Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LK: Viscous Flows II |
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Chair: Howard Brenner, Massachusetts Institute of Technology Room: Hilton Chicago Joliet |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LK.00001: Mixing Properties of Spinning Rods in Low Reynolds Number Fluids Richard McLaughlin, Roberto Camassa, Terry Jo Leiterman We examine the properties of passive tracers advected by motion induced by rods spinning in low Reynolds number fluids. We describe the exact, and asymptotic fluid motion, and in turn study the induced behavior upon the tracers. Comparison of table-top experiments as well as micro fluidic experiments using spinning nano-rods will be made. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LK.00002: The motion of a rod in a rotating Stokes flow James Seddon, Tom Mullin Results are presented of experimental investigations into the motion of a heavy rod in a rotating horizontal cylinder which is completely filled with highly viscous fluid. For a given rotation rate, a short, wide rod ($\xi$ ($=\mathrm{length/diameter}$) $\ll 1$) adopts a fixed position and rotates adjacent to the cylinder wall, in accord with previous measurements for spheres, cf. Ashmore \textit{et al.} [Phys. Rev. Lett. \textbf{94}, 124501 (2005)]. A rotation rate can be ascribed to the rods, which is dependent on the position of the rod as well as the cylinder speed. As in the case of spheres, cavitation bubbles are present and have a direct effect on the motion. Longer rods ($\xi \gg 1 $) exhibit full, 3-dimensional motion and tilt with respect to the cylinder axis. The effect of tilting is the rods drop down the wall and then laterally translate back and forth along it. Further interesting back spin effects are also found over a range of rotation rates. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LK.00003: A pendulum experiment on added mass and equivalence. Russell Donnelly, Douglas Neill, Dean Livelybrooks The concept of added mass in fluid mechanics has been known for many years. A familiar example is the accelerated motion of a sphere through an inviscid fluid which has an added mass of one-half the mass of the fluid displaced. This result is widely used in quantum fluids; for example giving a finite mass to a trapped electron in superfluid helium-4, which is a free electron in a bubble about 36 Angstroms in diameter. A derivation of this result is contained in Landau-Lifshitz ``Fluid Mechanics'', Section 12. The period of oscillation of a simple pendulum in a vacuum is independent of the mass because of the principle of equivalence of gravitational and inertial masses. In a fluid however, both buoyancy and added mass enter the problem. We present results of experiments of simple pendulums of different materials oscillating in various fluids. The results agree closely with the results obtained for the added mass in inviscid fluids, as expected. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LK.00004: Symmetry breaking for drag minimization Marcus Roper, Todd M. Squires, Michael P. Brenner For locomotion at high Reynolds numbers drag minimization favors fore-aft asymmetric slender shapes with blunt noses and sharp trailing edges. On the other hand, in an inertialess fluid the drag experienced by a body is independent of whether it travels forward or backward through the fluid, so there is no advantage to having a single preferred swimming direction. In fact numerically determined minimum drag shapes are known to exhibit almost no fore-aft asymmetry even at moderate \textit{Re}. We show that asymmetry persists, albeit extremely weakly, down to vanishingly small \textit{Re}, scaling asymptotically as \textit{Re}$^{3}$. The need to minimize drag to maximize speed for a given propulsive capacity gives one possible mechanism for the increasing asymmetry in the body plans seen in nature, as organisms increase in size and swimming speed from bacteria like E-Coli up to pursuit predator fish such as tuna. If it is the dominant mechanism, then this signature scaling will be observed in the shapes of motile micro-organisms. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LK.00005: Stress induced cavitation for the streaming motion of a viscous liquid past a sphere Juan Padrino, Daniel Joseph, Toshio Funada, Jing Wang Cavitation induced by stresses in the streaming flow of a viscous liquid past a stationary sphere is studied here. The maximum tension criterion for cavitation used here was proposed by Joseph 1995, 1998: ``Liquids at atmospheric pressure which cannot withstand tension will cavitate when and where tensile stresses due to motion exceed one atmosphere. A cavity will open in the direction of the maximum tensile stress which is 45$^{\circ}$ from the plane of shearing in pure shear of a Newtonian fluid.'' The analysis leads to a dimensionless expression for the maximum tensile stress as a function of position which depends on the cavitation and Reynolds numbers. The main conclusion is that at a fixed cavitation number the cavitation threshold decreases with the Reynolds number and the extent of the region of flow at risk to cavitation increases as the Reynolds number decreases. This prediction that more viscous liquids at a fixed cavitation number are at greater risk to cavitation seems not to be addressed, affirmed or denied, in the cavitation literature known to us. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LK.00006: Reduced Navier-Stokes Equations Near a Flow Boundary Mustafa Kilic, Gustaaf Jacobs, George Haller We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes Equations are defined on the boundary of the original flow domain, hence have reduced spatial dimensionality. This has advantages both for computation and flow control-design. Members of the RNS hierarchy are well-posed if appended with boundary conditions from wall-based sensors. For several benchmark problems, our numerical simulation show close finite-time agreement between the solutions of RNS and those of the full Navier-Stokes equations. [Preview Abstract] |
Tuesday, November 22, 2005 9:18AM - 9:31AM |
LK.00007: Stokesian flow around a slip-particle of an arbitrary shape Sergey Senchenko, Huan J. Keh The Stokes relations for a rigid slightly deformed sphere in an unbounded Stoksean flow are generalized to the case where the surrounding fluid may slip at the surface of the particle (e.g. aerosol particle). To the first order in the small parameter characterizing the deformation, explicit expressions are derived for the hydrodynamic force and torque on the particle. It is demonstrated that these expressions can be derived solely from a knowledge of the solutions of the Stokes equations for the cases where the sphere is held stationary in a flow field which is uniform or pure rotational, respectively. The resulting formulas and flow disturbances are compared with the classical results for a no-slip rigid spherical particle and an axisymmetrical slip -- surface particle. [Preview Abstract] |
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