Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L18: Flow Instability: Interfacial and Thin Films III |
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Chair: Ranga Narayanan, University of Florida Room: 206 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L18.00001: Reactive thin film flows over spinning discs Kun Zhao, Alex Wray, Junfeng Yang, Omar Matar We consider the dynamics of a thin film flowing over a spinning disc in the presence of a chemical reaction, and associated heat and mass transfer. We use a boundary-layer approximation in conjunction with the Karman-Polhausen approximation for the velocity distribution in the film to derive a set of coupled one-dimensional evolution equations for the film thickness, radial and azimuthal flow rates, concentration of the reagents and products, and temperature. These highly nonlinear partial differential equations are solved numerically to reveal the formation of large-amplitude waves that travel from the disc inlet to its periphery. The influence of these waves on the concentration and temperature profiles is analysed for a wide range of system parameters: the Damkohler and Schmidt numbers, the thermal Peclet numbers, and the dimensionless disc radius (a surrogate for the Eckman number). It is shown that these waves lead to significant enhancement of the rates of heat and mass transfer associated with the reactive flow; these are measured by tracking the temporal evolution of local and spatially-averaged Nusselt and Sherwood numbers, respectively. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L18.00002: Thin-film coating of surfactant-laden liquids on rotating cylinders Weihua Li, Satish Kumar Motivated by the need to improve fundamental understanding of the coating of discrete objects, the influence of surfactants on the flow of thin liquid films around rotating cylinders is considered in this work. The lubrication approximation is applied to derive three coupled nonlinear evolution equations describing the variation of the film thickness, surfactant surface concentration, and surfactant bulk concentration as a function of time and the angular coordinate. In the absence of gravitational effects, linear stability analysis reveals that Marangoni stresses suppress the growth rate of instabilities driven by centrifugal forces and hinder the leveling of perturbations to the film thickness. When gravitational effects are present, Marangoni stresses lower the critical rotation rate needed to cause motion of a liquid lobe around the cylinder. These stresses also lead to faster damping of oscillations in the film thickness at relatively short times, but at longer times can increase the oscillation amplitude. In all cases examined, surfactant solubility has the effect of weakening the influence Marangoni stresses. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L18.00003: Dynamics and stability of thin films and drops subjected to magnetic fields Devin Conroy, Alex Wray, Omar Matar We consider the interfacial dynamics of a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly-conducting. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and continuity equations. The magnetisation of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure and velocity fields inside the film. The potential in the gas phase is solved with the use of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape via use of the kinematic condition. The magnetic effects give rise to a non-local contribution. We conduct a parametric study of the system stability to spanwise perturbations in order to evaluate the effects of the magnetic field. Two canonical configurations are considered: constant volume, and constant flux, corresponding to a thin drop and a thin film flowing down the incline. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L18.00004: Faraday instability in electrostatically forced liquid-air systems Kevin Ward, Farzam Zoueshtiagh, Satoshi Matsumoto, Ranga Narayanan When stacked multi-fluid systems are periodically accelerated in a direction normal to the fluid interfaces, complex patterns on the interfaces develop as a result of resonance between the imposed oscillation frequency and the natural frequency of the system, a phenomenon known as Faraday instability. Experimental research at JAXA has successfully generated Faraday instability in electrostatically oscillated liquid-air systems constrained radially by insulating sidewalls and axially by externally controlled electrodes. In this work, we present the design and methodology for electrostatically oscillated experiments, experimentally determined stability curves, and the distinctions and commonalities between mechanically and electrostatically forced Faraday systems. Multiple geometries are examined in order to illustrate the effects of aspect ratio and sidewall boundary conditions. Pure AC forcing and AC forcing with a DC offset are both discussed. Videos of the generated patterns are shown and compared to theoretical predictions of their corresponding Faraday mode shapes. Subharmonic responses with respect to the base state oscillation of the system are observed upon the onset of the instability, a feature indicative of parametric instabilities. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L18.00005: Coherent-structure theory and bound-state formation in electrified falling films Te-Sheng Lin, Dmitri Tseluiko, Mark Blyth, Serafim Kalliadasis We consider a perfectly conducting viscous liquid film flowing down an inclined wall and subjected to a normal electric filed. The electric field introduces a destabilizing non-local term in the long-wave evolution equation [1] and the solutions may evolve into arrays of interacting pulses. We develop a weak-interaction theory for these pulses using elements from previous coherent-structure interaction theories we have developed [2,3]. We show that the standard first-neighbor approximation is no longer valid and it is essential to take into account long-range interactions. We also develop numerical continuation techniques to explore bifurcation diagrams in systems possessing translational symmetry, including traveling waves and spatially varying time-periodic solutions. We find that each bound state bifurcates from the primary branch when continuing with respect to the domain size, and we then construct full bifurcation diagrams taking into account all the bound states. Finally, we compare the bound states for the long-wave evolution equation with the ones found in Stokes calculations and find excellent agreement.