Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L18: Flow Instability: Thin Film |
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Chair: Satish Kumar, University of Minnesota Room: D135 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L18.00001: Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids Sumeet Thete, Christopher Anthony, Pankaj Doshi, Michael Harris, Osman Basaran Rupture of thin liquid sheets (free films) is central to diverse industrial and natural phenomena, e.g. foam stability. Rupture of Newtonian films is analyzed under the competing influences of inertial, viscous, van der Waals, and capillary forces by solving numerically a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. As the dynamics close to the rupture singularity is self-similar, the dynamics is also analyzed by solving a set of ordinary differential equations in similarity space. For sheets with negligible inertia, the dominant balance of forces involves solely viscous and van der Waals forces. By contrast, for sheets of inviscid fluids, the dominant balance is between inertial, capillary, and van der Waals forces. For real fluids, the afore-mentioned viscous and inertial regimes are demonstrated to be transitory and hence can only describe the initial thinning of highly viscous and slightly viscous sheets. Moreover, regardless of the fluid’s viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a final inertial-viscous regime in which all forces except capillary force remains important, in accordance with Vaynblat, Lister, and Witelski (2001). [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L18.00002: Intrinsic instability of thin liquid films on nanostructured surfaces Arif Rokoni, Han Hu, Liyong Sun, Ying Sun The instability of a thin liquid film on nanostructures is not well understood but is important in liquid-vapor two-phase heat transfer (e.g., thin film evaporation and boiling), lubrication, and nanomanufacturing. In thin film evaporation, the comparison between the non-evaporating film thickness and the critical film breakup thickness determines the stability of the film: the film becomes unstable when the critical film breakup thickness is larger than the non-evaporating film thickness. In this study, a closed-form model is developed to predict the critical breakup thickness of a thin liquid film on 2D periodic nanostructures based on minimization of system free energy in the limit of a liquid monolayer. Molecular dynamics simulations are performed for water thin films on square nanostructures of varying depth and wettability and the simulations agree with the model predictions. The results show that the critical film breakup thickness increases with the nanostructure depth and the surface wettability. The model developed here enables the prediction of the minimum film thickness for stable thin film evaporation on a given nanostructure. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L18.00003: Liquid-Film Coating on Topographically Patterned Rotating Cylinders Weihua Li, Marcio Carvalho, Satish Kumar The coating of discrete objects having surface topography is an important step in the manufacturing of a broad variety of products. To develop fundamental understanding of this problem, we study liquid-film flow on rotating cylinders having sinusoidal topographical features. The Stokes equations, augmented with a term accounting for centrifugal forces, are solved in a rotating reference frame using the Galerkin finite element method. When gravitational effects are negligible, there is a critical rotation rate below which liquid accumulates over the troughs before merging to form multiple larger drops whose number depends on the topography wavelength and rotation rate. When the rotation rate is above this critical value, liquid accumulates over the crests with similar merging events. When gravitational forces become significant, liquid accumulates over the troughs, leading to a more even distribution of liquid around the cylinder relative to the case where topography is absent. These observations are in agreement with predictions from a lubrication-theory-based model provided that the free-surface curvatures are sufficiently small. For sufficiently large pattern amplitude, recirculation and flow reversal are observed, phenomena that could strongly influence film drying. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L18.00004: Drying of Multicomponent Thin Films on Substrates with Topography Truong Pham, Xiang Cheng, Satish Kumar Drying of multicomponent thin liquid films is an important step in coating and printing processes. In many cases, the substrate on which the film rests may possess topography, either intended or unintended. We present a lubrication-theory-based model describing the fundamentals of drying on such substrates. The film consists of volatile solvent and additional non-volatile components such as colloidal particles, surfactants, and non-volatile solvents. A system of one-dimensional partial differential equations accounting for the film height, depth-averaged concentration of bulk non-volatile components, and interfacial concentration of insoluble surfactant is derived. Evaporation is included using the well-known one-sided description, and the governing equations are solved with finite-difference methods to study various limiting cases. The results highlight the influence of evaporation rate, and thermal, surfactant, and solutal Marangoni flows on the final film thickness and colloidal particle distribution. We find that in a realistic region of parameter space, the addition of a non-volatile solvent yields a dried film that conforms to the substrate topography. [Preview Abstract] |
Monday, November 21, 2016 5:22PM - 5:35PM |
