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 FG: Instability: Interfacial and Thin Films I |
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Chair: Prabir Daripa, Texas A&M University Room: Salt Palace Convention Center 250 A |
Monday, November 19, 2007 8:00AM - 8:13AM |
FG.00001: Linear stability analysis of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid Kirti Sahu, Prashant Valluri, Peter Spelt, Omar Matar The linear stability of pressure-driven channel flow of a Newtonian layer past a non-Newtonian fluid is studied; the latter is assumed to possess a finite yield stress and to exhibit a power-law behaviour. Coupled Orr-Sommerfeld-type eigenvalue equations are derived and solved using a spectral collocation method in the absence of unyielded regions. The numerical solutions of these equations are in agreement with analytical predictions valid in the long-wave limit. Our results indicate that increasing the yield stress (prior to the formation of unyielded regions) and shear thickening tendency of the non-Newtonian fluid promote instability. An analysis of the disturbance `energy' illustrates the presence of an unstable, `interfacial' mode at all Reynolds numbers studied, and an additional, less unstable `shear' mode at relatively high Reynolds numbers. The influence of non-Newtonian rheology on the stability characteristics of these modes is elucidated. [Preview Abstract] |
Monday, November 19, 2007 8:13AM - 8:26AM |
FG.00002: Wave regimes in two-layer channel flow Grigori Sisoev, Daniele Sileri, Chris Lawrence, Omar Matar Interfacial instabilities in two-layer channel flow are studied at moderate flow rates. We use the integral method in conjunction with the Karman-Polhausen approximation to derive coupled evolution equations for the interfacial position and the flow rate in either of the two layers; a similar approach has previously been used to model laminar film flows. Bifurcation theory is used to determine the dependence of the emerging regimes of travelling waves on system parameters. Transient numerical simulations are also carried out, which provide insight into the selection mechanisms of stable waves. [Preview Abstract] |
Monday, November 19, 2007 8:26AM - 8:39AM |
FG.00003: Electrohydrodynamic linear stability of two immiscible fluids in channel flow under the influence of a parallel electric field A. Kerem Uguz, Nadine Aubry The instability of a flat interface between two viscous, immiscible and incompressible liquids in plane Poiseuille flow is studied in the presence of an electric field parallel to the flat interface. In practice, either the stability or instability of the interface is desired depending on the application such as material deposition, mixing, or droplet formation. For that purpose the effect of various parameters was studied via linear stability analysis. The electric field was found to be either stabilizing or destabilizing depending on the electrical properties of the fluids. An interesting feature of this problem is the presence of a second window of stability, namely for some parameters there exist two regions of wavenumbers in which the system is stable. Our results are compared with the case where the electric field is normal to the fluid-fluid interface [1, 2]. \newline \newline [1] O. Ozen, N. Aubry, D. T. Papageorgiou and P. G. Petropoulos, Electrochimica Acta, \textbf{51}, 5316-5323 (2006) \newline [2] F. Li, O. Ozen, N. Aubry, D.T. Papageorgiou and P.G. Petropoulos, Journal of Fluid Mechanics, \textbf{583}, 347-377 (2007) [Preview Abstract] |
Monday, November 19, 2007 8:39AM - 8:52AM |
FG.00004: Nonlinear global modes in miscible coreannular flows Balakrishnan Selvam, Laurent Talon, Eckart Meiburg We perform linear stability analyses and nonlinear simulations of variable viscosity, miscible coreannular flows in cylindrical tubes. For high viscosity ratios, these flows are found to be absolutely unstable, and they exhibit intrinsic oscillations different from the forcing frequency. These self-sustained oscillations give rise to nonlinear global modes. In the supercritical regime, with the core radius being the critical parameter, the nonlinear global mode frequencies match the linear absolute frequencies. This is in accordance with theory when the absolute frequencies are evaluated for the parameters at the inlet. We compare our simulations with recent experiments and observe excellent agreements. [Preview Abstract] |
Monday, November 19, 2007 8:52AM - 9:05AM |
FG.00005: Stability Results on Multi-Layer Hele-Shaw Flows Prabir Daripa The upper bound results on the growth rates in unstable multi-layer Hele-Shaw flows will be derived. The cases treated are constant viscosity layers and variable viscosity layers. The upper bound provides a way to assess cumulative effects of many layers and many interfaces on the growth rates of unstable waves. As an application of the bound, we obtain some sufficient conditions for suppressing instability of two-layer flows by introducing arbitrary number of constant viscosity fluid layers in between. This sufficient condition has very practical relevance because it narrows the choice of internal layer fluids based on surface tensions of all interfaces and viscosities of fluids. Importance of this condition which has been hitherto unknown is also discussed. Other consequences of these upper bounds and sufficient conditions are discussed. The case of internal fluid layers having unstable viscous profiles is also treated for three-layer and four-layer flows only. Implications of these stability results for these various multi-layer flows are discussed and compared from practical standpoint. [Preview Abstract] |
