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 GK: Viscous Flows I |
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Chair: Michael Brenner, Harvard University Room: Hilton Chicago Joliet |
Monday, November 21, 2005 10:34AM - 10:47AM |
GK.00001: 2D Mixed Convection Thermal Incompressible Viscous Flows Blanca Bermudez, Alfredo Nicolas Mixed convection thermal incomprressible viscous fluid flows in rectangular cavities are presented. These kind of flows may be governed by the time-dependent Boussinesq approximation in terms of the stream function-vorticity variables formulation. The results are obtained with a simple numerical scheme based mainly on a fixed point iterative process applied to the non-linear system of elliptic equations that is obtained after a second order time discretization. Numerical experiments are reported for the problem of a cavity with fluid boundary motion on the top. Some results correspond to validation examples and others, to the best of our knowledge, correspond to new results. To show that the new results are correct, a mesh size and time independence studies are carried out, and the acceptable errors are measured point-wise. For the optimal mesh size and time step the final times when the steady state is reached, as solution from the unsteady problem, are reported; it should be seen that they are larger than the ones for natural convection which, physically speaking, show the agreement that mixed convection flows are more active than those of natural convection due to the fluid boundary motion on the top of the cavity. The flow parameters are: the Reynolds number, the Grashof number and the aspect ratio. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GK.00002: Enhancement and reduction of Nusselt numbers in unsteady laminar parallel flows by macroscopic flow control Y. Jiang, G.J. Brereton In fully developed laminar pipe and channel flows that undergo transients from a known initial state, exact analytical solutions for the momentary velocity field as a functional of the flow rate can be determined from the Navier-Stokes equations, for arbitrary flow unsteadiness [\textit{Phys. Fluids} \textbf{12, 3}, 518, (2000)]. When these flows experience heat transfer at their walls, the companion thermal energy equation can be linearized and may also be solved analytically when flow transients are large. Under this restriction, solutions can be found for the instantaneous temperature field, for arbitrary time unsteadiness in both the flow and the wall heat flux. Expressions for Nusselt numbers in convective heat transfer in duct flows with arbitrary temporal flow and heat flux unsteadiness can then be found, which illustrate how the flow and heat flux transient histories determine whether the unsteadiness enhances or reduces the overall heat-transfer effectiveness. These expressions are used to show how significant enhancements or reductions in the average Nusselt number can be achieved in duct flow by applying appropriate temporal bulk-flow control. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GK.00003: Brownian motion in the presence of temperature gradients. Sedimentation-equilibrium phenomena in single-component fluids Howard Brenner Einstein's theory of Brownian motion, which addresses only isothermal fluids, is here extended to situations in which the fluid is subject to an externally imposed temperature gradient. This extension involves adding a temperature-gradient animated ``drift velocity'' ${\rm {\bf U}}_D $ to the diffusive Brownian contribution $D$ appearing in the Fokker-Planck equation governing the coarse-grained conditional probability density. The \textit{ansatz }underlying the theory is derived by elementary sedimentation-equilibrium-type arguments of the type invoked by Einstein in his classic 1905 paper. The underlying theory is supported by experimental thermophoretic data, as well as by a recent theory of diffusive volume transport. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GK.00004: General Solutions of Unsteady Stokes Equations D. Palaniappan The linearized viscous flow at low-Reynolds numbers is described by a pair of partial differential equations connecting the velocity with the pressure field. Many years ago, Lamb proposed an infinite series representation of the general solution for oscillatory flow in terms of three independent scalar functions. On the other hand, spherical geometry provides the most widely used framework for representing small particles and obstacles embedded within a viscous, incompressible fluid characterizing transient creeping flow. In the interest of producing differential representations similar to Papkovich-Neuber and Boussinesq-Galerkin, a general solution in terms of two scalar functions $A$ and $B$ is proposed here for the unsteady Stokes equations. New formulae connecting the differential representation and other solutions describing unsteady viscous flow are provided. In particular, it is shown that the Lamb's general solution follows from the differential representation by a suitable choice of the scalar functions. The connections to other representations are briefly discussed. Another differential representation suitable for bounded flows constrained by plane wall is also given. This general representation is shown to generate solution forms that are suitable for studying oscillatory motions of disks at low Reynolds numbers. The unified approach presented here further demonstrates an important link between oscillatory flows and flow through porous media using Brinkman models. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GK.00005: Elastic-plated gravity currents Neil Balmforth, Andrew Belmonte, Anja Slim We present theoretical models of the fingering and wrinkling of gravity currents overlain by an elastic plate, or ``skin''. The model consists of Stokes equations for the gravity current, and the nonlinear plate equations of von Karman and F\"oppl for the skin. The model rationalizes fingering in terms of the transverse instability of a sharp front, much like surface-tension driven fingering of skinless gravity current. A variety of buckling instabilities are also captured by the model which rationalizes how surface wrinkling may occur. [Preview Abstract] |
Monday, November 21, 2005 11:39AM - 11:52AM |
GK.00006: Study of gravity driven droplets on completely wetting substrates Ryan Haskett, Shomeek Mukhopadhyay, Tom Witelski, Robert Behringer We present a detailed study of gravity driven droplets(silicone oil of viscosities from 10 to 1000 centistokes) on a prewetted silicon wafer. In this study we revisit the scenario of Huppert's 1982 work in which he derived scaling relations for one dimensional motion in the absence of surface tension. Using an interferometric arrangement we find that experimental results indicate a different asymptotic state for the drop which is different form Huppert's classical result. Using a combination of numerics and analytical arguments we show that these deviations are due to the Van der Waals like interactions between the completely wetting substrate and the droplet. This work is supported by NSF Grant No. DMS- 0239125. [Preview Abstract] |
Monday, November 21, 2005 11:52AM - 12:05PM |
GK.00007: Creeping motion of a deformable drop or bubble near an inclined wall Andrew Griggs, Alexander Zinchenko, Robert Davis Experiments were conducted to investigate the gravity-driven motion of a deformable drop or bubble through a viscous liquid in the vicinity of an inclined wall at low-Reynolds number. We study the steady-state drop/bubble velocity as a function of the Bond number, drop-to-medium viscosity ratio, and the wall inclination angle. The drop/bubble is able to approach the wall very closely (to less than 1 percent of the drop radius) in steady motion, even for moderate Bond numbers. The steady drop velocities increase with increasing Bond number and decreasing viscosity ratio for small inclination angles (i.e. less than 15 degrees above horizontal). Viscous drops maintain smaller separations and deform more than bubbles at fixed Bond number over a large range of inclination angles. Experimental results are compared with boundary-integral calculations for an extensive portion of the parameter space. [Preview Abstract] |
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