Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session G27: Flow Instability: Interfacial and Thin Film III |
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Chair: Fredrik Lundell, KTH Royal Institute of Technology Room: Georgia World Congress Center B315 |
Monday, November 19, 2018 10:35AM - 10:48AM |
G27.00001: Computational analysis of interfacial instabilities in Hele-Shaw cells with small gap gradient Daihui Lu, Federico Municchi, Ivan C. Christov We present a theoretical and numerical study on the stability of the interface between two fluids in a Hele-Shaw cell. Specifically, we consider the effect of a geometric taper in the direction of flow, across a range of capillary numbers $Ca$. We supplement linear stability results with fully-resolved 3D simulations (thus computing the flow field in the Hele-Shaw cell) carried out using the InterFoam solver in OpenFOAM, which employs the volume-of-fluid method to evolve the fluid-phase-field and enhances accuracy via an interface-compressing term in the continuity equation. |
Monday, November 19, 2018 10:48AM - 11:01AM |
G27.00002: Linear stability of viscoelastic film flow over structured surfaces. Dionysis Pettas, George Karapetsas, Yiannis Dimakopoulos, John Tsamopoulos Viscoelastic film flows driven by a body force can be encountered in various engineering applications which range from coating applications in microelectronics to biomedical flows and biofilms. In the literature elastic phenomena are often overlooked since most theoretical works consider the case of Newtonian liquids. The effects of fluid elasticity, though, can play an important role in applications where a viscoelastic liquid is involved as in the case of a polymeric coating solution. In this study, we perform a linear stability analysis for a liquid, that follows the PTT constitutive equation, flowing over a substrate with sinusoidal corrugations. We develop a 2D finite element model and employ Floquet theory to predict the stability of periodic disturbances of arbitrary wavelengths over deep substrate structures. We will present detailed flow stability maps over a wide range of parameters and discuss about the mechanisms through which elasticity affects the present system. We will also discuss about the stability of the flow when it is subjected to 3D disturbances. |
Monday, November 19, 2018 11:01AM - 11:14AM |
G27.00003: Thermo-electrical reflowing of pre-patterned thin films Hadi Nazaripoor, Mohtada Sadrzadeh The electrohydrodynamic (EHD) instabilities are combined with thermocapillary (TC) instabilities to reflow the pre-patterned nanofilms aiming at creating high aspect ratio and well-ordered nanopillar arrays. Thin film (initial thickness of h_{0}) is sandwiched between two electrodes and the electric field and the thermal gradient is applied in the transverse direction. Using the long-wave approximation simplified the governing equations and boundary conditions leading to thin film equation that describes the dynamics and spatiotemporal evolution of the interface. Increasing the height of the protrusions, ξ, leads to a single columnar structure forming (with lower aspect ratio) whereas for the smaller values hierarchical patterns are formed. To have equally-sized pillars and to avoid a multi-scale pattern formation, using ξ/h_{0}≥2 is recommended. The effect of protrusions width is examined on the pattern fidelity and pillars’ aspect ratio.The optimum width ratio of w/Λ_{LS} =0.4 is found as for protrusions with smaller size leads to larger sized pillars with lower aspect ratios. Term Λ_{LS} is the characteristic wavelength for the growth of the instabilities found from linear stability analysis. |
Monday, November 19, 2018 11:14AM - 11:27AM |
G27.00004: Scaling transitions during rupture of thin liquid sheets of power-law fluids Sumeet Suresh Thete, Vishrut Garg, Osman A Basaran Rupture of thin liquid sheets is critical in applications as diverse as crop spraying, foam stability, coating flows, and polymer processing. Here, the van der Waals-driven thinning and rupture of sheets of power-law fluids are analyzed for fluids with a range of Ohnesorge numbers Oh ≡ µ_{0}/√(ρh_{0}σ), where µ_{0}, ρ, h_{0} and σ represent the zero-deformation-rate viscosity, density, initial sheet thickness and surface tension, and power-law exponent n. The variation with time remaining until rupture of the film thickness, lateral length scale, and lateral velocity is determined analytically through asymptotic analysis of the governing spatially one-dimensional partial differential equations obtained by taking advantage of the long wavelength approximation. This analysis is confirmed and extended by numerical solution of the multi-dimensional continuity and Cauchy momentum equations. A plethora of scaling regimes that arise for different dominant balances between inertial, viscous, van der Waals, and capillary forces are identified, and transitions between these regimes are determined and delineated in the parameter space of (Oh, n). |
Monday, November 19, 2018 11:27AM - 11:40AM |
G27.00005: Low-order modelling of inertial instabilities in thick film flows Alexander W. Wray, Radu Cimpeanu, Omar K Matar The expected ranges of applicability of low-order models of film flows have typically been quite restrictive; indeed, for many years good agreement with experiments and numerics was only found for thin films at zero Reynolds numbers. Ruyer-Quil and Manneville have demonstrated that a weighted residual technique can relieve the latter constraint for thin films, while Wray, Papageorgiou and Matar demonstrated that the former can be relaxed at zero Reynolds number. We combine these approaches to investigate the accuracy of low-order models for thick films with moderate levels of inertia, including validation against direct numerical simulations. |
Monday, November 19, 2018 11:40AM - 11:53AM |
