Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q22: Flow Instability: Viscous Fingering and FilmsInstabilities
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Chair: Prabir Daripa, Texas A&M University Room: 708 |
Tuesday, November 21, 2017 12:50PM - 1:03PM |
Q22.00001: Oxidation-Mediated Fingering in Liquid Metals Karen Daniels, Collin Eaker, David Hight, John O'Regan, Michael Dickey We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a gallium-based liquid metal alloy to values approaching zero, thereby inducing drastic shape changes, including the formation of fractals. The measured fractal dimension ($D = 1.3 \pm 0.05$) places the instability in a different universality class than other fingering instabilities. By characterizing changes in morphology and dynamics as a function of droplet volume and applied electric potential, we identify the three main forces involved in this process: interfacial tension, gravity, and oxidative stress. Importantly, we find that electrochemical oxidation can generate compressive interfacial forces that oppose the tensile forces at a liquid interface. Thus, the surface oxide layer not only induces instabilities, but ultimately provides a physical and electrochemical barrier that halts the instabilities at larger positive potentials. [Preview Abstract] |
Tuesday, November 21, 2017 1:03PM - 1:16PM |
Q22.00002: The Stability and Interfacial Motion of Multi-layer Radial Porous Media and Hele-Shaw Flows Craig Gin, Prabir Daripa In this talk, we will discuss viscous fingering instabilities of multi-layer immiscible porous media flows within the Hele-Shaw model in a radial flow geometry. We study the motion of the interfaces for flows with both constant and variable viscosity fluids. We consider the effects of using a variable injection rate on multi-layer flows. We also present a numerical approach to simulating the interface motion within linear theory using the method of eigenfunction expansion. We compare these results with fully non-linear simulations. [Preview Abstract] |
Tuesday, November 21, 2017 1:16PM - 1:29PM |
Q22.00003: Artificial neural network for simulation of thin liquid films over spinning discs Dunhui Xiao, Kun Zhao, Omar K. Matar In this research the dynamics of a thin film flowing over a rapidly spinning, horizontal disc is considered. A set of non-axisymmetric evolutional equations for the film thickness, radial and azimuthal flow rates are derived using a boundary-layer approximation in conjunction with the Karman-Polhausen approximation for the velocity distribution in the film. The numerical solutions of these highly nonlinear partial differential equations are obtained from a finite difference scheme which are computationally expensive. For this reason, we investigate utilizing the Integral Boundary Layer (IBL) model with a neural network (NN) model to predict the evolution of waves following the simulation of the IBL equations under the same operation condition (e.g. rotational speed, initial flow rate), or even under conditions where the traditional numerical schemes yield no solutions. The NN is trained on a dataset from multiple simulations from the IBL model and then used to simulate film evolution from outside this set. Overall, the resulting model predicts the evolution of waves under the various operation conditions reasonably well when compared with the full numerical solution. [Preview Abstract] |
Tuesday, November 21, 2017 1:29PM - 1:42PM |
Q22.00004: Thin films coating the interior of cylindrical substrates: from rivulets to dripping droplets Francois Gallaire, Gioele Balestra, Nicolas Kofman, Pierre-Thomas Brun, Benoit Scheid A liquid film coated on the underside of a planar substrate is subject to the Rayleigh-Taylor instability so that its interface deforms into waves that lead to the formation of dripping droplets. When the substrate is curved, gravity not only acts as the destabilizing force at the origin of the instability but also as a stabilizing force originating in the progressive drainage of the film. As a consequence, a two-dimensional thin-film in a circular geometry is asymptotically stable to infinitesimal perturbations. Nevertheless, we have found that the system acts as a strong transient amplifier. A transverse instability appears for moderator Bond numbers (gravity over surface tension forces ratio). The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most unstable mode of the classical Rayleigh-Taylor instability. On the other hand, when the Bond number is high, a two-dimensional lattice of droplets prevails. We investigate the characteristics of the rivulet flow, as well as the transition between the two instability types both theoretically and experimentally. A linear stability analysis based on lubrication equations is performed and the results are found to be in good agreement with experiments and numerical simulations. [Preview Abstract] |
Tuesday, November 21, 2017 1:42PM - 1:55PM |
