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 M18: Flow Instability: Interfacial |
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Chair: Demetrios Papageorgiou, Imperial College Room: D135 |
Tuesday, November 22, 2016 8:00AM - 8:13AM |
M18.00001: Buckling of thin viscous sheets with inhomogenous viscosity under extensional flows Siddarth Srinivasan, Zhiyan Wei, L Mahadevan We investigate the dynamics, shape and stability of a thin viscous sheet subjected to an extensional flow under an imposed non-uniform temperature field. Using finite element simulations, we first solve for the stretching flow to determine the pre-buckling sheet thickness and in-plane flow velocities. Next, we use this solution as the base state and solve the linearized partial differential equation governing the out-of-plane deformation of the mid-surface as a function of two dimensionless operating parameters: the normalized stretching ratio $\alpha$ and a dimensionless width of the heating zone $\beta$. We show the sheet can become unstable via a buckling instability driven by the development of localized compressive stresses, and determine the global shape and growth rates of the most unstable mode. The growth rate is shown to exhibit a transition from stationary to oscillatory modes in region upstream of the heating zone. Finally, we investigate the effect of surface tension and present an operating diagram that indicates regions of the parameter space that minimizes or entirely suppresses the instability while achieving desired outlet sheet thickness. Therefore, our work is directly relevant to various industrial processes including the glass redraw \& float-glass method. [Preview Abstract] |
Tuesday, November 22, 2016 8:13AM - 8:26AM |
M18.00002: Dynamics of oil film spreading and dewetting on aqueous substrates Jie Feng, Orest Shardt, Howard A. Stone The spreading and dewetting dynamics of liquids on substrates has been studied intensively in recent years because of their fundamental role in nature and fluid dynamics, as well as practical relevance to many technological processes, such as coating flows. However, little is known about the wetting dynamics in a state called pseudo-partial wetting, which can contribute to efficient interfacial emulsification by bubble bursting. Here we describe the dynamics of the rim that forms when an oil film dewets in a pseudo-partial wetting state on an aqueous substrate. We observe that the rim around the expanding hole displays an instability which leads to the rim break-up into a series of humps. By using confocal microscopy and systematically manipulating the parameters of the multi-phase system, we quantify the dynamics of the oil rim and the formation of humps. We further study the mechanism underlying the break-up of the retracting oil rim. In particular, we theoretically explain the critical conditions at which humps form and highlight the roles of competing time scales during hole expansion and the growth of oil humps. Our work not only contributes to the fundamental understanding of film dynamics in pseudo-partial wetting but also may help improve the understanding and utilization of liquid film flows in industrial processes. [Preview Abstract] |
Tuesday, November 22, 2016 8:26AM - 8:39AM |
M18.00003: Faraday instability in two-fluid mechanically forced rectangular and annular geometries Kevin Ward, Farzam Zoueshtiagh, Ranga Narayanan In this work, we theoretically and experimentally investigate Faraday instability in immiscible two-fluid rectangular and annular systems. Within the examined frequency regime, the selected modes are discretized and experiments for comparison to theory are possible. A stress-free sidewall condition is adopted in the theoretical model, and is realized experimentally through careful selection of the testing fluids. Rectangular geometries offer ease of visualization and testing cell fabrication when compared to cylindrical geometries, but can give rise to discrepancies between ideal theory and experiments due to corner effects and wall damping. Theoretical and experimental results for a large square geometry are first presented to highlight the discrepancies due to corner effects. Next, multiple high aspect ratio rectangular geometries, where corner effects should be suppressed, are shown. Annular geometries of comparable dimension to these rectangular geometries are also presented to confirm the absence of corner effects. Agreement between the theoretical and experimental modes for a given frequency are obtained for all geometries. However, agreement between the predicted and observed threshold amplitude is shown to depend strongly on the cell size due to sidewall damping. [Preview Abstract] |
