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 AL: Free Surface Flows I |
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Chair: Wendy Zhang, University of Chicago Room: Hilton Chicago Astoria |
Sunday, November 20, 2005 8:00AM - 8:13AM |
AL.00001: Thin-film flow on a stationary or uniformly rotating cylinder subject to a prescribed uniform surface shear stress Stephen Wilson, Brian Duffy, Gavin Black We investigate thin-film flow on a stationary or uniformly rotating horizontal circular cylinder subject to a prescribed uniform shear stress at the free surface of the film. For a stationary cylinder we show that the ``full-film'' solution always has forwards flow, but that both the ``curtain'' and ``shock'' solutions always have a region of recirculating flow. For the full-film and shock solutions we calculate the maximum supportable mass. We also show how gravity effects can smooth the shock in the leading-order shock solution for rimming flow but not for coating flow, whereas surface-tension effects can do so in both situations. For a uniformly rotating cylinder there are two different full-film solutions, namely a ``Moffatt mode'' and a ``shear mode'', the latter of which is possible only for sufficiently strong shear in the opposite direction to the rotation of the cylinder. We show that the Moffatt mode always has forwards flow throughout the film, but that the shear mode always has a region of recirculating flow. In addition, we calculate the maximum and minimum supportable masses for both modes. [Preview Abstract] |
Sunday, November 20, 2005 8:13AM - 8:26AM |
AL.00002: Capillary Driven Flows along Rounded Interior Corners Yongkang Chen, Mark Weislogel, Cory Nardin The problem of capillary flow along interior corners that are rounded is re-visited analytically in this work. By careful selection of geometric length scales and with the introduction of a corner roundedness parameter $\lambda$, the Navier-Stokes equation is reduced to a convenient $\sim$O(1) form for both analytic and numeric solutions for all values of corner half-angle $\alpha$ and $\lambda$ for perfectly wetting fluids. Local and global scaling analysis of the problem captures much of the intricate geometric dependence of the viscous resistance, significantly reduces the reliance on numerical data compared to several previous solution methods, and leads to an intricate second order nonlinear evolution equation for the free surface. In general, three asymptotic flow regimes may be clearly identified: the `sharp corner' regime, the narrow `rectangular section' regime, and the `thin film' regime. Flows may be observed to transition between regimes, or may exist essentially in a single regime depending on the system. Perhaps surprisingly, for the case of imbibition in tubes or pores with rounded interior corners, similarity solutions are possible and are obtained numerically for all conditions with analytic solutions obtained under the constraints of the three regimes. [Preview Abstract] |
Sunday, November 20, 2005 8:26AM - 8:39AM |
AL.00003: Splitting a Jet Srinivas Paruchuri, David Berdy, Henry Chong, David Weitz, Michael Brenner Splitting a fluid jet using surface stresses is explored using thermal gradients and electrical stresses. Feasibility estimates are calculated for both methods and a splitting criteria for the minimum stress is developed. We explore the electrical case in greater detail. A one dimensional model is constructed and studied numerically. We show that splitting is set by a balance of in plane inertia and the applied shear stress. Using this balance an estimate for the time to splitting is calculated. Finally we discuss experimental attempts to observe jet splitting using electric fields. [Preview Abstract] |
Sunday, November 20, 2005 8:39AM - 8:52AM |
AL.00004: Electrohydrodynamic free-surface motions: (I) Dielectric breakdown and (II) Onset of menisci Alexandre Persat, Thomas Ward, Howard Stone We report experiments on electrically driven transient motions of (poorly conducting) dielectric liquids in a cylindrical configuration. A wire in contact with the liquid bath is raised to a potential $\phi_0$ with an outer grounded ring electrode. The liquid rises along the wire to establish a new equilibrium shape that is substantial higher than that provided by surface tension. Above a critical field an instability sets in: the fluid convects and the interface shape and motion are time dependent. We provide evidence that the instability is due to dielectric breakdown and the associated fluid motion then comes from electrical stresses due to free charge density. A model of the time-dependent electrical response is given and is in qualitative agreement with the experiments. In addition, for low fields we study the transient evolution of the interface as wetting occurs. We find distinct dynamical responses that depend on an electrical Reynolds number and provide physical arguments to explain the different power laws (height versus time) measured for low and high viscosity liquids. [Preview Abstract] |
Sunday, November 20, 2005 8:52AM - 9:05AM |
AL.00005: Jet Formation in a Tube Devaraj van der Meer, Erik de Jong, Jean-Baptiste Choimet, Raymond Bergmann, Detlef Lohse A vertical cylinder is partially immersed in a water-filled container and pressurized to lower the fluid level inside the tube. A sudden release of the pressure in the tube creates a singularity on top of the rising free surface: At the very beginning of the process a jet emerges at the center of the surface, the strength of which strongly depends on the initial shape of the meniscus. Here we study the jet formation process. The time-evolution of the complex shape of the free surface and the flow around the cylinder are analyzed using high-speed imaging, velocimetry and numerical simulations. [Preview Abstract] |
Sunday, November 20, 2005 9:05AM - 9:18AM |