G27.00006: Evolution of waves in inertia-dominated thin liquid films flowing over a rapidly rotating disc Jason Stafford, Omar K Matar We study the complex wave regimes in thin film flows over rotating discs through direct numerical simulations (DNS) using a volume-of-fluid approach. Agreement is shown between the DNS results, and experimental data from the literature on global wave features over the disc and local measurements of the film height. With increasing inertial levels, the length of the smooth waveless zone decreases, wave intensity increases, and there is a transition from axisymmetric and spiral waves to three-dimensional waves. The evolution to complex three-dimensional waves begins with a destabilising periodic disturbance of the two-dimensional wavefront. This perturbed wavefront experiences differences in acceleration along the radial direction, amplifying the effect, ultimately leading to small wave humps that break away. A detailed analysis of the flow field within the liquid film shows how the local strain rate is influenced significantly by the presence of the primary wave and the smaller capillary ripples that precede. The parabolic, self-similar shape of velocity profiles within the film are also assessed. |
Monday, November 19, 2018 11:53AM - 12:06PM |
G27.00007: Three-dimensional numerical simulations of a thin film falling vertically down the inner surface of a rotating cylinder Usmaan Farooq, Jason Stafford, Camille Petit, Omar K Matar Whilst gravity driven flow down the inside and outside of a stationary vertical cylinder has been investigated in some detail (Mayo et al., 2013), the flow of thin films associated with a rotating horizontal cylinder (Pougatch and Frigaard, 2011) is rare, and flow down the inside of a vertical rotating cylinder is rarer still. In this study, we focus on the latter, where a thin liquid film flows down a concave surface which itself has an imposed velocity in the azimuthal direction. A key feature of this setup is the presence of waves inclined in the expected direction of flow. An investigation of the wave dynamics is performed using three-dimensional direct numerical simulations and a volume-of-fluid approach to treat the interface. The impact of cylinder Reynolds number on the stability of these falling, rotating films is examined. As Reynolds number increases, the centrifugal force increases, producing a stabilising effect (Iwasaki and Hasegawa, 1981). An analysis of the predicted films provide a detailed insight into the relationship between the wave dynamics and internal flow fields. |
Monday, November 19, 2018 12:06PM - 12:19PM |
G27.00008: Three-dimensional numerical simulations of wave dynamics in falling films Richard V Craster, Assen Batchvarov, Lyes Kahouadji, Mirco Magnini, Lachlan R Mason, Omar K Matar Ever since the ground-breaking experiments by father and son Kapitza & Kapitza, falling films have not stopped fascinating the scientific community (Kapitza and Kapitza, 1949). This problem has since seen a number of experimental and theoretical studies trying to tackle the wave evolution hydrodynamics of falling films (Shkadov, 1970; Alekseenko et al., 1985; Ramaswamy et al, 1996; Karimi and Kawaji, 1998; Park and Nosoko, 2003; Zadrazil and Markides, 2014). The majority of the computational efforts in the field have primarily focused on two-dimensional domains. Attempts have also been made to carry out 3D simulations of falling films on flat plates, however, those are only limited to low Reynolds numbers (Kunugi and Kino, 2005; Yu, 2014). This work aims to study the wave dynamics of planar and circular falling films for a wide range of Reynolds numbers. The numerical investigations are carried out using 3D direct numerical simulations using different codes: a volume-of-fluid solver, and hybrid front-tracking/level-set method code (Shin et al., 2018). Comparisons with experimental data are also performed. |
Monday, November 19, 2018 12:19PM - 12:32PM |
G27.00009: Absolute and convective instabilities in creeping Couette flow with an elastic boundary. Cristobal Arratia, Dhrubaditya Mitra In the zero Reynolds number limit of Stokes flow, the plane Couette flow between moving walls becomes unstable if one of the walls is covered by a layer of soft elastic solid. This instability, which has been studied experimentally and theoretically for a variety of solid constitutive laws, is triggered at the fluid-solid interface where the coupling between these two phases takes place. Considering an incompressible solid in the approximation of linear elasticity, we analytically obtain the dispersion relation in closed form. We relate the origin of the instability to the phase difference between the vertical components of the solid displacement and the fluid velocity at the interface. We then characterize the spatiotemporal properties of the instability, i.e., its absolute/convective nature in different reference frames, with a recent method whereby the imaginary part of the complex wavenumber is related to the observer's velocity by a Legendre transform. |
Monday, November 19, 2018 12:32PM - 12:45PM |
G27.00010: Three-dimensional numerical simulation of solute capillary flow of a binary mixture with a nonlinear surface tension in an annular pool Chuanyin Tang, Jiajia Yu, Yourong Li, Chunmei Wu A series simulations were performed to investigate the influence of the nonlinear surface tension on solute capillary flow of ethanol-water mixture (Sc=888) in an annular pool. The results show that when the solute capillary Reynolds number (Re_{C}) is small, the flow is axisymmetric and steady. When Re_{C} exceeds a threshold of 101, the steady flow convertes to a standing wave. A secondary flow bifurcation occurs at Re_{C}=484, the standing wave transforms into a traveling wave, which is characterized by propagating waves in the azimuthal direction. Compared with the thermocapillary flow of a high Pr fluid with a liner surface tension, the nonlinear surface tension has little effect on the steady flow. However, with the increase of Re_{C}, the surface tension concentration coefficient of the fluid near the inner cylinder is much larger than the other fluid. Therefore, the strength near the inner cylinder and flow bifurcation are respectively greater and more complicated than the thermocapillary flow. Moreover, the nonlinear surface tension promotes the flow instability. |
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