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 H9: Instability: Interfacial and Thin-Film IV - Elasticity and Substrates |
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Chair: Yuan-nan Young, New Jersey Institute of Technology Room: 333 |
Monday, November 25, 2013 10:30AM - 10:43AM |
H9.00001: Long-wave Dynamics of a Membrane in an Electric Field Yuan-Nan Young, Shravan Veerapaneni, Michael Miksis We investigate the long-wave non-linear dynamics of an inextensible capacitive elastic membrane under electric fields. The long-wave formulation allows us to analyze the equilibrium membrane profile in a d.c. field. Numerical studies of the governing equation with an integral constraint (for the constant membrane area) elucidate how the membrane bending modulus, electric potential, and frequency of the a.c. electric field gives rise to various membrane dynamics and equilibrium profiles. Pillar formation under the constant area constraint is found as we decrease the membrane bending modulus or increase the electric potential. Increasing the a.c. field frequency stabilizes the membrane profile, and we find the surrounding fluid flow to correlate closely with the local membrane curvature. [Preview Abstract] |
Monday, November 25, 2013 10:43AM - 10:56AM |
H9.00002: The effect of structuring on the stability of electrolyte films Christiaan Ketelaar, Vladimir Ajaev We investigate the stability of a thin liquid film of an electrolyte on a structured surface with a periodic array of gas-filled grooves. The electrostatic component of disjoining pressure is incorporated into the system of lubrication-type equations to derive a nonlinear evolution equation for film thickness. Electric charges are present at the liquid-gas interface at the top of the film, as well as the solid-liquid interface segments between the grooves and the menisci separating the gas phase in the grooves from the liquid film. We analyze how the length of the groove, the slip length at the groove menisci, and the electric charges at the interfaces affect the stability of the electrolyte film. In particular, we identify the conditions when a stable electrolyte film on a charged surface becomes destabilized by the effect of the structuring. [Preview Abstract] |
Monday, November 25, 2013 10:56AM - 11:09AM |
H9.00003: The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells Draga Pihler-Puzovic, Anne Juel, Matthias Heil The development of viscous fingers in circular Hele-Shaw cells is a classical and widely-studied fluid mechanical problem. The introduction of wall elasticity (via the replacement of one of the bounding plates by an elastic membrane) can weaken or even suppress the fingering instability, but it also makes the system susceptible to additional solid-mechanical instabilities. We show that in elastic-walled Hele-Shaw cells that are bounded by sufficiently thin elastic sheets the (fluid-based) viscous fingering instability can arise concurrently with a (solid-based) wrinkling instability. We study the interaction between these distinct instabilities, using a theoretical model that couples the depth-averaged lubrication equations for the fluid flow to the F\"{o}ppl--von K\'{a}rm\'{a}n equations which describe the deformation of the thin elastic sheet. By using a combination of a linear stability analysis and direct numerical simulations, we show that system's behaviour may be characterised by a non-dimensional parameter that indicates the strength of the fluid-structure interaction. For small [large] values of this parameter the system's behaviour is dominated by viscous fingering [wrinkling], with strong interactions between the two instabilities arising in an intermediate regime. [Preview Abstract] |
Monday, November 25, 2013 11:09AM - 11:22AM |
H9.00004: Bending of an elastic cantilever by gravity-driven flow of a liquid film Marinela Popova, Hyoungsoo Kim, Peter Howell, Howard Stone We experimentally study a gravity-driven liquid flow on a flexible beam. The elastic material bends due to the weight of the liquid. The relationship between hydrodynamics and elasticity is investigated by varying an applied flow rate, the bending stiffness of the beam, and the beam length. Surface tension effects are negligible for these experiments. We compare our results with a model that predicts the beam deformation in terms of two dimensionless parameters, one representing a dimensionless beam length and the other representing a dimensionless beam stiffness. The results span both small deformations as well as large deformations of the cantilever. [Preview Abstract] |
Monday, November 25, 2013 11:22AM - 11:35AM |
H9.00005: Stability Theory for Interfacial Patterns in Magnetic Pulse Welding Ali Nassiri, Gregory Chini, Brad Kinsey Magnetic Pulse Welding (MPW) is a solid state, high strain-rate joining process in which a weld of dissimilar or similar materials can be created via high-speed oblique impact of two workpieces. Experiments routinely show the emergence of a distinctive wavy pattern, with a well defined amplitude and wavelength of approximately 20 and 70 micrometers, respectively, at the interface between the two welded materials. Although the origin of the wavy pattern has been the subject of much investigation, a unique fundamental physical theory for this phenomenon is as yet not widely accepted. Some researchers have proposed that the interfacial waves are formed in a process akin to Kelvin-Helmholtz instability, with relative shear movement of the flyer and base plates providing the energy source. Here, we employ a linear stability analysis to investigate whether the wavy pattern could be the signature of a shear-driven high strain-rate instability of an elastic-plastic solid material. Preliminary results confirm that an instability giving rise to a wavy interfacial pattern is possible. [Preview Abstract] |