L18.00005: Doubly-excited pulse-waves on flowing liquid films: experiments and numerical simulations Idris Adebayo, Zhihua Xie, Zhizhao Che, Alex Wray, Omar Matar The interaction patterns between doubly-excited pulse waves on a flowing liquid film are studied both experimentally and numerically. The flowing film is constituted on an inclined glass substrate while pulse-waves are excited on the film surface by means of a solenoid valve connected to a relay which receives signals from customised Matlab routines. The effect of varying the system parameters i.e. film flow rate, inter-pulse interval and substrate inclination angle on the pulse interaction patterns are then studied. Results show that different interaction patterns exist for these binary pulses; which include a singular behaviour, complete merger, partial merger and total non-coalescence. A regime map of these patterns is then plotted for each inclination angles examined, based on the film Re and the inter-pulse interval. Finally, the individual effect of the system parameters on the merging distance of these binary pulses in the merger mode is then studied and the results validated using both numerical simulations and mathematical modelling. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L18.00006: Mass transfer in thin films under counter-current gas: experiments and numerical study Mathieu Lucquiaud, Gianluca Lavalle, Patrick Schmidt, Ilja Ausner, Marc Wehrli, Lennon O Naraigh, Prashant Valluri Mass transfer in liquid-gas stratified flows is strongly affected by the waviness of the interface. For reactive flows, the chemical reactions occurring at the liquid-gas interface also influence the mass transfer rate. This is encountered in several technological applications, such as absorption units for carbon capture. We investigate the absorption rate of carbon dioxide in a liquid solution. The experimental set-up consists of a vertical channel where a falling film is sheared by a counter-current gas flow. We measure the absorption occurring at different flow conditions, by changing the liquid solution, the liquid flow rate and the gas composition. With the aim to support the experimental results with numerical simulations, we implement in our level-set flow solver a novel module for mass transfer taking into account a variant of the ghost-fluid formalism. We firstly validate the pure mass transfer case with and without hydrodynamics by comparing the species concentration in the bulk flow to the analytical solution. In a final stage, we analyse the absorption rate in reactive flows, and try to reproduce the experimental results by means of numerical simulations to explore the active role of the waves at the interface. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L18.00007: Three-dimensional modelling of thin liquid films over spinning disks Kun Zhao, Alex Wray, Junfeng Yang, Omar Matar In this research the dynamics of a thin film flowing over a rapidly spinning, horizontal disk is considered. A set of non-axisymmetric evolution 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. These highly nonlinear partial differential equations are then solved numerically in order to reveal the formation of two and three-dimensional large-amplitude waves that travel from the disk inlet to its periphery. The spatio-temporal profile of film thickness provides us with visualization of flow structures over the entire disk and by varying system parameters(volumetric flow rate of fluid and rotational speed of disk) different wave patterns can be observed, including spiral, concentric, smooth waves and wave break-up in exceptional conditions. Similar types of waves can be found by experimentalists in literature and CFD simulation and our results show good agreement with both experimental and CFD results. Furthermore, the semi-parabolic velocity profile assumed in our model under the waves is directly compared with CFD data in various flow regimes in order to validate our model. [Preview Abstract] |
Monday, November 21, 2016 6:01PM - 6:14PM |
L18.00008: Three-dimensional wave evolution on electrified falling films. Ruben Tomlin, Demetrios Papageorgiou, Greg Pavliotis We consider the full three-dimensional model for a thin viscous liquid film completely wetting a flat infinite solid substrate at some non-zero angle to the horizontal, with an electric field normal to the substrate far from the flow. Thin film flows have applications in cooling processes. Many studies have shown that the presence of interfacial waves increases heat transfer by orders of magnitude due to film thinning and convection effects. A long-wave asymptotics procedure yields a Kuramoto-Sivashinsky equation with a non-local term to model the weakly nonlinear evolution of the interface dynamics for overlying film arrangements, with a restriction on the electric field strength. The non-local term is always linearly destabilising and produces growth rates proportional to the cube of the magnitude of the wavenumber vector. A sufficiently strong electric field is able promote non-trivial dynamics for subcritical Reynolds number flows where the flat interface is stable in the absence of an electric field. We present numerical simulations where we observe rich dynamical behavior with competing attractors, including ``snaking'' travelling waves and other fully three-dimensional wave formations. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L18.00009: On self-similar rupture of thin-film equations Michael Dallaston, Dmitri Tseluiko, Zhong Zheng, Marco Fontelos, Serafim Kalliadasis Many interfacial fluid dynamical settings consist of a thin film in the presence of two physical mechanisms, one stabilizing, typically surface tension, and the other one destabilizing. Examples include the Marangoni instability of a film heated from below, Rayleigh-Taylor instability of a film on a cylinder, and film dewetting due to intermolecular forces. Lubrication-type models of these phenomena lead to very similar equations for the evolution of the film thickness, differing only in the exponent of the coefficient function of the destabilizing term. However, the behavior of solutions can vary, depending on the value of this exponent. Here we report the results of analysis based on self-similarity, elements from dynamical systems theory and fully time-dependent computations. We find that branches of self-similar rupture solutions merge at critical values of the exponent, and, surprisingly, there are no stable solutions beyond the first value at which merging occurs. In this regime, time-dependent computations indicate the existence of a cascade of instabilities of increasingly short wavelengths. [Preview Abstract] |
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