Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session AY: Instability: Interfacial and Thin Film I |
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Chair: Omar Matar, Imperial College Room: Hyatt Regency Long Beach Regency E |
Sunday, November 21, 2010 8:00AM - 8:13AM |
AY.00001: Stationary shapes of confined rotating magnetic liquid droplets Jose Miranda, Sergio Lira, Rafael Oliveira We study the family of steady shapes which arise when a magnetic liquid droplet is confined in a rotating Hele-Shaw cell, and subjected to an azimuthal magnetic field. Two different scenarios are considered: first, the magnetic fluid is assumed to be a Newtonian ferrofluid, and then it is taken as a viscoelastic magnetorheological fluid. The influence of the distinct material properties of the fluids on the ultimate morphology of the emerging stationary patterns is investigated by using a vortex-sheet formalism. Some of these exact steady structures are similar to the advanced time patterns obtained by existing time-evolving numerical simulations of the problem. A weakly nonlinear approach is employed to examine this fact, and to gain analytical insight about relevant aspects related to the stability of such exact stationary solutions. [Preview Abstract] |
Sunday, November 21, 2010 8:13AM - 8:26AM |
AY.00002: Breakup of an electrified jet in an AC field Demetrios Papageorgiou, Devin Conroy, Richard Craster, Omar Matar We study the axisymmetric break-up and satellite formation of slender jets subjected to time-dependent electric fields. The jet is surrounded by a concentrically-placed cylindrical electrode with an oscillating voltage; the annular fluid is assumed to be hydrodynamically passive. We use the long-wave approximation to derive coupled evolution equations for the interface position and axial velocity component, which account for electrostatic forcing. Numerical solutions of these equations permit the study of the effect of various forms of the electrode potential time-dependence on the dynamics. Our results indicate that it may be possible to use the AC field to control the number of satellites accompanying breakup as well as their size. [Preview Abstract] |
Sunday, November 21, 2010 8:26AM - 8:39AM |
AY.00003: Breakup of an electrified viscous thread with charged surfactants Devin Conroy, Richard Craster, Demetrios Papageorgiou, Omar Matar The dynamics and breakup of electrified viscous jets in the presence of ionic insoluble surfactants are investigated. Axisymmetric configurations are considered and the jet is surrounded by a concentrically placed cylindrical electrode with at a constant voltage potential. The annular region between the jet and the electrode is taken to be inviscid and an electric field is set up there and drives the flow, along with other physical mechanisms including capillary instability and viscous effects. The jet fluid is taken to be a symmetric electrolyte and modeling of the cationic and ionic species is used by consideration of the Nernst-Planck equations in order to find the volume charge density that influences the electric field in the jet. A positively charged insoluble surfactant is present at the interface and its evolution as well as the resulting value of the local surface tension coefficient, are coupled to the voltage potential at the interface. The resulting coupled nonlinear systems are derived using a slender jet approximation. We show the jet ruptures in finite time provided the outer electrode is sufficiently far away, and demonstrate how the dimensionless parameters can be used to control the size of the satellite drops and time to breakup. Pinching solutions follow the self-similar dynamics of clean viscous jets at times close to the breakup time. [Preview Abstract] |
Sunday, November 21, 2010 8:39AM - 8:52AM |
AY.00004: The Dynamics of Drop Impact John Kolinski, Shmuel M. Rubinstein, Shreyas Mandre, L. Mahadevan There are many aspects of the dynamics of liquids wetting solid surfaces that are not fully understood. One such aspect is what happens at the first instance of contact. We study the dynamics of a partially wetting fluid drop as it approaches a solid surface with velocities ranging from microns- to meters-per-second. We use TIR (total internal reflection) microscopy to probe what happens immediately above the surface as the drop approaches and study two different regimes previously inaccessible experimentally: 1. A high impact velocity regime where the initial dynamics are governed by inertia and the formation and breakup of a thin air film trapped under the approaching liquid at microsecond timescales and 2. A slow approach regime where the dynamics, also occurring at microsecond timescales, are governed mainly by the solid liquid interactions and contact line dynamics. [Preview Abstract] |
Sunday, November 21, 2010 8:52AM - 9:05AM |
AY.00005: Shock-wave solutions and their stability in two-layer channel flow Aliki Mavromoustaki, Richard Craster, Omar Matar We study the dynamics of an interface separating two immiscible layers in an inclined channel. Lubrication theory is used to derive an evolution equation for the interface position that models the two-dimensional flow in both co- and counter-current configurations. This equation is parameterized by viscosity and density ratios, and a total dimensionless flow rate; the system is further characterized by the height of the interface at the channel inlet and outlet, which are treated as additional parameters. For one-dimensional flows, we use an entropy-flux analysis to delineate the existence of various types of shock- like solutions, which include compressive Lax-shocks, pairs of Lax and undercompressive shocks, and rarefaction waves. Flows characterised by unstably-stratified layers are accompanied by the formation of propagating, large-amplitude interfacial waves, which are not shock-like in nature. The results of our transient numerical simulations agree with our analytical predictions and elucidate the mechanisms underlying spatio-temporal development of the various types of waves. The linear and nonlinear stability of these waves to spanwise perturbations is also investigated. [Preview Abstract] |
