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 LY: Viscous Flows |
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Chair: Catalin D. Mitescu, Pomona College Room: Hyatt Regency Long Beach Regency E |
Monday, November 22, 2010 3:35PM - 3:48PM |
LY.00001: Exchange flow of two immiscible fluids and the principle of maximum flux Rich Kerswell The steady, coaxial flow in which two immiscible, incompressible fluids of differing densities move past each other slowly in a vertical cylindrical tube has a continuum of possibilities due to the arbitrariness of the interface between the fluids. Experiments clearly indicate that the realised exchange solution can vary depending on the viscosity ratio. By invoking the presence of surface tension to at least restrict the shape of any interface to that of a circular arc or full circle, we consider the following question: which flow will maximise the exchange when there is only one dividing interface. Surprisingly, the answer differs fundamentally from the better-known co-directional two-fluid flow situation. [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LY.00002: A New Theory of Oscillating Flows Vladimir Vladimirov A new theory of viscous oscillatory flows has been developed. Our theory represents an adaptation of the Vishik-Lyusternik approach combined with the two-timing and averaging methods. We consider the high Re viscous incompressible flows driven by a vibrating boundary for the simple geometry of a half-space. From the physical viewpoint the considered boundary conditions may be seen as the tangential vibrations of material points of a plane stretchable membrane. The main result is the obtaining of the general, global, and uniformly valid asymptotic solutions of the Navier-Stokes equations. These solutions satisfy general oscillating boundary conditions and three different settings of the scaling parameters (that correspond to the strong, moderate, and weak nonlinearities). We have derived that the streaming part of any solution is governed by either the full Navier-Stokes equations or Stokes' equations (both with the unit Re) as well as by the precisely derived effective boundary conditions. The examples of the spatially periodic vibrations of the boundary and the angular torsional vibrations of an infinite rigid disc have been considered. In the sharp contrast to all previous theories of oscillating flows (see $e.g.$ Batchelor's ``Introduction to fluid dynamics,'' formula 5.13.15) our solutions do not deal with any secular (infinitely growing with the inner normal coordinate) terms. This new approach may be seen as a revolutionary step in the field, since for the very first time it does not use the asymptotic matching procedures and the boundary layer theories. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LY.00003: The asymptotic structure of a slender coiling fluid thread Maurice Blount, John Lister The buckling of a viscous fluid thread as it falls through air onto a stationary surface is a well-known breakfast-time phenomenon which exhibits a rich variety of dynamical regimes [1]. Since the bending resistance of a slender thread is small, bending motion is largely confined to a short region of coiling near the surface. If the height of fall is large enough, then the thread above the coiling region forms a `tail' that falls nearly vertically under gravity but is deflected slightly due to forces exerted on it by the coil. Although it is possible to use force balances in the coil to estimate scalings for the coiling frequency, we analyse the solution structure of the entire thread in the asymptotic limit of a very slender thread and thereby include the dynamic interaction between the coil and the tail. Quantitative predictions of the coiling frequency are obtained which demonstrate the existence of leading-order corrections to scalings previously derived. In particular, we show that in the regime where the deflection of the tail is governed by a balance between centrifugal acceleration, hoop stress and gravity, the tail behaves as a flexible circular pendulum that is forced by bending stress exerted by the coil. The amplitude of the response is calculated and the previously observed resonance when the coiling frequency coincides with one of the eigenfrequencies of a free flexible pendulum is thereby explained. [1] N.M. Ribe \emph{et al.}, \emph{J. Fluid Mech.} {\bf 555}, 275-297. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LY.00004: The shape of an elastic filament in a two-dimensional corner flow Laura Guglielmini, Nicolas Autrusson, Sigolene Lecuyer, Roberto Rusconi, Howard Stone The deformation of a flexible filament held fixed at one end in a nonuniform viscous flow with curved streamlines is considered, with a focus on the filament dynamics and steady-state shape. Our motivation arises from recent microfluidic experiments on biofilm formation: in a channel with bends, thread-like structures, or streamers, were observed, attached to the side walls downstream of each corner and connecting consecutive corners while floating in the channel middle plane (Rusconi et al., {\it J. Roy. Soc. Interface} 2010). We discuss the time evolution and final shape of the filament in different corner geometries as a function of a non-dimensional elasticity parameter that compares viscous and elastic effects. Since the filament develops tension, when the flow has curved streamlines the filament does not align with the flow, but rather it crosses the streamlines, in contrast with the behavior observed for rectilinear flows. We also discuss the buckling instabilities that occur when the filament undergoes compression for the specific case of a stagnation point flow near a wall. