Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session G9: Instability: Interfacial and Thin-Film III |
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Chair: Paul Steen, Cornell University Room: 333 |
Monday, November 25, 2013 8:00AM - 8:13AM |
G9.00001: Dynamics of a thin ferrofluid film subjected to a magnetic field Devin Conroy, Alex Wray, Omar Matar We consider a thin film flowing down a rigid, impermeable inclined plane subjected to a magnetic field. The film corresponds to a ferrofluid and is bounded from above by a hydrodynamically-passive gas. The ferrofluid is considered to be weakly-conducting, and its dynamics are governed by the steady Maxwell's equations, coupled to the Navier-Stokes, and continuity equations. The magnetisation of the ferrofluid is a function of the magnetic field, which can be represented by a nonlinear Langevin function. We use long-wave theory to determine the velocity and pressure fields in the film, and use Fourier transforms to solve for the potential field in the gas phase. Application of the interfacial and kinematic boundary conditions then leads to a one-dimensional partial differential equation for the interface with a non-local contribution from the magnetic effects. A linear stability analysis of this equation is carried out. This equation is then solved numerically for a wide range of system parameters. The results of this parametric study will be presented. [Preview Abstract] |
Monday, November 25, 2013 8:13AM - 8:26AM |
G9.00002: Transition to disorder: the effects of elasticity on thin film flow inside a tube Jeffrey Olander, Roberto Camassa, G.M. Forest, H. Reed Ogrosky Previous studies of non-Newtonian flows driven up a tube by a high volume flux flow of air have suggested that a transition to disordered core-annular wave dynamics occurs when the liquid becomes elastic. Understanding this transition may shed light on the behavior of mucus in the human trachea. We present results from experiments of thin-film liquid flows of a Newtonian fluid and a non-Newtonian, dilute mixture of oligomers. These so-called Boger fluids are elastic, non-thixotropic liquid solutions made by dissolving a non-Newtonian solute in a Newtonian base. We compare, through video analysis, the wave dynamics of the Boger fluid to those of its Newtonian base under identical inflow conditions. We describe observed differences between the Newtonian and non-Newtonian cases. Finally, quantitative comparisons of wave properties and liquid mass transport are discussed. [Preview Abstract] |
Monday, November 25, 2013 8:26AM - 8:39AM |
G9.00003: Laminar flow over a thin film Thomas Ward, Paul Troupe Thin film deformation that is driven by an external laminar flow over a flat plate is considered using both theoretical and computational analysis. To perform theoretical analysis we utilize the Blasius boundary layer solution to develop the thin film evolution equation. Non-dimensionalization of the resulting film evolution equations yields two dimensionless parameters, the Weber and Reynolds numbers. The film thickness is computed for a wide range of both Weber ($>1$) and Reynolds ($>1$) numbers using standard disjoining pressure models. The scaling and computed results suggest strong dependence on the Reynolds number, where in the limit of large Reynolds number the evolution equations are self similar. [Preview Abstract] |
Monday, November 25, 2013 8:39AM - 8:52AM |
G9.00004: Buckling of a thin, viscous film in an axisymmetric geometry Morris Flynn, Sanjay Bhattacharya, Richard Craster By adapting the F{\" o}ppl-von K{\` a}rm{\` a}n equation, which describes the deformation of an elastic membrane, we consider the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution by spectral methods, yields the most unstable azimuthal wave-number, $m^*$. Contrary to the discussion of Slim et al.~({\it J. Fluid Mech.}, {\bf 694}, pp. 5-28, 2012), we argue that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart so that at the onset of instability, $m^*$ is indefinitely large. Away from this point, however, a comparison with analogue experimental measurements is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of $m^*$, the phase speed and the wave amplitude; no prediction concerning the latter two quantities can be made using the present (self-adjoint) theory. Experiments reveal a limited range of angular velocities where waves of either small or large amplitude may be excited. In contrast to the analogue problem from solid mechanics, transition from one to the other regime does not appear to be associated with a notable change in $m^*$. [Preview Abstract] |
Monday, November 25, 2013 8:52AM - 9:05AM |
