Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session AQ: Instability: Interfacial and Thin-Film I |
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Chair: Andreas Acrivos, Stanford University Room: 200E |
Sunday, November 22, 2009 8:00AM - 8:13AM |
AQ.00001: Surfactant- and elasticity-induced inertialess instabilities in vertically vibrated liquids Satish Kumar, Balram Suman We investigate instabilities that arise when the free surface of a liquid covered with an insoluble surfactant is vertically vibrated and inertial effects are negligible. In the absence of surfactants, the inertialess Newtonian system is found to be stable, in contrast to the case where inertia is present. Linear stability analysis and Floquet theory are applied to calculate the critical vibration amplitude needed to excite the instability, and the corresponding wavenumber. A previously reported long-wavelength instability is found to persist to finite wavelengths, and the connection between the long-wavelength and finite-wavelength theories is explored in detail. The instability mechanism is also probed and requires the Marangoni flows to be sufficiently strong and in the proper phase with respect to the gravity modulation. For viscoelastic liquids, we find that instability can arise even in the absence of surfactants and inertia. Mathieu equations describing this are derived and these show that elasticity introduces an effective inertia into the system. [Preview Abstract] |
Sunday, November 22, 2009 8:13AM - 8:26AM |
AQ.00002: Anatomy of a wave J\'er\^ome Hoepffner, Ralf Blumenthal, St\'ephane Zaleski A perturbation is induced at the sheared interface between a stream of liquid and a stream of gas. This initial perturbation then evolves as the response of inertia, viscosity and interfacial tension. We observe that the wave obtained by this procedure tends to a self-similar regime after a short transient. We describe the anatomy of this well-defined growing wave as the physical parameter are varied, in particular as the density ratio of the two phases is changed. This study is aimed at identifying a possible recurrent agent in atomization processes. [Preview Abstract] |
Sunday, November 22, 2009 8:26AM - 8:39AM |
AQ.00003: Interfacial flow control in two-phase systems with application to liquid bridges Ilya Ryzhkov, Valentina Shevtsova We perform a theoretical study of thermocapillary flows and their stability in a two-phase system of infinite liquid column surrounded by the gas layer. This study is a complementary step in the JEREMI project (Japanese--European Research Experiment on Marangoni Instability). It is devoted to the development of efficient means for controlling thermocapillary flows in liquid bridges (columns) and scheduled to fly on ISS in 2011. The flows are controlled by applying mechanical stresses to the interface and varying the interfacial heat exchange by blowing gas around the liquid. The analytical solution describing stationary velocity and temperature profiles in the liquid and gas is derived. It is shown that liquid motion can be completely suppressed by the gas flow. The linear stability analysis of stationary flows is performed. It is shown that when the gas flow is opposite to (co-directed with) that of liquid on the interface, the system becomes more (less) stable. It occurs due to mechanical stresses applied to the interface and interfacial heat exchange. Consideration of liquid bridge with the surrounding gas provides better agreement with experimental results than previous calculations without gas phase. [Preview Abstract] |
Sunday, November 22, 2009 8:39AM - 8:52AM |
AQ.00004: Stability and structure formation in films of binary mixtures Santiago Madruga, Uwe Thiele Films of polymer blends are used in technological applications such as coatings or structured functional layers. The evolution of those films is involved by the coupling of decomposition within the film and the dewetting of the film. We present a model for films of binary mixtures, such as polymer blends, with free evolving surfaces. The model is based on model-H describing the coupled transport of concentration and momentum fields supplemented by boundary conditions at the substrate and free surface. We analyze the linear stability of vertically stratified base states of free surface films with respect to lateral perturbations [1]. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. The inclusion of convective transport leads to further destabilization as compared to the purely diffusive case [2]. We study as well the dependence of the instability on parameters such as the Reynolds number, the surface tension number and the ratio of velocities of convective and diffusive transport. [1] U. Thiele, S. Madruga, and L. Frastia. Phys. of Fluids. 19, 122106, (2007). [2] S. Madruga and U. Thiele. To appear in Phys. of Fluids. [Preview Abstract] |
Sunday, November 22, 2009 8:52AM - 9:05AM |
AQ.00005: Dynamics and stability of turbulent falling films Aliki Mavromoustaki, Lennon O'Naraigh, Omar Matar We study the dynamics of thin turbulent films falling under the action of gravity. A base state, corresponding to a waveless film, is obtained by balancing gravity against viscous drag. The latter includes turbulent viscosity contributions characterised by a simple mixing length model. A linear stability analysis of this base state is then carried out leading to the derivation of an Orr-Sommerfeld-type eigenvalue problem. Numerical solutions of this problem reveal a Reynolds number-dependent competition between destabilising contributions arising from the turbulent base state and stabilising ones from the turbulent stresses at the interface and in the bulk. An energy budget analysis demonstrates clearly that the destabilising mode corresponds to an interfacial one. Our results also reveal that the most dangerous mode is in the long-wave regime. This provided motivation for the derivation of a long-wave model for the nonlinear film dynamics, which represents an extension of the Shkadov equations for turbulent falling films. The results of a brief parametric study of this model are presented. [Preview Abstract] |
