Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C33: Thin Film Theory I |
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Chair: Alexander Wray, University of Strathclyde Room: 615 |
Sunday, November 24, 2019 8:00AM - 8:13AM |
C33.00001: Feedback control of Marangoni instability in a thin film Anna Samoilova, Alexander Nepomnyashchy We use the feedback control for the suppression of Marangoni instability in a thin film heated from below. Our keen interest is focused on the oscillatory mode that was recently revealed in the case of the thermally insulated substrate. We apply the lubrication approximation to derive nonlinear amplitude equations which govern the coupled evolution of the layer thickness and the characteristic temperature. To stabilize the no-motion state of the film we apply the linear feedback control. The principle of such control is that we feed the information about instability back into the dynamics by changing the heat flux through the substrate that can affect the instability. Linear analysis shows that the control of the temperature deviation at the deformable free surface stabilizes the thin film heated from below effectively. To render the subcritical instability supercritical we apply the quadratic feedback control. The weakly nonlinear analysis of the amplitude equations is provided for two types of regime: a pair of the travelling waves and a pair of the standing waves. The conditions of stable supercritical solutions are obtained for both types of regime. [Preview Abstract] |
Sunday, November 24, 2019 8:13AM - 8:26AM |
C33.00002: Linear stability analysis of plane Poiseuille-Couette flow over a permeable surface Saman Hooshyar, Parisa Mirbod The instability of plane Poiseuille-Couette flow (PCF) over a porous medium has been studied extensively due to their wide range of applications in environmental engineering, oil and pharmaceutical industries, and geophysical problems. This study investigates the effect of imposing Couette to the instability of plane Poiseuille flow over a porous surface. We performed linear stability analysis to analyze the impact of upper moving wall on the porous media with different geometrical parameters and to obtain the most unstable perturbation modes. The Navier-Stokes and Brinkman equations are coupled to characterize the behavior of the fluid and porous layers, respectively. It was found that the presence of Couette flow always destabilizes the Poiseuille flow when the velocity of the upper moving wall is smaller than the cutoff velocity, defined as the velocity at which the flow stabilizes and it is a function of the depth ratio and porous resistivity. The flow becomes more stable as the wall velocity exceeds the cutoff velocity. Also, increasing the wall velocity results in an instability mode shift from the fluid layer mode to the porous layer mode. [Preview Abstract] |
Sunday, November 24, 2019 8:26AM - 8:39AM |
C33.00003: Oscillatory states in two-pulse dynamics in falling liquid films Marc Pradas, Dmitri Tseluiko, Serafim Kalliadasis A liquid film flowing down an inclined plane is an example of a convectively unstable open-flow hydrodynamic system with a rich variety of spatiotemporal structures. At the latest stage of the evolution, the film surface is dominated by interacting solitary pulses, which under certain conditions may form bound states. In our previous coherent-structure theories [1-3], we showed that bound states play a crucial role in the dynamics of film flows and can be described in terms of weak interactions. In this study, we analyse strong interactions between pulses and in particular the dynamic states emerging when pulses are sufficiently close to each other, namely oscillatory states. We show that the oscillatory dynamics is associated with a peculiar object, the so-called resonance pole, which may give rise to either self-sustained or damped oscillations, something that largely depends on the particular values of the system parameters and the initial pulse separation length. We find excellent agreement between analytical and numerical work. [1] M. Pradas, D. Tseluiko, S. Kalliadasis. Phys. Fluids 23, 044104 (2011). [2] M. Pradas, S. Kalliadasis, P.-K. Nguyen, V. Bontozoglou. J. Fluid Mech. 716 R2 (2013). [3] D. Tseluiko, S. Kalliadasis. IMA J. Appl. Math. 79, 274 (2014). [Preview Abstract] |
Sunday, November 24, 2019 8:39AM - 8:52AM |
C33.00004: Electrostatic control of instabilities in thick liquid layers Alexander Wray, Radu Cimpeanu We apply a recently developed method for modelling thick flows (Wray et al., 2017) to the Moffatt problem for flow on the outside of a rotating cylinder, and the control thereof using electric fields. Via comparison with Direct Numerical Simulations, we show that good accuracy can be maintained even for thick films at moderate levels of inertia. The nonlocal effect of the electric field solution in particular is examined in detail. [Preview Abstract] |
Sunday, November 24, 2019 8:52AM - 9:05AM |
C33.00005: Low-order modelling of non-axisymmetric flow on the exterior of a fibre James Reilly, Alexander Wray, Stephen Wilson, Omar Matar Flows on the outside of fibres have received extensive attention over the years. Even in the Stokes limit they exhibit interesting behaviour due to dual role of capillarity, exhibiting simultaneously both a destabilising ``hoop stress'' in the azimuthal direction as well as a more conventional stabilising effect in the axial direction. In this limit, the flow is always axisymmetric. However, for sufficiently thick films and with a sufficiently high Reynolds number, non-axisymmetric instabilities are observed. While this has been predicted using linear stability theory and confirmed using direct numerical simulations and experimentation, it has proven problematic to model. Existing models have either required that films be both thin and close to threshold (Shlang and Sivashinsky, 1982) or that the flow be axisymmetric (Ruyer-Quil {\it et al.}, 2008). Using the methodology of Wray {\it et al.}, 2017, we develop a fully nonlinear model for thick flow down the outside of a fibre at moderate levels of inertia. We compare its predictions against those from numerical computations in both the linear and nonlinear regimes to assess its validity, before using it to elucidate the complex interplay of viscosity, capillary, inertia, and gravity that gives rise to the observed flow patterns. [Preview Abstract] |
