Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session GD: Interfacial and Thin-Film Instability IV |
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Chair: Omar Matar, Imperial College Room: Tampa Marriott Waterside Hotel and Marina Grand Salon CD |
Monday, November 20, 2006 10:30AM - 10:43AM |
GD.00001: Long-wave dynamics in two-layer channel flow Chris Lawrence, Grigori Sisoev, Omar Matar The dynamics of an interface separating two viscous fluids in a channel are examined. The flow is taken to be either laminar in both layers or turbulent in one of them. In each case, asymptotic reduction and the integral method are used to derive a single evolution equation for the interface, which accounts for inertia, capillarity and shear stress. These equations are shown to reduce to Benney- like equations and the Kuramoto-Sivashinskii equation in the thin film limit. The linear stability characteristics of the interface in the long-wave limit are analysed and compared to those obtained via solution of the Orr-Sommerfeld equation. Bifurcation theory is then used to catalogue the various periodic wave regimes that accompany the flow as a function of system parameters. Finally, transient numerical simulations are carried out in order to elucidate the wave selection mechanism downstream of the channel inlet. [Preview Abstract] |
Monday, November 20, 2006 10:43AM - 10:56AM |
GD.00002: Landau-type saturation of weakly unstable disturbances in interfacial-surfactant instability David Halpern, Alexander Frenkel We study the weakly-nonlinear limit of the previously derived coupled evolution equations for the disturbances to the position of the interface and the concentration of an insoluble surfactant, in certain longwave regimes. In general, small disturbances of the semi-infinite two-fluid shear flow always grow to be non-small, so--in contrast to a number of other similar flows--there is no regime in which the nonlinear saturation can be described by weakly-nonlinear equations$^*$. However, for spatially periodic disturbances with the period slightly exceeding that of the marginal linear mode of the longwave instability, the saturation occurs with small amplitudes. We verify the fact that considering the interaction of the fundamental and the first overtone gives a good approximation. Next the problem is reduced to a nonlinear system of four ordinary differential equations, which is solved by using multiple time scales. The slow leading-order amplitude evolution and the saturated traveling wave are described by four coupled Landau-type equations with cubic nonlinearities. These follow from the non-secularity conditions for the diagonalized non-homogeneous linear system governing the next-order amplitude corrections, whose four-by-four coefficient matrix has a double zero eigenvalue. \\ $^*$A. Frenkel and D. Halpern, http://arxiv.org/pdf/nlin.CD/0601025. [Preview Abstract] |
Monday, November 20, 2006 10:56AM - 11:09AM |
GD.00003: Interfacial instability of rotating liquid-liquid two-phase flow Shuhei Fujimoto, Shizuo Yoshida, Yuji Tasaka, Yasushi Takeda Rotating a cylindrical container that contains oil and water deforms the interface between oil and water. While the interface near the center of the container rises up, near the wall of it comes down. Furthermore, certain instability wave propagates on the interface. The aim of this study is to investigate the instability mechanism of the rotating oil-water liquid-liquid two-phase flow. A velocity profile of the rotating flow was analyzed theoretically. The boundary conditions at the oil-water interface are given from a solution of momentum diffusion equation. The theoretical velocity profile was in good agreement with result of flow visualization by using fluorescein dye and hydrogen bubbles. [Preview Abstract] |
Monday, November 20, 2006 11:09AM - 11:22AM |
GD.00004: Stability of Liquid Bridges Subject to Shear-Induced Flow Abdullah Uguz, Nick Alvarez, Ranga Narayanan The volume of liquid held between two solid disks is called a liquid bridge. Liquid bridges have often been investigated for their importance in technological applications, particularly in the floating-zone method for crystal growth of semi-conductors. In this technique a molten zone, i.e., a liquid bridge is created between a polycrystalline feed rod and a monocrystalline seed rod. To control the escape of volatile constituents, encapsulants are added and the float zone is concentrically surrounded by an immiscible liquid. The thermocapillary convection in the presence of an encapsulant generates a shear flow and this shear flow has an effect on the bridge stability. Our interest lies in the stability of the zone in the presence of shear flow. In this study, the flow is created by moving the outer wall that surrounds the encapsulant. It is shown that a returning flow in both the encapsulating liquid and the bridge offers stability of a non-vertical bridge depending on the direction of shear. [Preview Abstract] |
Monday, November 20, 2006 11:22AM - 11:35AM |
