Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session BK: Free Surface Flows I |
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Chair: Wendy Zhang, University of Chicago Room: Salt Palace Convention Center 250 E |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BK.00001: The Normal Impact of Small Hydrophobic Bodies Jeff Aristoff, John Bush We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a horizontal water surface. Particular attention is given to characterizing the shape of the resulting air cavity in both the low Bond number and low Weber number limits. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups, which we rationalize by scaling arguments. A theoretical model is developed to describe the evolution of the cavity shape, and is found to compare favorably with our experimental observations. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BK.00002: Cavity Dynamics in Vertical Water Entry of a Body at Low Froude Numbers Hongmei Yan, Yuming Liu The dynamics of a cavity induced by the vertical water entry of a three-dimensional rigid body is investigated both theoretically and computationally. The study is focused in the relatively low Froude number range, i.e. $F_r \equiv V(gD)^{-1/2}$ = $1 \sim 10$ ($V$ is the dropping velocity of the body, $D$ characteristic length of the body, and $g$ the gravitational acceleration), when the surface closure is preceded by deep closure of the cavity. To understand the basic mechanism for the formation and collapse of cavity, an asymptotic theory is developed based on the slender-body assumption. Direct comparisons with existing experimental data (for disks and spheres) show that the theory properly captures the key physical effects involved and gives a satisfactory prediction on the cavity height and closure time, but is incapable of accurately accounting for the effects associated with the details of the body geometry. To complement the theory, a complete numerical model is developed based on fully nonlinear computations using the boundary integral equation method. Both theoretical and numerical solutions for the dependence of cavity height and closure time on Froude number and body geometry are obtained and compared with available experiments. This study is of importance to the understanding of the mechanics of (small) animal walking on water surface and to the design of projectiles. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BK.00003: Impact of a large-viscosity liquid drop: Rim dynamics Robert D. Schroll, Christophe Josserand, St\'{e}phane Zaleski, Wendy W. Zhang Recent experiments suggest that whether the rim of the liquid sheet ejected after impact remains stable against azimuthal perturbations is crucial for splash formation in large-viscosity liquids. Without air, the rim of the ejected sheet remains smooth. With sufficiently high air pressure, azimuthal undulations develop on the rim and slowly grow into a splash [Xu, PRE {\bf 75}, 056316 (2007)]. Motivated by these observations, we simulate large-viscosity liquid impact and focus on the rim dynamics when air effects are small. We found that, surprisingly, the height of the rim increases at a nearly constant rate, independent of whether the impacting drop is expanding or contracting. This decoupling of the rim growth dynamics from the overall radial deformation appears because the large-viscosity drop evolves towards a flat pancake shape. The pancake thickness is controlled by liquid viscosity and, once formed, remains constant over the duration of the impact. Thus the rim always grows from a sheet of the same thickness. We have in addition compared these results against existing scaling predictions, measurements as well as results from different numerical implements and found good agreement throughout. [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BK.00004: Onset of air-induced splash at low impact speeds for low-viscosity liquids Wendy W. Zhang, Lei Xu, Priyanka Jindal, Sidney R. Nagel Recent experiments [Xu et al. PRL {\bf 94}, 184505 (2005)] revealed that the presence of air is essential for the splash formed after a low-viscosity liquid drop hits a dry, smooth solid. As the impact speed $U_0$ is increased from $2$ m/s to $8$ m/s, the threshold gas pressure, $P_T (U_0)$, below which the splash is suppressed, exhibits $2$ distinct trends. Above a critical impact speed $U_*$, $P_T$ decreases as $1/\sqrt{U_0}$. Below $U_*$, however, $P_T$ decreases much more rapidly with $U_0$. Here we show that a simple idea can account for both the different trend and the form of $P_T(U_0)$ below $U_*$. The idea is that, within the leading-edge of the thin liquid sheet ejected after impact, the flow dynamics is initially dominated by viscous effects. For a drop of radius $a$, surface tension $\sigma$, dynamic viscosity $\mu_L$, density $\rho_L$ falling in ambient gas with sound speed $C_g$, this idea gives the scaling law $U_* \sim (U^2_\rho U_\mu)^{1/3}$, where $U_\rho \sim \sqrt{\sigma/\rho_L a}$ is the capillary wave speed and $U_\mu \sim \sigma/\mu$ is the viscous decay speed for surface deformation. It also yields $P_T(U_0) \sim \sigma^2/(\mu_L a C_g U^2_0)$ for $U_0 \leq U_*$. The dependencies on $\mu_L$, $C_g$ and $a$ are all consistent with available measurements. In addition, our results suggest that, at fixed $U_0$, a different physical mechanism becomes relevant for splash formation when the liquid viscosity is increased above a cross-over value. The predicted cross-over value agrees with the measured value for $4$ m/s impact [Xu, PRE {\bf 75}, 056316 (2007)]. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BK.00005: The splash of a ball hitting a liquid surface: Numerical simulation of the influence of wetting Gustav Amberg, Minh Do-Quang The impact of a solid object on a free liquid surface is quite complex. This problemchallenged researchers for centuries and remains of interest today. Recently, Duez et al [1] published experimental results on the splash when solid sphere enters water. Surprisingly, a small change in the surface chemistry of an object can turn a big splash into an inconspicuous disappearance and vice versa. We study this problem by solving the Navier-Stokes together with the Cahn-Hilliard equations. This system allows us to simulate the motion of a free air-water surface in the presence of surface tension, as a sphere impacts the surface. Including the surface energies of the dry and wet solid surface in the formulation gives a reasonably quantitative description of the dynamic wetting that takes place. Numerical results at different wetting properties and impact speeds will be presented and compared with the recent experiments of Duez et al. \newline [1] Duez, C. et al. Nature Phys. 3, 180--183 (2007). [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BK.00006: Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films Taeil Yi, Harris Wong A liquid film of thickness h $<$ 100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure P. Since dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives P=P(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-$>$0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of that depends on the slope as well as the height h of the film.[1] When this theory is implemented for Lennard-Jones liquid films, the new P=P(h,hx) is bounded near a contact line as h-$>$0. Thus, the singularity in P(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with an unbounded precursor film is linearly stable. \newline [1] Wu {\&} Wong, J. Fluid Mech. \underline {506}, 157 (2004) \newline [2] Yi {\&} Wong, J. Colloid Inter. Sci. \underline {313}, 579 (2007) [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BK.00007: The Freezing of Free Films Anthony Anderson, Stephen Davis We investigate the steady, longitudinal solidification of thin, free, liquid films of pure metallic melts. The dynamics of the liquid films are influenced by several factors when freezing is present: viscosity, capillarity, thermocapillarity, van der Waals instabilities, and flows resulting from volume-change upon solidification. Results are first established for a non-deformable liquid film. We investigate contact conditions, Gibbs-Thompson effects, and volume-change convection using perturbation and transform methods. The analysis is extended to a deformable liquid film. These results provide the foundation for further study of the dynamics and stability of thin liquid films during freezing. The implications of our results for the freezing of metallic foams is discussed and future directions for our work highlighted. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BK.00008: Direct numerical simulations of EHD-enhanced film boiling Payam Sharifi, Asghar Esmaeeli Boiling is one of the most efficient modes of heat exchange. Yet, in applications involving boiling in micro-devices or under microgravity conditions it is extremely desirable to enhance the heat transfer rate even further to increase the efficiency of these systems. An enhancement mechanism that is particularly attractive is the one due to application of an electric field to the bulk of fluid. Here, the dielectric mismatch between the liquid and vapor phases results in convective flows and, therefore, a higher heat transfer coefficient. While the enhancement of heat and mass transfer by electric field has been known for decades, a fundamental understanding of the problem is still lacking primarily due to difficulties in conduct of experimental and theoretical studies. The current advances in development of numerical methods for direct simulations of multiphase flows, however, have opened up enormous possibilities for detailed understanding of this problem. Such simulations can make it possible to capture the highly unsteady dynamics of the boiling flows. Here, we present a front tracking algorithm in conjunction with a leaky-dielectric electrohydrodynamic (EHD) model to study EHD-enhanced film boiling on horizontal surfaces. The goal is to compare the average wall Nusselt number at different strengths of the electric field and to correlate the macroscopic behavior of the flow with the dynamics of the phase boundary. [Preview Abstract] |
Sunday, November 18, 2007 12:18PM - 12:31PM |
BK.00009: Domain Relaxation in Langmuir Films Andrew J. Bernoff, James C. Alexander, Elizabeth K. Mann, J. Adin Mann, Lu Zou, Jacob R. Wintersmith We report on an experimental, theoretical and computational study of a molecularly thin polymer Langmuir layer domain on the surface of a subfluid. When stretched (by a transient stagnation flow), the Langmuir layer takes the form of a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape relaxes to the circular minimum energy configuration. The tether is never observed to rupture, even when it is more than a hundred times as long as it is thin. We model these experiments as a free boundary problem where motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. We process the digital images of the experiment to extract the domain shape, use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics, and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1\%. [Preview Abstract] |
Sunday, November 18, 2007 12:31PM - 12:44PM |
BK.00010: ABSTRACT WITHDRAWN |
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