Q22.00005: 35. Reduced-order models for two-phase annular flows in vertical pipes Thomas Ewers, Kun Zhao, Omar K. Matar Two-phase annular flow in vertical pipes is studied under conditions wherein gas (liquid) entrainment into the liquid (gas) is neglected. The gas core is taken to be turbulent whilst the thin annular film is assumed to be laminar. Reduced-order models are developed using asymptotic analysis for axisymmetric and non-axisymmetric flows. Turbulence is modelled using a Reynolds-averaged Navier-Stokes equations approach via a mixing length relation. A reduced-order model is developed to include temperature variations for the axisymmetric case only. Numerical simulations are carried out, which reveal the development of large-amplitude waves in the axisymmetric, and non-axisymmetric cases; only results for the isothermal case are presented. Comparisons with results obtained from full-scale direct numerical simulations of the annular flow are also presented. [Preview Abstract] |
Tuesday, November 21, 2017 1:55PM - 2:08PM |
Q22.00006: Air-driven viscous film flow coating the interior of a vertical tube H. Reed Ogrosky, Roberto Camassa, Jeffrey Olander We discuss a model for the flow of a viscous liquid film coating the interior of a vertical tube when the film is driven upwards against gravity by airflow through the center of the tube. The model consists of two components: (i) a nonlinear model, exploiting the slowly-varying liquid-air interface, for the interfacial stresses created by the airflow, and (ii) a long-wave asymptotic model for the air-liquid interface. The stability of small interfacial disturbances is studied analytically, and it is shown that the modeled free surface stresses contribute to both an increased upwards disturbance velocity and a more rapid instability growth than those of a previously developed model. Numerical solutions to the long-wave model exhibit saturated waves whose profiles and velocities show improvement, with respect to the previous model, in matching experiments. The model results are then compared with additional experiments for a slightly modified version of the problem. [Preview Abstract] |
Tuesday, November 21, 2017 2:08PM - 2:21PM |
Q22.00007: Thermally driven film climbing a vertical cylinder Linda Smolka The dynamics of a Marangoni driven film climbing the outside of a vertical cylinder is examined in numerical simulations of a thin film model. The model has three parameters: the scaled cylinder radius $\hat{R},$ upstream film height $h_{\infty}$ and downstream precursor film thickness $b,$ and reduces to the model for Marangoni driven film climbing a vertical plate when $\hat{R} \to \infty.$ The advancing front displays dynamics similar to that along a vertical plate where, depending on $h_{\infty},$ the film forms a Lax shock, an undercompressive double shock or a rarefaction-undercompressive shock. A linear stability analysis of the Lax shock reveals the number of fingers that form along the contact line increases linearly with cylinder circumference while no fingers form below $\hat{R} \approx 1.15$ with $b=0.1.$ The substrate curvature controls the Lax shock height, bounds on $h_{\infty}$ that define the three solutions and the maximum growth rate of perturbations when $\hat{R}=O(1),$ whereas the shape of solutions and the stability of the Lax shock converge to the behavior on a vertical plate when $\hat{R} \ge O(10).$ The azimuthal curvatures of the base state and perturbation, arising from the annular geometry of the film, promote instability of the advancing contact line. [Preview Abstract] |
Tuesday, November 21, 2017 2:21PM - 2:34PM |
Q22.00008: Linear Stability analysis of a Newtonian film flowing over a substrate with topographical features Yiannis Dimakopoulos, Dionisis Pettas, George Karapetsas, John Tsamopoulos In a typical coating process, liquid flows under the action of a body force and coats a substrate of variable topography leaving a thin film on it. The wetting state of the substrate is highly dependent on its geometric characteristics and the liquid properties. The liquid may fully wet (Wenzel state), not wet (Cassie state) or partially wet it. It is important to determine the prevailing steady flow patterns and their stability. The former has been studied by examining the 2D steady flow over a structured surface either by solving the 2D NS equations or by using the lubrication approximation. In this work, we consider the stability of the 2D steady solution by performing a linear stability analysis subjected to 2D and 3D perturbations. We employ the finite element method to solve the full NS equations to examine cases where the lubrication approximation is not applicable and investigate the stability of all flow configurations: Wenzel, Cassie, and partially wetted states. It is shown that the fully wetted state in the lubrication limit is stable in line with previous studies. Moving away from the lubrication limit, though, we find that the flow becomes unstable for finite Re, when long- or short-wave instabilities arise. The stability of partially wetting states will also be discussed. [Preview Abstract] |
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