Sunday, November 21, 2010 9:05AM - 9:18AM |
AY.00006: Numerical study of the evaporation of sessile drops: formation of hydrothermal waves Khellil Sefiane, George Karapetsas, Pedro Saenz, Prashant Valluri, Omar Matar We investigate theoretically the spontaneous evaporation of sessile drops and the formation of hydrothermal waves induced by thermal gradients. We use integral balance equations in combination with lubrication theory to model the motion and evaporation of the drop taking into account inertia. Contact line singularities are avoided through the adsorption of ultra- thin films wherein evaporation is suppressed by the disjoining pressure. We discuss our numerical results and compare them with 3D simulations, the latter performed using the volume-of-fluid method. [Preview Abstract] |
Sunday, November 21, 2010 9:18AM - 9:31AM |
AY.00007: Thermal fluctuations and the breakup length of Savart capillary jets F. Javier Garc\'Ia How long can a capillary jet be before it breaks up into droplets? Much time after the pioneering experimental work of Savart\footnote{F. Savart, {\emph{Annal. Chim.}} {\bf{53}}, 337 (1833), plates in Vol.\ 54.} on the breakup of liquid jets isolated from external acoustic noise, no analytical prediction for their length has been derived yet. Even the precise nature of the perturbations leading to the natural breakup of a capillary jet remains a mystery. Only empirically fitted estimates have been proposed up to now, assuming an exponential growth of an unknown initial amplitude of those perturbations. Here, the evolution of a liquid jet emerging from a thin-wall orifice and subjected to thermal-noise fluctuations is explored through a stochastic linear modal analysis. Contrary to what has been assumed before, it is proven that the average amplitude of noisy perturbations does not grow exponentially. For the first time, a simple analytical estimate of the natural breakup length of a liquid jet is derived without the aid of any adjusting parameter. The breakup length of Savart liquid jets exiting through $3\mathrm{mm}$-diameter orifices are well predicted by this formula. The parametric range of application of this analysis and its accuracy are discussed. [Preview Abstract] |
Sunday, November 21, 2010 9:31AM - 9:44AM |
AY.00008: Drift and symmetry breaking in Faraday waves Nicolas Perinet, Damir Juric, Laurette Tuckerman, Edgar Knobloch Faraday waves which break reflection symmetry and manifest horizontal flux have been investigated experimentally and theoretically by Fauve, Douady, Thual and by Knobloch, Martel, Vega. We perform the first numerical calculations of such states by means of fully-resolved simulations of the Navier-Stokes equations in superposed layers of air and water, coupled via a front-tracking algorithm for the interface. We find that these states are bistable with flux-free reflection-symmetric Faraday waves. [Preview Abstract] |
Sunday, November 21, 2010 9:44AM - 9:57AM |
AY.00009: Numerical and analytical studies of the electric field effects on interfacial waves subject to Rayleigh-Taylor instability Lyudmyla Barannyk, Demetrios Papageorgiou, Peter Petropoulos A system of two stratified immiscible incompressible fluids in a horizontal channel of infinite extent is considered. Of particular interest is the case with the heavier fluid initially lying above the lighter fluid, so that the system is susceptible to the classical Rayleigh-Taylor instability. An electric field acting in the horizontal direction is imposed on the system and it is shown that it can act to completely suppress Rayleigh-Taylor instabilities and produces a dispersive regularization in the model. Dispersion relations are derived and a class of nonlinear traveling waves (periodic and solitary) is computed. Numerical solutions of the initial value problem of the system of model evolution equations that demonstrate a stabilization of Rayleigh- Taylor instability due to the electric field are presented. For weak electric fields, it is found that interface develops a finite-time singularity in the form of touchdown with the wall. [Preview Abstract] |
Sunday, November 21, 2010 9:57AM - 10:10AM |
AY.00010: Capillary wave motion excited by high frequency surface acoustic waves Ming Tan, Omar Matar, James Friend, Leslie Yeo We present the results of a numerical and experimental study of capillary wave motion excited by high frequency surface acoustic waves (SAWs). A two-dimensional numerical model is constructed that couples the motion of the piezoelectric substrate to a thin liquid layer atop the substrate. A perturbation method, in the limit of small-amplitude acoustic waves, is used to decompose the equations governing fluid motion to resolve the widely differing time scales associated with the high frequency excitation. Transformation of time series data from both experiments and simulations into the frequency domain reveals that, in the low-amplitude regime, a fundamental resonant frequency, identical to that of the applied SAW, and a superharmonic frequency are found in the frequency spectra. The free surface displacement magnitude is comparable to that of the the substrate displacement. In the high-amplitude regime, strong nonlinearities shift the acoustic energy to a lower frequency than that of the SAW. Comparisons with experiments are also carried out yielding good qualitative agreement. [Preview Abstract] |
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