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LY.00005: Shape dynamics of a thin loop sedimenting in a viscous fluid James Hanna, Christian Santangelo Thin elastic filaments and chains in viscous fluids are idealizations of biological and polymeric systems. We consider the non-local shape evolution, due to hydrodynamic self-interaction, of a chain-like, locally inextensible loop settling under gravity in the creeping flow regime. We find that the rigid translation of a circle along its gravitationally-aligned axis is unstable. A recirculating blob and tail arrangement is explored as a possible attracting state of a long chain. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LY.00006: Slender soft-magnetic body in highly viscous flows James Martindale, Roberto Camassa, Richard McLaughlin, Leandra Vicci, Longhua Zhao For a tilted soft-magnetic slender body in a highly viscous fluid whose motion is driven by a prescribed background rotating magnetic field, the interaction between hydrodynamic and magnetic forces must be understood in order to predict the combined motion of a rod in silicon oil. Such a system arises in an experiment emulating primary cilia-driven fluid flows in developing embryos. Using classical slender body theory, the magnetic contribution to this dynamical system results in a system of equations for the torque balance. Further, analysis of body geometry such as fixed curvature will be explored, and their influence on the fluid motion illustrated. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LY.00007: Pressures Losses in Grooved Channels M. Mohammadi, Jerzy M. Floryan Pressure losses associated with presence of two-dimensional grooves in a channel are analyzed. Grooves can be oriented in an arbitrary manner with respect to the direction of the flow. When grooves' ridges are orthogonal to the flow direction (transverse grooves) the flow remains two-dimensional. As the grooves rotate away from this direction, the flow becomes three-dimensional. The largest losses occur in the case of transverse grooves. Reduction of pressure loss may occur in the case of longitudinal grooves with properly selected geometry. The analysis is carried out using an auxiliary coordinate system which is defined in such a way that one of its axes is aligned with the grooves. It is shown that the governing equations expressed in this system decouple into a two-dimensional flow across the grooves and a flow in the direction along to the grooves resulting in improved solution efficiencies. The field equations are solved using a gridless algorithm that takes advantage of the immersed boundary concept and permits efficient analysis of arbitrary grooves' geometry. The optimal shape of the grooves required either for the maximization of pressure loss or for the minimization of the loss has been identified. [Preview Abstract] |
Monday, November 22, 2010 5:06PM - 5:19PM |
LY.00008: Cavitation in a squeeze film James Seddon, Maarten Kok, Erik Linnartz, Detlef Lohse We have experimentally investigated the formation of vapour cavities in the squeeze film between a sphere and wall. Surprisingly, we find that these cavities are formed {\it during approach} rather than after rebound, i.e. as the lubricating gap thickness is reduced and as the pressure rapidly increases. The key is that the shear stress also rapidly increases as the gap narrows, and acts to oppose pressure. Thus, despite the enhanced pressure, the liquid is forced to cavitate due to shear stress. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LY.00009: Viscous gravity currents on a plane with leaks John Lister, Jerome Neufeld, Dominic Vella, Herbert Huppert Axisymmetric similarity solutions for viscous gravity currents spreading on a uniform plane are well-known. The addition of regions of leakage destroys both the symmetry and the self-similarity by introduction of preferred directions and length scales. We examine the effect of such leaks on the asymptotic long-time behaviour of viscous and porous gravity currents in a variety of geometries, showing how novel self-similar structures can emerge in the far-field, fed by quasi-steady near-field solutions that are nonlinear analogues of problems in electrostatics. Matching the two allows predictions of the asymptotic rate of spread and increase in volume of the current. The problems are motivated by the proposed geological sequestration of CO$_2$ and bear on the time scales over which CO$_2$ may be stored in saline aquifers that have an imperfect seal in the cap rock. [Preview Abstract] |
Monday, November 22, 2010 5:32PM - 5:45PM |
LY.00010: Binary solidification in confined geometries: Towards efficient solar cells Tobias M. Schneider, Michael P. Brenner Electrical properties of semiconductors are mainly controlled by the concentration of dopants. While the highest dopant concentrations reachable in most traditional doping methods are limited by the equilibrium solubility of the dopant in the pure semiconductor material, much higher concentrations are observed after femtosecond laser treatment of silicon in a sulfur containing atmosphere. We propose a mechanism underlying \emph{Laser-Hyperdoping} by showing that the Laser induced melting dynamics of the silicon surface in combination with dopant diffusion alone can give rise to the observed high doping concentrations. Modeling the re-solidification of the binary silicon-sulfur mixture in a semi-infinite domain allows to predict the dependence of doping concentrations on depth and provides a method to control the shape of concentration profiles and thereby electrical properties of the semiconductor material. Controlling those properties in a range not accessible to traditional doping methods provides new avenues for optimizing the efficiency of photovoltaic cells. [Preview Abstract] |
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