Monday, November 19, 2007 9:05AM - 9:18AM |
FG.00006: Influence of Interface Thickness on the Digitation of Miscible Fluids Georges Gauthier, Alban Aubertin, Jerome Martin, Laurent Talon, Dominique Salin The influence of the interface thickness on miscible viscous fingering instability, has been studied in a Hele-Shaw cell. Using a pair of fluids with a small density contrast, we took advantage of parabolic flights sequences, to either restore a flat thick initial interface under MACROGRAVITY or get rid of buoyancy effects during the unstable displacement under MICROGRAVITY conditions. The experiments demonstrate that the initial thickness of the interface does not affect significantly the instability mechanism, but only postpones the appearance of the digitation. More precisely, the initial thickness delays the formation of a shock in the base state concentration profile, but the shock formation still triggers the instability. [Preview Abstract] |
Monday, November 19, 2007 9:18AM - 9:31AM |
FG.00007: Convective and Absolute Instability of Two Miscible Fluids Core-Annular Flow Marguerite d'Olce, Jerome Martin, Nicole Rakotomalala, Laurent Talon, Dominique Salin To address the issue of the convective or absolute nature of the instability of core annular flows in a pipe, we report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected co-currently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. For a given viscosity ratio, the two experimental control parameters are the total flow rate of the two fluids which monitors the Reynolds number $Re$ whereas the ratio of the two fluid flow rates leads to the relative radius of the core fluid $R_{I}$, under condition of parallel flow. In the space of these two parameters, we characterize experimentally the convective or absolute nature of the instability and delineate the transition between absolute and convective instability. These results are compared linear stability analysis of the problem and numerical simulations. [Preview Abstract] |
Monday, November 19, 2007 9:31AM - 9:44AM |
FG.00008: Sudden Thickening in Flowing Soap Films Walter Goldburg, Stanley Steers, Nikolaus Hartman There is no difficulty in creating soap films that flow vertically downward under gravity at speeds of the order of a m/s. If the height of the film $L_0$ is of the order of 1 m or less, the film thickness $h(x)$ is a few microns (The coordinate $x$ increases downward below the injection point at $x$ = 0.) However if $L_0$ is of the order of 2 m, one finds that $h$ abruptly increases at a sharply defined value of $x =L$. In the experiments to be described, $L \simeq$ =.9 m. As expected, the vertical film velocity $v_x(x)$ correspondingly drops to a small fraction of its upstream value at $x \simeq L$. In the narrow transition region from thin to thick film at $x=L$, both $h(x)$ and the $v_x(x)$ oscillate at a well-defined frequency of the order of 1 Hz. The abrupt thickening is expected on the basis of singular perturbation theory (T. Tran, following paper). [Preview Abstract] |
Monday, November 19, 2007 9:44AM - 9:57AM |
FG.00009: Abrupt thickening of soap films Tuan Tran, Pinaki Chakraborty, Gustavo Gioia, Nigel Goldenfeld In steady-state experiments with soap films flowing vertically downward under gravity (Goldburg et al., preceding paper), Goldburg has observed a curious phenomenon. If the height of the film is more than about 1 m, the film becomes thinner and thinner in the direction of the flow, but then it thickens abruptly at a certain distance from the top, and it remains constant thereafter. The flows in these experiments are low Reynolds-number flows and the thickness of the film depends only on the distance from the top. Based on lubrication theory, we obtain an ODE for $h(x)$, where $h$ is the thickness of the film and $x$ is the distance from the top. Via computational and theoretical analyses of this ODE, we make detailed predictions and show that these predictions (a) compare well with the experimental measurements and (b) provide an explanation for the abrupt thickening observed by Goldburg et al. [Preview Abstract] |
Monday, November 19, 2007 9:57AM - 10:10AM |
FG.00010: Resolution Requirements for Direct Numerical Simulation of Unstable Sheared Interfaces Svetlana Sushchikh, Robert Nourgaliev, Suthee Wiri Direct Numerical Simulations of sheared interfaces in immiscible fluids are discussed, with a particular focus on prediction of interfacial (Yih-) instability in a wide range of flow parameters and wavenumbers. Both, Sharp-Interface (SIM) and Diffuse-Interface (DIM) methods are considered. Using Orr-Sommerfeld analyses for sharp and for diffuse interfaces, we identify the instability-driving, interfacial critical layer mechanism, and we show that a sufficiently thin and resolved diffuse layer can be made to approach a Yih-instability behavior. With SIM, it is found that simply resolving the critical layer (typically 10 nodes over the distance of the critical layer from the interface) is quite sufficient. Providing that the resolved DIM is as good as diffuse-interface Orr-Sommerfeld (O-S) method, the O-S analysis provides guidelines for how thin the diffuse interface should be in order to approach the Yih mode. We find that even with O-S greatly augmented with virtual interfaces and quadruple precision, in many cases the approach to Yih is so gradual in the high wavenumber range so as to remain incomplete and beyond the capability of the computation. [Preview Abstract] |
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