Monday, November 25, 2013 11:35AM - 11:48AM |
H9.00006: Instability-Driven Streak Formation During Convective Deposition Alexander Weldon, Kedar Joshi, James Gilchrist The formation of streaks, often unwanted localized multilayer particle deposition oriented in the direction of deposition, is studied across a robust variety of process conditions. In systems where streaks form, many streaks are initiated and then coarsen and merge as the deposition progresses. Image analysis of streaks give a detailed account of their formation and development. Insights into the formation of this stochastic process will be given and suggest ways to suppress the formation of streaks. [Preview Abstract] |
Monday, November 25, 2013 11:48AM - 12:01PM |
H9.00007: Effect of lateral vibrations during convective deposition Tanyakorn Muangnapoh, Alexander Weldon, James Gilchrist Vibration-assisted convective deposition is an advanced technique for improving a convective deposition. By adding a mechanical substrate vibration, drastic alterations of an interfacial liquid surface and an evaporate rate were observed. Bond, capillary and Reynolds dimensionless numbers were investigated for describing a change of an interfacial liquid surface. In this experiment, aqueous binary suspensions of colloidal microspheres and nanoparticles were used for studying effect of the amplitudes (0-250 $\mu $m) and the frequencies (1-50 Hz) of substrate vibration. The quality of deposited thin films was characterized by using a confocal laser scanning microscope, a scanning electron microscope and an image analysis. The monolayer structures formed from this rapid process can be used in a variety of optical, chemical, and biochemical sensing applications such as optical microlens arrays, microporous membranes and cell capture substrates. [Preview Abstract] |
Monday, November 25, 2013 12:01PM - 12:14PM |
H9.00008: Faraday instability on patterned surfaces Jie Feng, Gregory Rubinstein, Ian Jacobi, Howard Stone We show how micro-scale surface patterning can be used to control the onset of the Faraday instability in thin liquid films. It is well known that when a liquid film on a planar substrate is subject to sufficient vibrational accelerations, the free surface destabilizes, exhibiting a family of non-linear standing waves. This instability remains a canonical problem in the study of spontaneous pattern formation, but also has practical uses. For example, the surface waves induced by the Faraday instability have been studied as a means of enhanced damping for mechanical vibrations (Genevaux, et. al. 2009). Also the streaming within the unstable layer has been used as a method for distributing heterogeneous cell cultures on growth medium (Takagi, et al. 2002). In each of these applications, the roughness of the substrate significantly affects the unstable flow field. We consider the effect of patterned substrates on the onset and behavior of the Faraday instability over a range of pattern geometries and feature heights where the liquid layer is thicker than the pattern height. Also, we describe a physical model for the influence of patterned roughness on the destabilization of a liquid layer in order to improve the design of practical systems which exploit the Faraday instability. [Preview Abstract] |
Monday, November 25, 2013 12:14PM - 12:27PM |
H9.00009: Bottom reconstruction in power-law thin-film flow over topography Symphony Chakraborty, Usha Ranganathan We consider a thin film of a power-law fluid flowing over an undulated substrate under the action of gravity. Instead of determining the free surface position as in the case of the direct problem, we focus on the inverse problem where for a specific free surface shape, we find the corresponding bottom topography which causes the free surface profile. As an asymptotic approach for thin films and moderate Reynolds numbers, we apply the WRIBL method which enables us to derive a set of two evolution equations for the film thickness $h$ and the flow rate $q$. We obtain the steady solutions of the above model equation for the inverse problem for weakly undulated free surface profile by a perturbation method. For a strongly undulated free surface shape, we solve the model equation numerically and obtain the bottom topography. We examine the influence of of viscosity of fluid, inertia, film thickness, hydrostatic pressure and surface tension on the reconstructed bottom topography for shear-thinning as well as shear-thickening fluids. The results reveal that compared to shear-thickening fluid, wavy free surfaces for shear-thinning fluid require strongly undulated topographies with steep troughs. Parametric studies show that this effect increases with increasing free surface amplitude. [Preview Abstract] |
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