Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G9: Interfacial/Thin Film Instability III |
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Chair: Devin Conroy, Imperial College London Room: 25B |
Monday, November 19, 2012 8:00AM - 8:13AM |
G9.00001: Electrosprays: cone-jet breakup in the presence of DC electric fields Omar Matar, Devin Conroy, Richard Craster, Demetrios Papageorgiou, Hsueh-Chia Chang The breakup of an electrified jet in a gas with an axially applied electric field is investigated theoretically. The jet fluid is taken to be a symmetric electrolyte and modelling of the cationic and anionic species is carried out by considering the Nernst-Planck equations in order to find the volume charge density that influences the electric field in the jet. At high flow rates, the governing equations are investigated asymptotically in the long-wave limit and the one-dimensional model is solved numerically for a wide range of hydrodynamic, electrostatic, and electrokinetic parameters. For low flow rates, a boundary integral method is used to solve for the electrostatic potential surrounding the interface, which assumes a cone-like shape from which a thin jet emanates. In both cases, the electric field causes the jet to stretch and thin to a point where ion repulsion forces the jet to undergo Rayleigh fission. We measure the axial distance at which this point occurs by comparing the jet radius to the distance at which ion repulsion is important. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G9.00002: On the minimum size of drops composing the type of monodisperse microemulsions obtained via tip streaming Jose Manuel Gordillo, Alejandro Sevilla, Elena Castro-Hernandez On a recent paper, Castro et al (JFM (2012), 698, 423-445, JFM12) reported the generation of concentrated monodisperse emulsions composed of drops with sizes even below 1 $\mu m$. Drops are generated from the capillary breakup of a long and thin ligament which strongly stretches downstream from the exit of an injector of radius $R_i$. The ligament is formed when a flow rate $Q_i$ of a fluid with a viscosity $\mu_i$ discharges into an immiscible liquid of viscosity $\mu_o$ flowing in parallel with the axis of the injector at a velocity $qU_0$, with $q=Q_i/(\pi R^2_iU_o)$. It was theoretically found that the diameter of the drops obtained is $D_i\propto R_iq^{1/2}$. However, experiments showed that the predicted drop size is only found when the highly stretched ligament is formed. But this occurs for values of $\lambda=\mu_i/\mu_o$ and the capillary number $Ca_o=\mu_o U_o/\sigma$, with $\sigma$ the interfacial tension coefficient, above a certain threshold which depends on the flow rate ratio $q$. In this presentation we theoretically show that the boundaries in the ($Ca_o$,$\lambda$,$q$) space in which highly stretched long ligaments are formed, corresponds to the conditions under which the jet, calculated using the slender-body description of JFM12, is \emph{globally stable}. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G9.00003: Simulating the capillary breakup of a liquid torus Hadi Mehrabian, James J. Feng Capillary instability of a Newtonian liquid torus suspended in a bath of Newtonian liquid is computed using Cahn-Hilliard diffuse interface method. The main difference between the torus and a straight thread is the presence of curvature and flow filed caused by the shrinkage of the torus. We show that the capillary wave initially grows linearly as on a straight thread. The azimuthal curvature decreases the growth rate while the flow field enhances the growth rate of the capillary waves. The initially dominant mode does not necessarily persist into nonlinear growth and eventual breakup. Breakup depends on the competition of two timescales: torus retraction and neck pinchoff. We demonstrate that it is determined by the initial amplitude, the aspect ratio and the viscosity ratio of the torus viscosity ratio. The numerical results are in agreement with experimental results. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G9.00004: Marangoni convection in a thin film: Formation of a fractal hierarchy of droplets Arthur Straube, Anton Ashmanov, Sergey Shklyaev, Arkady Pikovsky A thin liquid film heated from below is known to demonstrate rupture due to the longwave Marangoni convection [J. Fluid Mech. 345, 45 (1997)]. Despite a number of numerical and theoretical studies nothing has been known about the final state that sets in as a result of the instability. In our recent one-dimensional analysis [Phys. Rev. E 82, 020601 (2010)] we have shown that the terminal state is a fractal built of a hierarchy of droplets, each of which can be represented as a dissipative compacton. The latter can be thought of as the stationary droplet with the zero contact angle and whose profile is determined by the interaction of the surface tension and thermocapillary flow. We show that the dimension of a set of the compactons is equal to unity or, equivalently, the dimension of gaps between the droplets is zero. For a generalized axisymmetric problem, two types of compactons are found: hat-like and ring-like ones, with the maximum either at the symmetry axis or at a finite radius, respectively. Again, an initially flat film becomes unstable, forming a hat-like compacton and a fractal sequence of ring-like compactons, whose stability is analyzed with respect to the perturbations breaking the axial symmetry. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G9.00005: The effect of charge regulation on the stability of electrolyte films Christiaan Ketelaar, Vladimir Ajaev The stability of a thin liquid film of an electrolyte on a solid substrate is investigated. We show that the commonly used approximation of constant charge densities at the solid-liquid and solid-gas interfaces does not lead to predictions of film rupture. To reconcile the model with experimental observations, the effects of charge regulation are incorporated into the model using a linear relationship between charge density and potential. Linear stability criteria are formulated in terms of charge regulation parameters and electrolyte properties. A nonlinear evolution equation for film thickness is derived and solved numerically over a range of parameters to determine the conditions of film rupture. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G9.00006: Self-similar rupture of thin heated viscous sheets M. Bowen, B.S. Tilley We consider the evolution and rupture dynamics of a thin viscous planar sheet subject to a symmetric initial disturbances in the thermal and velocity fields. We consider the long-wave limit where deviations from the mean sheet velocity are small, but thermocapillary stresses, fluid inertia, van der Waals effects, capillarity, and heat transfer to the environment can be significant. The result is a coupled system of three equations that describe the sheet thickness, the sheet velocity, and the sheet temperature. When van der Waals effects are dominant, the sheet ruptures due to disjoining pressures for sufficiently long-wave disturbances on a faster time-scale than convection or conduction. However, in cases when disjoining pressures are small, we find a self-similar rupture process where inertia, viscous stresses, thermocapillarity, convection and conduction all balance. We quantify how solutions transition from this similarity solution to the van-der-Waals-driven self-similar solution when the thickness of the sheet becomes sufficiently thin. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G9.00007: Capillary structures formed with viscous threads in microchannels Samira Darvishi, Thomas Cubaud We investigate two-fluid flows with highly viscous threads formed within a sheath of a less viscous liquid. An experimental study is conducted in long plane microfluidic chambers to examine the formation of periodic capillary structures that result from the viscous folding instability. For the case of a non-wetting thread, a phase diagram of flow patterns is presented including thread breakup, partially coalesced folds, and fully coalesced folds regimes. When the thread is partially wetting, a range of forced wetting and thin film instabilities is observed during the thread lubrication transition in the cell. Novel combinations of viscous and capillary instabilities are shown to offer innovative mechanisms for manipulating the lubrication properties of high-viscosity fluids in microsystems. [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G9.00008: Application of Stress Jumps in Free Surface Films for Noise-Free and Controlled Growth of 3D Microarrays Nan Liu, Sandra Troian Linear stability analysis of a nanoscale, free surface viscous film exposed to a large and uniform transverse thermal gradient has revealed how a flat interface deforms spontaneously into a large area, periodic array consisting of elongated protrusions. These formations, however, are extremely sensitive to noise and exhibit substantial variation in position, shape and growth rate, unacceptable for film patterning strategies based on fluid instability. In this talk, we demonstrate how patterned thermal fields can be used to induce large amplitude stress jumps which help better localize periodic formations and trigger more rapid growth. In particular, we present results of finite element simulations in which waveform trains develop in response to thermocapillary stress jumps induced by an adjacent cooled protrusion with sharp sidewalls. We compare the shapes and growth rates of two different regions of the film, one grown by linear instability and the other by a large amplitude stress jump. In general, stress jumps lead to more rapid and regular formation of pillar arrays insensitive to noise. Despite the large amplitude perturbation, the wavelength remains close to the value predicted by linear stability, a significant advantage for technological applications. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G9.00009: Dynamics of a moving liquid sheet in the presence of acoustics Mahesh Tirumkudulu, Manjula Paramati, Peter Schmid A moving liquid sheet produced by impinging two collinear jets of water was recently shown to be unstable to a select set of acoustic frequencies (Mulmule et al, Vol 22, 022101, Phys. Fluids, (2010)). In order to better understand the phenomenon, we have developed a non-contact technique based on laser induced fluorescence to measure both the displacement and the thickness variation of the liquid sheet. As expected, the liquid sheet thickness varies inversely with radial distance from the point of impingement in the absence of acoustics. In the presence of acoustic forcing (50-150 Hz), experiments reveal that while the sinuous deformation mode is present at all frequencies, the sheet break at the select set of frequencies occurs due to significantly high growth rates of the varicose mode. We present the variation of the measured wave speeds and growth rates as a function of the forcing frequency. These results agree qualitatively with the predictions of the aforementioned study which shows that the varicose and sinuous modes are coupled at the lowest order when the sheet is subjected to acoustics. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G9.00010: Thin Film Behavior Under External Vibrations Michael Bestehorn, Qi Han We study the dynamics of a thin liquid film on a horizontal or weakly inclined substrate. The film is parametrically excited by mechanical vertical and horizontal oscillations. Inertia effects are taken into account and the standard thin film formulation is extended by a second equation for the mean flow rate \[ q(x,t) = \int_0^{h(x,t)}u(x,z,t)\,dz \ , \] where $h$ is the film thickness and $u$ the horizontal velocity. The set of two coupled PDEs for $h$ and $q$ allows for resonances and instabilities of the flat film due to external vibrations. Linear results based on a damped Mathieu equation as well as fully nonlinear results in the frame of longwave approximation found numerically will be presented. For certain regions in the amplitude-frequency plane as well as for certain forms of the excitations we obtain standard Faraday patterns like oscillating squares, but also hexagons and much more involved spatial and temporal pattern formation are observed. [Preview Abstract] |
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