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 NL: Waves IV |
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Chair: William Phillips, University of Illinois, Urbana-Champaign Room: Hilton Chicago Astoria |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NL.00001: Axisymmetric free surface waves and drops Kuan-Khoon Tjan, William R.C. Phillips The numerical simulation of the deformation of a liquid free surface subjected to an impulse (accoustically generated or otherwise) in an axisymmetric semi-infinite domain is considered. Using an inviscid boundary integral formulation, the free surface is evolved under the influence of inertial, interfacial and gravitational forces. Within a critical envelope of Weber and Froude numbers, there are two types of impulse of interest, one which led to the ejection of droplets and the other to the entrainment of bubbles. This research is part of a study of the lung damage caused by ultrasonic imaging. It has been observed in animal experiments that a focused ultrasonic beam can cause lung lesions. Since the lung tissue is mostly water and the lung is filled with air, such a mathematical model is a plausible realisation of the actual physics. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NL.00002: Faraday Instability in a Surface-Frozen Liquid Satish Kumar, Patrick Huber Faraday surface instability measurements of the critical acceleration, $a_c$, and wavenumber, $k_c$, for standing surface waves on a tetracosanol (C$_{24}$H$_{50}$) melt exhibit abrupt changes at $T_s= 54$ C, $\sim$4 C above the bulk freezing temperature. The measured variations of $a_c$ and $k_c$ vs. temperature and driving frequency are accounted for quantitatively by a hydrodynamic model, revealing a change from a free-slip surface flow, generic for a free liquid surface ($T > T_s$), to a surface-pinned, no-slip flow, characteristic of a flow near a wetted solid wall ($T < T_s$). The foundation of the hydrodynamic model is a vertically vibrated liquid-air interface covered by an insoluble surfactant. When the Marangoni number (ratio of surface-tension-gradient forces to viscous forces) becomes large, the contractions and expansions of the free surface are suppressed and it behaves like a no-slip surface. The abrupt change in instability behavior at $T_s$ is traced to the onset of surface freezing, where the steep velocity gradient in the surface-pinned flow significantly increases the viscous dissipation near the surface. These results shed light on the hydrodynamics associated with the surface freezing phenomenon, and may find use in other areas such as foam drainage, surface rheology, and microfluidic transport. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NL.00003: Drop ejection conditions from breaking capillary waves. Baburaj Puthanveettil, Emil J. Hopfinger An experimental study of parametrically excited non-linear surface waves is presented. Forcing frequencies are in the range 25 to 100 Hz, resulting in gravity/capillary waves for the liquids investigated. For a given frequency, the wave pattern evolution with forcing amplitude has been determined up to droplet ejection. The wave motion becomes rapidly chaotic with the wave lengths being approximated by a Gaussian distribution. Wave breaking with droplet ejection is closely approximated by the threshold acceleration proposed by Goodridge et al $^{1}$ for the capillary wave limit. A gravity/capillary scaling is here introduced from which the crossover from gravity to capillary dominated breaking conditions is deduced. The mean wave acceleration at breaking is an order of magnitude larger than the container acceleration and this remains valid for synchronous waves (horizontal forcing). The droplet ejection rate is shown to depend, in additions to the wave frequency, on the wavelength, hence the liquid properties. Drop sizes are shown to scale with the wave length. $^{1}$ Goodridge et al. Phys. Rev. E, Vol. 56, No. 1,1997, pp. 472. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NL.00004: Surface wave on a semi-toroidal water ring Sunghwan Jung, Erica Kim, Michael Shelley We study the nature of surface waves on a semi-toroidal ring of water. We create this fluid shape by patterning a glass plate with a hydrophobic film which confines the fluid to a precise geometric region. To excite the system, we vibrate the supporting plate up and down, thus accelerating/decelerating the fluid ring along the toroidal axis. When the amplitude of the driving acceleration is sufficiently large, the semi- toroidal water surface becomes unstable to azimuthal and radial waves whose character is constrained by the constraining geometry, and we investigate the dependence of the different surface wave patterns on driving amplitude and frequency. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NL.00005: Sloshing in Suspended Containers P.D. Weidman Cooker ({\it Wave Motion}, {\bf 20}, 1994) reported original work on the interactive dynamics between a fluid partially filling a single-compartment container suspended as a bifilar pendulum to determine the frequency of small amplitude motion of the system. Weidman ({\it Bull. APS}, {\bf 39}, 1994) extended the results of Cooker to include, {\it inter alia}, multi-compartment rectangular containers and a cylindrical container. Fundamental mode frequency measurements of the suspended system are presented here for fluids partially filling single- and multiple-compartment rectangular containers and a cylindrical container. The results confirm the validity of the shallow-water approach over a range of fluid/container mass ratios $M$ and pendulum lengths $l$ varying from 0.5~m to 3.5~m. The frequency approach to unconstrained container motion in the limit $l \to \infty$ is also evident. [Preview Abstract] |
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