Tuesday, November 22, 2016 8:39AM - 8:52AM |
M18.00004: Interface structure behind a moving contact line Mengfei He, Sidney Nagel When a flat solid substrate straddles the boundary between two fluids (e.g., water and air), there is a contact line where the two fluids and the solid meet. When the substrate is forced to penetrate further in either direction, it distorts the fluid interface and carries along with it a wedge of the trailing fluid. Numerous studies have investigated the onset of the contact-line motion in a two-dimensional geometry where it was assumed that no flows occurred in the direction along the surface of the substrate transverse to its direction of motion.~Contrary to this assumption, we discovered that in steady state the fluid interface develops dramatic three-dimensional structure; there are multiple thin and thick regions of the fluid film alternating in the transverse direction.~Thus the dynamics behind the contact line is not invariant in the transverse direction suggesting the existence of a new instability. We use interference to map the relative shape of this wedge-shaped region and a new interference technique to identify the absolute thickness of the wedge. It is particularly noteworthy that the same structure appears both in dewetting (when a substrate is removed from a liquid into the air) and in wetting (when it is plunged into the liquid). [Preview Abstract] |
Tuesday, November 22, 2016 8:52AM - 9:05AM |
M18.00005: Interfacial instability in vertical counter-current gas-liquid film flow: theory, direct numerical simulation and experiment Patrick Schmidt, Ilja Ausner, Lennon \'{O} N\'{a}raigh, Mathieu Lucquiaud, Prashant Valluri The dynamics of vertical counter-current gas-liquid flows are largely determined by interfacial instability, which gives rise to a multitude of complex wave patterns and internal flows. To study the genesis and evolution of the instability in detail, we employ theoretical stability analysis, experiment and a newly developed level set method based in-house solver to carry out direct numerical simulations. Crucial results of these simulations, such as growth rate and phase velocity of interfacial waves, are rigorously compared against linear and weakly nonlinear theory; thereby showing remarkable agreement. The analysis also reveals the spatio-temporal character of the waves, depicting regimes of absolute and convective instability. Complementing the benchmark set by (non-)linear theory, we perform film thickness measurements of a real gas-liquid system (air-silicone oil) by means of a non-intrusive light-induced fluorescence technique to further validate the solver regarding its capability of capturing interfacial dynamics accurately. These measurements are in good agreement with the results of the nonlinear direct numerical simulations with respect to wavelength and wave shape of the most unstable mode. [Preview Abstract] |
Tuesday, November 22, 2016 9:05AM - 9:18AM |
M18.00006: Transitional inertialess instabilities in driven multilayer channel flows Evangelos Papaefthymiou, Demetrios Papageorgiou We study the nonlinear stability of viscous, immiscible multilayer flows in channels driven both by a pressure gradient and/or gravity in a slightly inclined channel. Three fluid phases are present with two internal interfaces. Novel weakly nonlinear models of coupled evolution equations are derived and we concentrate on inertialess flows with stably stratified fluids, with and without surface tension. These are $2\times 2$ systems of second-order semilinear parabolic PDEs that can exhibit inertialess instabilities due to resonances between the interfaces - mathematically this is manifested by a transition from hyperbolic to elliptic behavior of the nonlinear flux functions. We consider flows that are linearly stable (i.e the nonlinear fluxes are hyperbolic initially) and use the theory of nonlinear systems of conservation laws to obtain a criterion (which can be verified easily) that can predict nonlinear stability or instability (i.e. nonlinear fluxes encounter ellipticity as they evolve spatiotemporally) at large times. In the former case the solution decays asymptotically to its base state, and in the latter nonlinear traveling waves emerge. [Preview Abstract] |
Tuesday, November 22, 2016 9:18AM - 9:31AM |
