Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session EB: Non-Newtonian Flows II |
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Chair: Pradeep Bhat, Purdue University Room: Salt Palace Convention Center 150 D-F |
Sunday, November 18, 2007 4:10PM - 4:23PM |
EB.00001: Nonlinear wave evolution in pressure-driven stratified flow of Newtonian and Herschel-Bulkley fluids Prashant Valluri, Kirti Sahu, Hang Ding, Peter Spelt, Omar Matar, Chris Lawrence Pressure-driven stratified channel flow of a Newtonian fluid flowing over a Herschel-Bulkley (HB) fluid is considered. The effects of yield stress and shear-thinning rheology on the nonlinear wave evolution are studied using numerical simulations; the HB rheology is regularized at low shear rates using a bi-viscosity formulation. Two different numerical methods were used to carry out the computations: a level-set method (based on that by Spelt, J. Comput. Phys. 2005) and a diffuse-interface method (based on that by Ding et al., J. Comput. Phys., in press). The simulations, which account for fluid inertia, surface tension and gravity are validated against linear theory predictions at early times. The results at later times show the spatio-temporal evolution into the nonlinear regime wherein waves are strongly deformed, leading to the onset of drop entrainment. It is shown that the apparent viscosity in the region of the HB fluid directly involved in the onset of entrainment is almost constant; unyielded regions are confined to wave troughs at late stages of the nonlinear evolution. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
EB.00002: Elastic turbulence in the Taylor-Couette system with a shear-thinning polymer solution Innocent Mutabazi, Noureddine Latrache, Olivier Crumeyrolle We have investigated the transition scenario to elastic turbulence for a semi-dilute solution of polyethylene oxide in the Couette-Taylor system with fixed outer cylinder. The control parameters are the Taylor number \textit{Ta}, the elastic number $E$ and the viscosity ratio $S$ = \textit{$\eta $}$_{p}$\textit{/$\eta $}$_{s}$ [1,2]. The solution is shear-thinning i.e. the viscosity decreases as the strain increases. The first instability mode from the base flow appears as a pattern of counterpropagating waves with a strong interaction that leads to large second harmonics in space and in time. We have found two regions in the parameter space with different higher instability modes : for small values $E$, a small increase of \textit{Ta} leads to a pattern dominated by spatiotemporal defects and holes, and a further increase of \textit{Ta} leads to spatiotemporal intermittency with determined critical parameters. For intermediate values of $E$, the pattern bifurcates to a pattern formed by large counter-rotating vortices with a localized strong inflow but a weak outflow. These large vortices are have an irregular size is of about 5$d$ where $d$ is the gap size. These vortices have been previously observed in solutions with constant viscosity [3]. [1] S. Muller, E. Shaqfeh {\&} R. Larson, J. Non-Newtonian Fluid Mech. \textbf{46}, 315(1993) [2] O. Crumeyrolle, I. Mutabazi {\&} M. Grisel, \textit{Phys. Fluids} \textbf{14}, 1681(2002) [3] A. Groisman {\&} V. Steinberg, \textit{Phys. Fluids} \textbf{10}, 2451(1998) [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
EB.00003: Development of Flow Instabilities associated with Micro-Channel Flows of Polymer Melts and Polymeric Suspensions: Experimental and modeling studies D.M. Kalyon, H.S. Tang A mathematical model is proposed to simulate the time-dependent circular micro-channel flow of compressible polymers and polymeric suspensions subject to a pressure-dependent wall slip boundary condition. The model relies on the apparent slip mechanism for the suspensions with the additional caveat of the polymer melt also slipping at the wall according to a pressure-dependent Navier's slip condition. The parameters of pressure-dependent wall slip velocity and shear viscosity material function of the polymer melt are determined using combinations of small-amplitude oscillatory shear, steady torsional and squeeze flows, whereas the parameters of the wall slip and the shear viscosity of the suspensions of the polymer melt are determined using squeeze flow in conjunction with inverse problem solution methodologies. Numerical solutions to the mathematical model suggest that steady flow is generated when the flow boundary condition at the wall is stable, i.e., contiguous weak slip or contiguous strong slip along the entire length of the tube wall. However, under conditions at which the flow boundary condition changes from weak to strong slip at any location along the length of the die wall, time-dependent variations in pressure and mean velocity are observed. [Preview Abstract] |
Sunday, November 18, 2007 4:49PM - 5:02PM |
EB.00004: Dynamics of thinning of viscoelastic filaments: scaling analysis and self-similarity Pradeep Bhat, Matteo Pasquali, Osman Basaran Numerical analysis of the formation and pinch-off of viscoelastic filaments is important in numerous applications involving the production of drops. The dynamics in the region close to where pinch-off occurs is known typically to (i) evolve independently of the global dynamics and (ii) be self-similar (Eggers 1993). More recently, Clasen et al. (2006) have demonstrated the existence of self-similar solutions in the corner region where a drop is connected to an adjoining filament. While the former solution is useful in understanding breakup of filaments into drops, the latter could be used in calculating the extensional viscosity of the liquid. Most studies to date have used the 1-D slender filament approximation to probe the self-similar dynamics of thinning viscoelastic filaments. This approximation is clearly invalid in regions where slenderness is lost. Here, we present a full 2-D analysis of the problem in which viscoelasticity is captured using the conformation tensor formalism (Pasquali and Scriven 2002) and the governing equations are solved using a fully-coupled finite element method that has been well benchmarked against experiments (Chen, Notz, and Basaran 2001, 2002). [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
EB.00005: ABSTRACT WITHDRAWN |
Sunday, November 18, 2007 5:15PM - 5:28PM |
EB.00006: Dynamics of Topological Defects around Drops and Bubbles Rising in a Nematic Liquid Crystal Siddharth Khullar, Chunfeng Zhou, James J. Feng We report numerical simulations and experimental observations of topological defects around drops and bubbles that rise through a vertically-aligned nematic liquid crystal. The moving interface is computed in a diffuse-interface framework, and the anisotropic rheology of the liquid crystal is represented by the Leslie-Ericksen theory, regularized to permit topological defects. Results reveal interesting coupling between the flow field and the orientational field surrounding the drop, especially the defect configuration. The flow generally sweeps the point and ring defects downstream, and may transform a ring defect into a point defect. The stability of these defects and their transformation are depicted in a phase diagram in terms of the Ericksen number and the ratio between surface anchoring and bulk elastic energies. The numerical predictions are confirmed by experimental observations with the help of polarizing microscopy. In particular, we provide direct evidence for downstream convection of the Saturn ring defect and its tranformation to a hyperbolic point defect. [Preview Abstract] |
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