AL.00006: Hole Dynamics in Polymer Langmuir Films J. Adin Mann, Jr., James Alexander, Andrew Bernoff, Lu Zou, Elizabeth Mann We develop a model for the closing of a gaseous hole in a liquid domain within a two-dimensional fluid layer, a Langmuir film, coupled to a fluid bulk substrate. This model is compared to experiments that follow hole dynamics in a polymer Langmuir film. Closure of such a hole in a fluid layer is driven by the difference in spreading pressure within the hole and far outside it, and by the line tension. The observed rate of hole closing is close to that predicted by our model and the line tension measured by other means, assuming that the spreading pressure in the surface-gas phase is negligible. This result both supports the model and suggests an independent means of determining the line tension. Unlike most previous hydrodynamics models of Langmuir films, the closing of a hole necessarily invloves vertical motion of the underlying incompressible fluid: that fluid is dragged along with the liquid monolayer towards the center of the hole, and must plunge away from the surface. An explicit expression is found for this vertical fluid flow in the bulk substrate. [Preview Abstract] |
Sunday, November 20, 2005 9:18AM - 9:31AM |
AL.00007: Transition of Thermocapillary Flow in Low Prandtl Number Liquid Bridge Hiroei Sasaki, Satoshi Matsumoto, Takashi Mashiko, Hiroaki Ohira, Erika Yoda, Nobuyuki Imaishi, Shinichi Yoda An experimental study of thermocapillary convection in the half-zone liquid bridge of low Prandtl number fluid was performed to observe the transition behavior from steady to oscillatory flows. In thermocapillary convection, one of the still open problems is the observation of onset of oscillatory flow in low Prandtl number fluids. Numerical simulations predicted that there would be two transition points which were a first and second critical Marangoni number (\textit{Ma}$_{c1}$ and \textit{Ma}$_{c2})$. However, an experimental verification has not been performed previously because of its difficulties. A molten tin was used as test fluid and a liquid bridge configuration was employed. The temperature distribution at the interface between the liquid bridge and the cold disk was measured by using several fine thermocouples. It could be experimentally detected that the axisymmetric steady flow changes to three-dimensional steady one with increasing the temperature difference. At higher temperature difference, onset of oscillatory flow was also observed. Experimental results concerning the critical Marangoni numbers agreed very well with numerical simulation. [Preview Abstract] |
Sunday, November 20, 2005 9:31AM - 9:44AM |
AL.00008: Axi-symmetric Marangoni flows in shear-thinning liquids -- jets and inner-linings Vineet Dravid, Zhengjun Xue, Carlos Corvalan, Paul Sojka This study's objective was to develop analytical models and computational tools for describing, analyzing, and predicting the nonlinear Rayleigh instability of generalized-Newtonian fluids with insoluble surfactant. An Arbitrary Eulerian-Lagrangian finite element method was used to solve the fully two-dimensional equations governing free surface flow and surfactant convective and diffusive transport. Results to be presented here extend our previous research showing that shear-thinning effects facilitate the formation of two-dimensional Marangoni flows that can locally reverse the capillary-induced flow in liquid jets to include the effect of surfactant diffusivity and show the effect of shear-thinning on the nonlinear stability of the inner lining of a capillary. This study's conclusions indicate that two-dimensional Marangoni flows in generalized Newtonian (Carreau) liquids are more complex than previously predicted and depend on chemical and physical properties that can be modulated to ultimately improve flows of industrial and biological significance. [Preview Abstract] |
Sunday, November 20, 2005 9:44AM - 9:57AM |
AL.00009: Sharp Interface Treatment for Free Surface Flows in an Unstructured Level Set Finite Element Framework Haegyun Lee, Ching-Long Lin, Larry Weber A numerical method that couples the incompressible Navier-Stokes equations with the sharp-interface level set method on an unstructured mesh is presented for study of free surface flows. The method is based on the previously developed diffuse-interface model of Lin et al. (Int. J. Numer. Meth. Fluids, 2005). The model employs characteristic finite element method together with the fractional four-step algorithm to discretize and time-integrate the governing equations. The sharp-interface treatment is known to have some advantage over the diffuse-interface method in that it does not suffer from the unphysical spurious parasitic velocity at the interface. The developed model is verified with several benchmark problems including the two-dimensional dam break problem. The results are in good agreement with experimental data and other numerical result. [Preview Abstract] |
Sunday, November 20, 2005 9:57AM - 10:10AM |
AL.00010: The Refined Level Set Grid Method for Simulating Primary Atomization Marcus Herrmann Simulating the primary atomization of turbulent liquid jets and sheets is a difficult task, since the liquid/gas interface can exhibit a wide range of scales. This is especially challenging for grid-based tracking schemes, like the Volume-of-Fluid method or the level set method, since it has to be demonstrated, that the simulated interface geometry becomes grid independent upon grid refinement. To this end, a novel level set approach geared towards massively parallel computers, termed Refined Level Set Grid (RLSG) method is presented. RLSG allows for the independent refinement of the interface tracking level set grid. This ensures grid converged representation of the phase interface with respect to a base-grid, on which the Navier-Stokes equations are solved. Furthermore, RLSG provides a natural, consistent interface to Lagrangian secondary breakup spray models, thereby ensuring that small-scale structures that are infeasible to resolve by a grid-based approach are treated correctly. Finally, using the RLSG method, a sub-grid model for the surface tension term in the multiphase Navier-Stokes equations can be derived, thus enabling LES simulation of the turbulent breakup process. [Preview Abstract] |
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