Sunday, November 24, 2019 9:05AM - 9:18AM |
C33.00006: Nonlinear evolution of a dewetting bilayer thin film on a soft-gel layer Pushpavanam Subramaniam, Dinesh Bhagavatula The nonlinear evolution of dewetting bilayer thin film on a soft-gel is investigated in this work. The fluids are considered to be Newtonian and the soft-gel-layer is modelled as a linear viscoelastic solid. The free surface of the top fluid is exposed to air. The van der Waals attractive forces between the soft-gel layer and the fluids are the primary driving forces responsible for breaking of the thin films. Short range repulsive forces play a key role in the dynamics of the system for very thin bilayers. The nonlinear evolution equations for this system are derived using a lubrication approximation. Linear stability analysis of the system confirms two long wave instabilities one at the liquid-liquid interface and other at the free surface arise in the system. The liquid-liquid instability is dominant when the attractive forces between the soft-gel-layer and the bottom fluid are strong. For a range of parameters both instabilities coexist in the system. The short range repulsive forces can suppress both these instabilities. The soft-gel layer has a destabilizing effect on the long wave instabilities. [Preview Abstract] |
Sunday, November 24, 2019 9:18AM - 9:31AM |
C33.00007: Asymptotics regimes in elastohydrodynamic and stochastic leveling on a viscous film Christian Pedersen, John Niven, Thomas Salez, Kari Dalnoki-Veress, Andreas Carlson We study the relaxation dynamics of an elastic plate resting on a thin viscous film that is supported by a solid substrate. By combining scaling analysis, numerical simulations and experiments, we identify asymptotic regimes for the elastohydrodynamic leveling of a surface perturbation when the flow is driven by either elastic bending of the plate or thermal fluctuations. In both cases we identify two distinct regimes when the perturbation height is either much larger or much smaller than the thickness of the pre-wetted viscous film. Our analysis reveals a distinct crossover between the similarity exponents with the ratio of the perturbation height to the film height. [Preview Abstract] |
Sunday, November 24, 2019 9:31AM - 9:44AM |
C33.00008: A theory for undercompressive shocks in tears of wine Hangjie Ji, Yonathan Dukler, Claudia Falcon, Andrea Bertozzi We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a new model for the climbing dynamics. The new formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus. In the lubrication limit we obtain an equation that is already well-known for rising films in the presence of thermal gradients. Such models can exhibit non-classical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive wave. We observe both compressive and undercompressive waves in new experiments and we argue that, in the case of a pre-coated glass, the famous ``wine tears'' emerge from a reverse undercompressive shock originating at the meniscus. [Preview Abstract] |
Sunday, November 24, 2019 9:44AM - 9:57AM |
C33.00009: Dewetting through Forests of Micropillars Yu Qiu, Ke Xu, Amir Pahlavan, Ruben Juanes When a low-viscosity nonwetting fluid displaces a higher-viscosity wetting liquid in a rough surface consisting of a forest of micropillars, a film of the viscous defending fluid is left behind the advancing fluid-fluid front. Here, we investigate experimentally the dewetting of this residual film, and we contrast it with the dewetting that occurs on a smooth surface. We find that there are three regimes: ``no film'' at low capillary number; ``thick film'' at sufficiently high capillary number, and a novel ``thin film'' regime at intermediate capillary number. In this latter regime, the dewetting occurs as the residual viscous fluid retracts as a film of uniform thickness through (and not over) the micropillars. We propose necessary geometric conditions for the emergence of this new dewetting dynamics, and delineate the different dewetting regimes on a phase diagram, which quantitatively matches lab experiments conducted on a microstructured Hele-Shaw cells. The long-term state of the system induced by dewetting is a pattern of residual film clusters confined in the micropillar forest---a fluid arrangement that impacts macroscopic hydrodynamics and heat transfer efficiency. [Preview Abstract] |
Sunday, November 24, 2019 9:57AM - 10:10AM |
C33.00010: Deformation and dewetting of liquid films under gas jets Chinasa Ojiako, Radu Cimpeanu, Hemaka Bandulasena, Roger Smith, Dmitri Tseluiko We study the deformation and dewetting of a liquid film in a cylindrical beaker under the influence of an impinging gas jet. To obtain initial insight into relevant regimes and timescales of the system, we first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on appropriate decoupling the gas problem from that for the liquid [1-3] and taking into account a disjoining pressure [4]. We also perform direct numerical simulations (DNS) of the full governing equations using two different approaches, the Computational Fluid Dynamics (CFD) package in COMSOL and the volume-of-fluid Gerris package. The DNS are used to validate the results for the thin-film equation and also to investigate the regimes that are beyond the range of validity of this equation. We additionally compare the computational results with experiments and find good agreement.\\ $[1]$ E. O. Tuck, J. Austral. Math. Soc. (Ser. B) 19, 66 (1975)\\ $[2]$ D. Tseluiko and S. Kalliadasis, J. Fluid Mech. 673, 9 (2011)\\ $[3]$ R. Vellingiri, D. Tseluiko and S. Kalliadasis, J. Fluid Mech. 56, 93 (2015)\\ $[4]$ M. Galvagno, D. Tseluiko, H. Lopez and U. Thiele, Phys. Rev. Lett. 112, 137803 (2014) [Preview Abstract] |
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