M18.00007: Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models Demetrios Papageorgiou, Radu Cimpeanu, Anna Kalogirou, Eric Keaveny The nonlinear stability of two-fluid Couette flows is studied using a novel evolution equation whose dynamics are validated by direct numerical simulations (DNS). The evolution equation incorporates inertial effects at arbitrary Reynolds numbers through a nonlocal term arising from the coupling between the two fluid regions, and is valid when one of the layers is thin. The equation predicts asymmetric solutions and exhibits bistability as seen in experiments. Related low-inertia models have been used in qualitative predictions using {\em ad hoc} modifications rather than the direct comparisons carried out here. Comparisons between model solutions and DNS show excellent agreement at Reynolds numbers of $\mathcal{O}(10^3)$ found in experiments. Direct comparisons are also made with the available experimental results of Barthelet et al. (1995) when the thin layer occupies $1/5$ of the channel height. Pointwise comparisons of the travelling wave shapes are carried out and once again the agreement is very good. [Preview Abstract] |
Tuesday, November 22, 2016 9:31AM - 9:44AM |
M18.00008: Singularities of the charge transport equation Omar Matar, Alex Wray, Demetrios Papageorgiou, Qiming Wang It has long been known (since the work of Taylor in the 60s) that electrohydrodynamic interfacial flows can exhibit singularities exemplified by the so-called `Taylor Cone', for instance. Despite the large attention devoted to such flows in the literature, achieving fundamental understanding of these singularities has proved elusive. This is also in spite of the observation that certain parameter regimes appear to demonstrate the unusual phenomenon of cusp-like touchdown (as reported by Wray et al., 2013, to be discussed in the talk). Via the use of mathematical analysis, low-order models, and direct numerical simulations, we classify these singularities and isolate their underlying causes. We also demonstrate where they deviate from experimental predictions, and investigate how such discrepancies may be resolved. [Preview Abstract] |
Tuesday, November 22, 2016 9:44AM - 9:57AM |
M18.00009: Tear Film Dynamics: the roles of complex structure and rheology Mohar Dey, James Feng, Atul S. Vivek, Harish N. Dixit, Ashutosh Richhariya Ocular surface infections such as microbial and fungal keratitis are among leading causes of blindness in the world. A thorough understanding of the pre-corneal tear film dynamics is essential to comprehend the role of various tear layer components in the escalation of such ocular infections. The pre-corneal tear film comprises of three layers of complex fluids, viz. the innermost mucin layer, a hydrophilic protective cover over the sensitive corneal epithelium, the intermediate aqueous layer that forms the bulk of the tear film and is often embedded with large number of bio-polymers either in the form of soluble mucins or pathogens, and finally the outermost lipid layer that stabilizes the film by decreasing the air/tear film interfacial tension. We have developed a comprehensive mathematical model to describe such a film by incorporating the effects of the non-uniform mucin distribution along with the complex rheology of the aqueous layer with/without pathogens, Marangoni effects from the lipid layer and the slip effects at the base of the tear film. A detailed linear stability analysis and a fully non-linear solution determine the break up time (BUT) of such a tear film. We also probe the role of the various components of the pre-corneal tear film in the dynamics of rupture. [Preview Abstract] |
Tuesday, November 22, 2016 9:57AM - 10:10AM |
M18.00010: Marangoni-induced symmetry-breaking pattern selection on viscous fluids Li Shen, Fabian Denner, Neal Morgan, Berend van Wachem, Daniele Dini Symmetry breaking transitions on curved surfaces are found in a wide range of dissipative systems, ranging from asymmetric cell divisions to structure formation in thin films. Inherent within the nonlinearities are the associated curvilinear geometry, the elastic stretching, bending and the various fluid dynamical processes. We present a generalised Swift-Hohenberg pattern selection theory on a thin, curved and viscous films in the presence of non-trivial Marangoni effect. Testing the theory with experiments on soap bubbles, we observe the film pattern selection to mimic that of the elastic wrinkling morphology on a curved elastic bilayer in regions of slow viscous flow. By examining the local state of damping of surface capillary waves we attempt to establish an equivalence between the Marangoni fluid dynamics and the nonlinear elastic shell theory above the critical wavenumber of the instabilities and propose a possible explanation for the perceived elastic-fluidic duality. [Preview Abstract] |
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