Sunday, November 22, 2009 9:05AM - 9:18AM |
AQ.00006: Coherent wave structures on falling fluid films flowing down a flexible wall Grigori Sisoev, Richard Craster, Satish Kumar, Omar Matar The dynamics of a thin fluid film flowing down a flexible vertical wall at moderate flow rates is studied in order to identify the dominant wave structures that will be observed in experiments. An asymptotic reduction using boundary-layer theory, and the von K\'arm\'an-Polhausen approximation, leads to coupled partial differential equations governing the nonlinear dynamics of the flow rate, and the gas-liquid and liquid-solid interfaces; closure is provided by a semi-parabolic fluid velocity profile. Fluid inertia, capillarity and viscous retardation effects are incorporated as are wall damping and tension. The validity of our approach is demonstrated using direct comparisons with predictions from the Orr-Sommerfeld equations. Nonlinear steady-travelling waves are identified from a nonlinear eigenvalue problem illustrating a multiplicity of solutions from which the dominating (attracting) solutions can be identified. Subsequent time-dependent numerical simulations of the fully-nonlinear partial differential equations demonstrate the selection of these dominant solutions, and, as such, they then constitute a point of direct comparison with physical experiments. [Preview Abstract] |
Sunday, November 22, 2009 9:18AM - 9:31AM |
AQ.00007: The Effect of Dynamic Wetting on the Stability of a Gas-Liquid Interface Subjected to Vertical Oscillations Andrew M. Kraynik, Louis Romero, John R. Torczynski, Carlton F. Brooks, Timothy J. O'Hern, Richard A. Jepson, Gilbert L. Benavides The stability of an interface in a container partially filled with silicone oil and subjected to gravity and vertical oscillations has been examined theoretically and computationally. An exact theory for the onset of a parametric instability producing Faraday-like waves was developed for arbitrary liquid viscosity, stress-free walls, and deep two-dimensional or axisymmetric containers. Finite-element simulations for stress-free walls are in excellent agreement with the theory, which predicts instability in discrete frequency bands. These simpler calculations are a departure point for examining the more realistic problem, which involves no-slip at the walls and dynamic wetting modeled with a Blake condition. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 22, 2009 9:31AM - 9:44AM |
AQ.00008: On contact line induced instability in flow of hanging fluid films Te-Sheng Lin, Lou Kondic We consider free surface instabilities of films hanging on inverted substrates within the framework of lubrication approximation. Contrary to all the previous works, we include fluid fronts in formulation. It is found that the presence of contact lines leads to free surface instabilities of convective type without any additional natural or excited perturbations. A single parameter $D=(3Ca)^{1/3}\cot\alpha$ , where $Ca$ is the capillary number and $\alpha$ is the inclination angle, is identified as a governing parameter in the problem. This parameter may be interpreted to reflect the combined effect of inclination angle, film thickness, Reynolds number and the fluid flux. Variation of D leads to change of the wave-like properties of the instabilities, allowing to observe traveling wave behavior, mixed waves, and the waves resembling solitary ones, which were observed in many other unstable flows. [Preview Abstract] |
Sunday, November 22, 2009 9:44AM - 9:57AM |
AQ.00009: Draw Resonance in Viscous Sheets Olus Boratav, Zheming Zheng, Alexey Amosov The instability known as the ``draw resonance'' in literature is studied for a viscous sheet considering the visco-gravity balances (Stokes number) and the heating/cooling effects (Stanton number). The analysis considers lubrication approximation for continuity, momentum and energy equations and determines the critical draw ratio for a range of Stokes numbers and Stanton numbers. The critical draw ratio is~very sensitive to the~variation of Stokes and Stanton numbers. It is shown that the decrease in Stokes number and/or the increase in Stanton number results in a decrease in the critical draw ratio. [Preview Abstract] |
Sunday, November 22, 2009 9:57AM - 10:10AM |
AQ.00010: Transience to Instabilty in a Liquid Sheet Nathaniel Barlow, S.P. Lin, Brian Helenbrook Series solutions are found which describe the evolution to absolute and convective instability in an inviscid liquid sheet flowing in an ambient gas and subject to a localized perturbation. These solutions are used to validate spatio-temporal stability predictions for sinuous and varicose modes. We show how recent disagreements in growth predictions stem from assumptions made when arriving at the Fourier integral response. Certain initial conditions eliminate (or reduce the order of) singularities in the Fourier integral. For the sinuous mode, deLuca and Costa (1997) predicted that an impulsive disturbance spreads both upstream and downstream and grows like $t^{1/3}$ when the Weber number is smaller than one. If a Gaussian perturbation is applied to both the position and velocity of the sheet, we observe this behavior in our series solution. However, when the initial disturbance velocity is taken to be zero, we find that the origin decays like $t^{-2/3}$. This is the growth predicted by Luchini (2004). [Preview Abstract] |
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