicated splashes. [Preview Abstract] |
Sunday, November 23, 2008 8:39AM - 8:52AM |
AG.00004: A droplet of spectroscopy Denis Terwagne, Tristan Gilet, Nicolas Vandewalle, St\'ephane Dorbolo Droplet coalescence in a liquid bath can be delayed by oscillating the surface of the bath vertically (frequency from 20 Hz to 400 Hz), the droplet bounces on the interface [1,2]. A low viscous oil droplet is dropped on a high viscous oil bath. We observe that the conditions for bouncing depends on the frequency, more precisely we observe resonance when the eigenfrequency of the droplet is excited. In some conditions, droplet presents a non axi-symmetric mode of deformation. That leads to a rotation of the drop and to a horizontal displacement. \newline [1] Y. Couder, E. Fort, C. H. Cautier and A. Boudaoud, Phys. Rev. Lett. \textbf{94}, 177801 (2005) \newline [2] N. Vandewalle, D. Terwagne, K. Mulleners, T. Gilet and S. Dorbolo, Phys. Fluids \textbf{18}, 091106 (2006) [Preview Abstract] |
Sunday, November 23, 2008 8:52AM - 9:05AM |
AG.00005: Viscous Impact Michelle Driscoll, Cacey Stevens, Sidney Nagel The splashing of both inviscid and viscous drops on smooth, dry surfaces can be completely suppressed by decreasing the pressure of the surrounding gas [1,2,3]. However, at sufficiently high pressure when splashing does occur, the shape and dynamics of the ejected liquid sheets depends strongly on the liquid viscosity. This, as well as the dependence of the threshold pressure on viscosity [2], suggests that the splashing of viscous and inviscid liquids is caused by different mechanisms. When a low-viscosity ($\sim 1$ cst) liquid splashes, a corona is ejected immediately upon impact. In more viscous fluids (10 cst silicone oil), our experiments show that a thin sheet, resembling a flattened version of the corona seen in the inviscid case, emerges out of a much thicker spreading film. However, for these viscous fluids, the ejection of the thin sheet does not occur immediately. As the ambient pressure is lowered, the sheet ejection time is delayed longer and longer after impact until no sheet is ejected at all. [1] L. Xu, W.W. Zhang, S.R. Nagel, Phys. Rev. Lett. 94, 184505 (2005). [2] L. Xu, Phys. Rev. E 75, 056316 (2007). [3] C. Stevens et al., FC.00003 DFD 2007 [Preview Abstract] |
Sunday, November 23, 2008 9:05AM - 9:18AM |
AG.00006: Impulsive water bells Arnaud Antkowiak, Christophe Josserand, St\'ephane Zaleski, Emmanuel Villermaux The impact of a liquid half-sphere located on a falling rigid rod is considered. Following the impact, the drop is strongly deformed into a liquid sheet evolving into the impulsive analogue of Savart's waterbell. We investigate the dynamics of this drop impact model by deriving the initial velocity field within the drop. Interestingly enough, it appears that viscosity plays a major role in the initial development of the liquid film. This behaviour is confirmed by detailed experiments conducted with high-speed video recording and numerical simulations. The subsequent development of the liquid layer, its ejection angle and ultimate formation of the waterbell is considered as well. [Preview Abstract] |
Sunday, November 23, 2008 9:18AM - 9:31AM |
AG.00007: Computational Analysis of Inkjet Drop Impact on Dry Surfaces with Different Wetting Characteristics Taehun Lee, Jeffrey Morris Numerical simulations of micron-scale water drop impact on dry surfaces are carried out over a wide range of impact velocities ($1\leq We\leq 100$, $100\leq Re\leq 1,000$, and $Oh\sim 0.015$) and equilibrium contact angles ($6^{\circ}-107^{\circ}$). A two-distribution function lattice Boltzmann equation (LBE) method is employed, which recovers the advective Cahn-Hilliard and the incompressible Navier-Stokes equations for binary fluids. Minimization of the total free energy subject to the polynomial wall free energy implicitly predicts the contact angle and the density profile at solid surfaces. The evolution of the drop on substrate after initial spreading is most sensitive to the wall free energy. Dimensionless diameter and height of the drop obtained from the simulations are compared with experimental results with reasonable accuracy. In inkjet printing, the maximum spreading ratio is an important parameter for its significant effect on the dot size. For higher contact angle surfaces, the maximum spreading ratio based on the wetted surface area is noticeably smaller than the maximum dimensionless diameter that is experimentally measured. [Preview Abstract] |
Sunday, November 23, 2008 9:31AM - 9:44AM |
AG.00008: The fluid trampoline: droplets bouncing on a soap film John Bush, Tristan Gilet We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that provides excellent agreement with experiment, and allows us to model the film as a nonlinear spring. This approach yields an accurate criterion for the transition between droplet bouncing and crossing on the static film; moreover, it allows us to rationalize the observed constancy of the contact time and scaling for the coefficient of restitution in the bouncing states. On the vibrating film, a variety of bouncing behaviours were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. Quantitative agreement between model and experiment is deduced for simple periodic modes, and qualitative agreement for more complex periodic and chaotic bouncing states. [Preview Abstract] |
Sunday, November 23, 2008 9:44AM - 9:57AM |
AG.00009: Impact of a complex fluid droplet on wettable and non wettable surfaces Daniel Bolleddula, Alberto Aliseda The impact of liquid droplets is a phenomenon prevalent in many natural and industrial processes. Such events include rain drops, fuel injection, and ink-jet printing. To date, research in atomization and droplet impact has been focused on Newtonian fluids. In the coating of pharmaceutical tablets, the coating solutions contain polymers, surfactants, and large concentrations of insoluble solids in suspension which inherently exhibit non-Newtonian behavior. In this work, we will present ongoing droplet impact experiments using complex rheology fluids under a wide range of Weber and Ohnesorge numbers. Both hydrophilic and hydrophobic surfaces are been studied, and the effect of surface roughness has also been considered. We will describe the limits of bouncing, spreading, and splashing for these complex fluids. We will also discuss quantitative information such as spreading rates and contact angle measurements on wettable and non-wettable surfaces obtained from high speed images. [Preview Abstract] |
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