GD.00005: Absolute Instability of Miscible Coreannular Flow Balakrishnan Selvam, Laurent Talon, Eckart Meiburg In this study, we perform a spatial stability analysis of variable viscosity, miscible coreannular flows. Although it is well known that this configuration can be unstable, recent experiments have shown that instability appears at a fixed location in the laboratory frame of reference. This behavior suggests that the system might have the behavior of absolute instability, exhibiting intrinsic characteristics. In order to validate this hypothesis, we perform a local spatial stability analysis of the flow. We investigate the influence of different parameters, namely the core radius, the viscosity contrast, the Reynolds and Peclet numbers, and the interface thickness. In accordance with the experiments, the results show that this system does exhibit the characteristics of absolute instability for some range of core radius and Reynolds number. [Preview Abstract] |
Monday, November 20, 2006 11:35AM - 11:48AM |
GD.00006: On the motion of an annular viscous jet Linda Smolka, Justin North, Bree Guerra We experimentally examine the motion of an annular jet of viscous fluid flowing down the outside of a thin, vertical fiber. As other authors have observed, perturbations develop along the free surface of the jet; our focus is on the instability that leads to the formation of these perturbations. We observe a striking transition in the perturbation dynamics at a critical flow rate, $Q_c$. Above $Q_c,$ the distance from the orifice that perturbations form oscillates in time, and the spacing between perturbations varies, typically leading to the coalescence of neighboring perturbations. For fixed $Q$ below $Q_c,$ the distance from the orifice that perturbations form is constant, and the spacing between consecutive perturbations remains fixed as they travel down the length of the fiber (2 meters). We find the growth of the perturbations is initially rapid followed by a slower phase as they saturate in size. We compare the nascent perturbation growth to theoretical predictions developed from a long-wave model (Craster \& Matar, J. Fluid Mech. 553, 85-105 (2006)). [Preview Abstract] |
Monday, November 20, 2006 11:48AM - 12:01PM |
GD.00007: Instability patterns in a miscible core annular flow Marguerite D'olce, Jerome Martin, Nicole Rakotomalala, Dominique Salin, Laurent Talon Laboratoire FAST, batiment 502, campus universitaire, 91405 Orsay Cedex (France). Experiments are performed with two miscible fluids of equal density but different viscosities. The fluids are injected co-currently and concentrically into a cylindrical pipe. The so-obtained base state is an axisymmetric parallel flow, for which the ratio of the flow rates of the two fluids monitors the relative amount (and so the radius) of the fluids. Depending on this relative amount and on the total flow rate of the fluids, unstable axisymmetric patterns such as mushrooms and pearls are observed. We delineate the diagram of occurrence of the two patterns and characterize the instabilities. [Preview Abstract] |
Monday, November 20, 2006 12:01PM - 12:14PM |
GD.00008: Large-amplitude wave evolution in two-layer pressure-driven flow Prashant Valluri, Peter Spelt, Chris Lawrence, Geoff Hewitt Large-amplitude wave evolution is investigated numerically for two-layer pressure-driven flow, with possible applications in slug initiation. The flow is laminar, 2D and involves two fluids that are of different density and viscosity. The numerical (level-set) method is verified by comparison with the Orr-Sommerfeld-type analysis for this flow, at small amplitudes. The wave growth in the linear regime is shown to be caused by the viscosity contrast. It is shown that waves of relatively large wave length trigger shorter waves (approximately corresponding to the most dangerous mode). Coalescence of the short waves eventually lead to a relatively long wave of very large amplitude. These findings are discussed in the context of previous experimental observations of slug initiation. [Preview Abstract] |
Monday, November 20, 2006 12:14PM - 12:27PM |
GD.00009: Breakup of a finite length fluid film Javier Diez, Lou Kondic We study the process of dewetting of thin liquid films using a long-wave approximation for the film thickness, $h$, under partial wetting conditions. The governing equation for $h$ includes the effects of surface tension as well as those of the gravity force, and incorporates an additional conjoining/disjoining pressure term to account for intermolecular forces. We perform standard linear stability analysis of infinite flat films, and identify the corresponding stable, unstable and metastable regions. Within this framework, we analyze the evolution of a semi-infinite film of length $L$ in one direction. The numerical simulations show that for long and thin films, the dewetting at the extremes of the strip generates a pearling process consisting of successive stages of formation of bumps at the ends and consecutive pinch off behind these bumps. On the other hand, for shorter and thicker films, the evolution ends up by forming a single central drop. The time evolution as well as the final drops pattern shows a competition between the dewetting mechanisms caused by nucleation and by free surface instability. [Preview Abstract] |
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