\\[4pt] [1] D. Tseluiko et al., J. Fluid Mech. (2006).\\[0pt] [2] D. Tseluiko et al., IMA J. Appl. Math. (2014).\\[0pt] [3] T.-S. Lin et al., SIAM J. Appl. Math. (2015) [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L18.00006: Numerical and experimental study of rotating jet flows Seungwon Shin, Zhizhao Che, Lyes Kahouadji, Omar Matar, Jalel Chergui, Damir Juric Rotating jets are investigated through experimental measurements and numerical simulations. The experiments are performed on a rotating jet rig and the effects of a range of parameters controlling the liquid jet are investigated, e.g. jet flow rate, rotation speed, jet diameter, etc. Different regimes of the jet morphology are identified, and the dependence on several dimensionless numbers is studied, e.g. Reynolds number, Weber number, etc. The breakup process of droplets is visualized through high speed imaging. Full three-dimensional direct numerical simulations are performed using BLUE, a massively parallel two-phase flow code. The novel interface algorithms in BLUE track the gas-liquid interface through a wide dynamic range including ligament formation, break up and rupture. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L18.00007: Instability and pattern formation in electrifield liquid layers Qiming Wang, Demetrios Papageorgiou The stability and axisymmetric deformation of two immiscible, viscous, perfect or leaky dielectric fluids confined in the annulus between two concentric cylinders are studied in the presence of radial electric fields. The fields are set up by imposing a constant voltage potential difference between the inner and outer cylinders. We derive a set of equations for the interface in the long-wavelength approximation which retains the essential physics of the system and allows for interfacial deformations to be as large as the annular gap hence accounting for possible touchdown at the inner or outer electrode. As the layer thickness is asymptotically small, the system recovers the standard (modified) Hammond equation in the absence (presence) of electric fields. For both perfect and leaky dielectric liquids, the full nonlinear system is investigated numerically. It is shown that a two-side touching solution is possible for both the non-electrified and perfect dielectric cases, while only one-side touching is found in the case of leaky dielectric liquids, where the flattened interface shape resembles the pattern solutions found in literature. Meanwhile the finite-time singular solution agrees qualitatively with the experiments. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L18.00008: Feedback control of falling liquid films Alice Thompson, Susana Gomes, Dmitri Tseluiko, Grigorios Pavliotis, Demetrios Papageorgiou Falling liquid films become unstable when the Reynolds number increases above a critical value dependent on slope angle. In the unstable regime, the system first exhibits two-dimensional travelling waves, followed eventually by a transition to chaos. For applications such as coating, a flat, smooth film is desired, while for heat and mass transfer purposes, a non-uniform interface is beneficial. Here we discuss the use of feedback control, based on observations of the film thickness, to enhance or suppress the instability. We use two contrasting long wave models to characterise the system dynamics, and investigate robustness to a number of static and dynamic control strategies for control towards uniform or non-uniform target states. We discuss the differences in control strategy required if feedback is to be delivered by the actuation of suction, heating, or time-dependent topography. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L18.00009: ABSTRACT WITHDRAWN |
Monday, November 23, 2015 6:02PM - 6:15PM |
L18.00010: Self-similarity of solitary pulses on falling liquid films Fabian Denner, Alexandros Charogiannis, Marc Pradas, Christos N. Markides, Berend G.M. van Wachem, Serafim Kalliadasis A gravity-driven liquid film is unstable to long-wave perturbations above a critical Reynolds number. At low frequencies these perturbations evolve into fast solitary pulses. These strongly non-linear structures have a dominant elevation with a long tail and steep front, typically with capillary ripples preceding the main wave hump. We present the results of a comprehensive numerical study of solitary pulses on gravity-driven inertia-dominated water films flowing down an inclined substrate for a range of inclination angles (45-90 degrees), Reynolds numbers (Re$=$20-120) and Kapitza numbers (Ka$=$2765-3887). Our results reveal a self-similarity of solitary pulses on falling films and provide an in-depth understanding of the driving physical mechanisms of such pulses. We formulate a consistent characterisation of the shape and non-linear dispersion of solitary pulses, founded on a newly proposed scaling derived from the Nusselt flat film solution. We present and discuss our findings and resulting correlations with respect to the self-similarity of the shape and non-linear dispersion of solitary pulses as well as the influence of gravity and surface tension on solitary pulses in general. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L18.00011: Parallelised direct numerical simulation of three-dimensional wavy falling films Damir Juric, Jalel Chergui, Lyes Kahouadji, Omar Matar, Seungwon Shin We present a computational study of falling liquid films in a three-dimensional inclined rectangular domain using the new massively parallel code, BLUE. Calculations are carried out in order to obtain several wave patterns such as occasional solitary waves, which travel downstream at a constant velocity, or less coherent structures. BLUE uses parallelization algorithms based on MPI and algebraic domain decomposition. The velocity field is solved by a parallel GMRES method for the viscous terms and the pressure by a parallel multigrid method. The method for the treatment of the fluid interfaces and capillary forces uses a parallelized Front Tracking/Level Set technique which defines the interface both by a discontinuous density field as well as by a local triangular Lagrangian mesh. This structure allows the interface to undergo large deformations including the rupture and/or coalescence of fluid interfaces. [Preview Abstract] |
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