G9.00005: Vortices catapult droplets in atomization J. John Soundar Jerome, Sylvain Marty, Jean-Philippe Matas, Stephane Zaleski, Jerome Hoepffner A droplet ejection mechanism in planar two-phase mixing layers is examined. Any disturbance on the gas-liquid interface grows into a Kelvin-Helmholtz wave and the wave crest forms a thin liquid film that flaps as the wave grows downstream. Increasing the gas speed, it is observed that the film breaks-up into droplets which are eventually thrown into the gas stream at large angles. In a flow where most of the momentum is in the horizontal direction, it is surprising to observe these large ejection angles. Our experiments and simulations show that a recirculation region grows downstream of the wave and leads to vortex shedding similar to the wake of a backward-facing step. The ejection mechanism results from the interaction between the liquid film and the vortex shedding sequence: a recirculation zone appears in the wake of the wave and a liquid film emerges from the wave crest; the recirculation region detaches into a vortex and the gas flow over the wave momentarily reattaches due to the departure of the vortex; this reattached flow pushes the liquid film down; by now, a new recirculation vortex is being created in the wake of the wave--just where the liquid film is now located; the liquid film is blown-up from below by the newly formed recirculation vortex in a manner similar to a bag-breakup event. [Preview Abstract] |
Monday, November 25, 2013 9:05AM - 9:18AM |
G9.00006: Collapse Dynamics in Rotating Thin Films Shomeek Mukhopadhyay, Joshua Dijksman, Richard Maclaughlin, Roberto Camassa, Robert Behringer We study the collapse of a dry cavity in a thin fluid film. Collapse dynamics driven by viscous gravity currents is well described by a self similar solution of the thin film equation. In the current analysis we include surface tension effects. We find both experimentally and numerically that for small capillary numbers, the collapse dynamics retains its power law scaling behavior, but with a power law clearly distinct from viscous collapse dynamics. [Preview Abstract] |
Monday, November 25, 2013 9:18AM - 9:31AM |
G9.00007: ABSTRACT WITHDRAWN |
Monday, November 25, 2013 9:31AM - 9:44AM |
G9.00008: Wrinkling of Thin Films Induced by Viscous Stress Sourav Chatterjee, Christina Mcdonald, Jiani Niu, Rui Huang, Sachin Velankar Compression of thin films attached to compliant solid substrates can induce a variety of highly ordered and complex wrinkling patterns. We study an analogous problem of the wrinkling instability of a thin film floating on a viscous fluid. Uniaxial compression of the fluid induces a viscous stress which leads to the wrinkling of the film. We experimentally determine the effect of geometry and material properties on the wrinkle wavelength. A shear lag approach is used to determine the stress distribution prior to buckling. A linear stability analysis of the film under this stress distribution is used to determine the maximally growing wavelength in the system. Both experiments as well as stability analysis show that the wavelength depends significantly on film length and the ratio of the film and fluid layer thickness. Most importantly, unlike previous research on fluid-supported films, the wrinkle wavelength is rate-dependent, and reduces with increasing compression rate. [Preview Abstract] |
Monday, November 25, 2013 9:44AM - 9:57AM |
G9.00009: Meniscus stability in the planar-flow melt spinning of thin metallic sheets Anthony Altieri, Paul Steen Planar-flow melt spinning is a process for the continuous fabrication of thin, metallic sheets or ribbons. During solidification, molten metal-air meniscus vibrations create periodic thickness variations on the final product. It has been observed that flow configuration and contact line conditions affect the frequency of thickness variations. A model problem of a free interface enclosing an inviscid fluid in a slot is examined. A linear stability analysis shows the effect of flow near the interface for various contact line constraints. [Preview Abstract] |
Monday, November 25, 2013 9:57AM - 10:10AM |
G9.00010: Experimental investigation of the stability of a moving radial liquid sheet Manjula Paramati, Mahesh Tirumkudulu Experiments were conducted to understand the stability of moving radial liquid sheets formed by the head-on impingement of two co-linear water jets using laser induced fluorescence technique (LIF). Acoustic sinusoidal fluctuations were introduced at the jet impingement point and we measured the displacement of the center line of the liquid sheet (sinuous mode) and the thickness variation (varicose mode) of the disturbed liquid sheet. Our experiments show that the sinuous disturbances grow as they are convected outward in the radial direction even in the smooth regime (We $<$ 800). In the absence of the acoustic forcing, the measured thickness has the expected 1/r dependence. Interestingly, we were unable to detect any thickness variation about the pre-stimulus values in the presence of acoustic forcing suggesting that the variation in the thickness is lower than the resolution of the technique ($\pm$ 1 $\mu$m). The growth rates of the sinuous mode determined from the wave envelope matches with the prediction of a recent theory by Tirumkudulu and Paramati (Communicated to Phys. Of Fluids, 2013) which accounts for the inertia of the liquid phase and the surface tension force in a radial liquid sheet while neglecting the inertial effects due to the surrounding gas phase. [Preview Abstract] |
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