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 M16: Flow Instability: Interfacial and Thin Films IV |
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Chair: L Mahadevan, Harvard University Room: 204 |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M16.00001: Elastohydrodynamics of a free cylinder near a soft wall L Mahadevan, Thomas Salez We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall. We use scaling arguments to establish different regimes of settling, sliding, rolling and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of behaviours such as spontaneously oscillations when sliding, lift via a Magnus-like effect, a spin-induced reversal effect, and an unusual sedimentation singularity. Our description also allows us to address a sedimentation-sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M16.00002: Effect of surfactants on inverted thin film flow Dominic Henry, Jamal Uddin, Jeremy Marston, Mohammad Mansoor, Sigurdur Thoroddsen We investigate the stability of a thin film containing insoluble surfactant that is flowing along the underside of an inclined plane, sloped at an angle $\theta$, taking the small $\theta$ limit so that the incline is near horizontal. Two cases are examined; as well as a single layered film, a two-layer film is considered whereby each liquid layer contains surfactant. The waveless solution in both cases is perturbed and a linear stability analysis conducted, with a discussion on the corresponding growth rates of the perturbations. This work is then compared to an experimental investigation, whereby the underside of a slide-fed coating die is considered as the inclined plane, and a series of liquid threads are formed with a uniform spacing. This thread spacing is compared to the most unstable mode of the preceding stability analysis, shown to improve upon the classical Rayleigh-Taylor wavelength which considers a constant surface tension. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M16.00003: Oscillatory behavior in two-pulse dynamics in active-dissipative systems Marc Pradas, Te-Sheng Lin, Dmitri Tseluiko, Serafim Kalliadasis Coherent structures appear in a wide variety of active-dissipative systems and are typically characterized by a rich and complex dynamics emerging as a consequence of their interaction. An example is the dynamics of a liquid film flowing down an inclined plane with the free surface of the film described by interacting solitary pulses, which under certain conditions may form bound states.\\ In our previous coherent-structure theories [1,2], we showed that bound states play a crucial role in the dynamics of film flows. In this study, we present a rigorous analysis of other 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).\\ $[$2$]$ D. Tseluiko, S. Kalliadasis. IMA J. Appl. Math. 79, 274 (2014). [Preview Abstract] |
Tuesday, November 24, 2015 8:39AM - 8:52AM |
M16.00004: Interfacial instability of thin liquid films at the walls of a parallel-plate channel, sheared by pressure-driven gas flow Mikl\'os V\'ecsei, Mathias Dietzel, Steffen Hardt Gas flow between liquid films is a commonly used model system for flows in the respiratory system and is also present during flow boiling in microchannels. The emergence of long-wavelength interfacial instabilities due to viscous stresses is a well-known property of these systems. We show that its description is often reducible to two coupled partial differential equations. Thus the characteristic quantities, such as the most unstable wavelength and the marginally stable wavenumber, can be obtained in a straightforward manner from the linear stability analysis. The analysis of the weakly nonlinear equations shows that if the material properties of the liquid films and their undisturbed thicknesses are identical, their interfaces should only be destabilized by the inertial forces. Moreover, for this configuration the emerging patterns on the two interfaces are found to be identical in the long-time limit. A different setup, where the liquid films have identical material properties, but their undisturbed thicknesses differ, is studied numerically. The results show that even for this configuration the interfacial deformations of the two films remain closely correlated for a broad range of parameters. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M16.00005: Direct Numerical Simulation of Nanofilm Instability Driven by Liquid/Solid Interactions Kyle Mahady, Shahriar Afkhami, Lou Kondic The nanoscale interaction between liquid and solid molecules underlies fundamental phenomena for systems involving liquids on surfaces. In addition to giving rise to the contact angle of drops, this interaction drives the spontaneous rupture of nanofilms. We study this process by means of direct simulation of the Navier-Stokes equations using the Volume of Fluid interface tracking method. Our numerical method simulates the liquid/solid interaction, and permits the study of the film rupture process with inertial effects and arbitrarily large contact angles, in both two and three dimensions. We focus in particular on the evolution of length scales in a perturbed film as it breaks up, and the spatial organization of the resulting drops. We compare our results to recent experiments, where this instability mechanism has been harnessed for the self-assembly of ordered arrays of metallic nanoparticles (ACS App. Mat. and Int., 2014, 6, 5835). [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M16.00006: Temporal interfacial instability in vertical gas-liquid flows Patrick Schmidt, Lennon \'{O} N\'{a}raigh, Mathieu Lucquiaud, Prashant Valluri We consider onset and dynamics of interfacial instability in gas-liquid flows, using two-dimensional channel flow of a thin falling film sheared by counter-current gas as a model. Our methodology consists of linear stability theory together with DNS of the two-phase flow in the case of nonlinear disturbances. We study the influence of three main flow parameters (density contrast between liquid and gas, film thickness, pressure drop applied to drive the gas stream) on the interfacial dynamics. Energy budget analyses based on Orr-Sommerfeld theory reveal coexisting unstable modes (interfacial, shear, internal) in the case of high density contrast, resulting in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. DNS of this scenario shows that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. In comparison, although linear stability theory successfully determines the most-dominant features in the interfacial wave dynamics at early-to-intermediate times in a high-density-contrast case, short waves selected by linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic. [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M16.00007: Dripping under an inclined plane Nicolas Kofman, Francois Gallaire, Benoit Scheid A liquid film flowing above an inclined plane can be unstable due to inertial effects : this instability, first studied by Kapitza in 1948, is always of convective nature. When the plane is reversed, there is also a destabilizing effect of gravity and the system exhibits a transition from convective to absolute instabilty as shown recently by Brun and coworkers using a lubrication equation. In addition, the latter authors observed experimentally that this transition corresponds roughly to the limit of dripping. We investigate further this idea numerically by using a more sophisticated set of equations including inertia and second-order viscous terms (Ruyer-Quil-Manneville model). When getting closer to horizontality, 2D stationary wave profiles computed by continuation exhibit a transition from Kapitza-like waves to more symmetric drop profiles riding on a thinner substrate. Their 2D/3D secondary modes of instability are anaylzed using a Floquet linear stability analysis and compared with time simulations of the equations model. [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M16.00008: Role of slip on the Yih-Marangoni instability in an interface dominated channel flow Geetanjali Chattopadhyay, R Usha A linear stability analysis of Poiseuille flow of two immiscible fluids of different viscosities and densities in a slippery channel, in the presence of an insoluble surfactant at the interface is examined, within the framework of Orr-Sommerfeld system. The equations governing the flow system are solved numerically by a Chebyshev collocation method for a wide range of dimensionless parameters describing the flow system. The effects of slip on the neutral stability boundaries for the interface modes in the presence/absence of an insoluble surfactant at the interface are examined for different thickness ratios of the two layers. Slip conditions at the wall show a promise for control of the Yih-Marangoni instability of the corresponding flow system in a rigid channel. The influence of the parameters on the critical Reynolds number for the shear mode is assessed. The interaction between the two modes under the influence of different parameters displays interesting scenarios such as coalescence of modes. The study reveals that it is possible to control instabilities in interface dominated rigid channel flows by designing the walls of the channel as hydrophobic/rough/porous or undulated surfaces as these can be modeled as one with slip at the substrates. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M16.00009: Thin film instabilities on heated substrates: conjugate heat transfer Michael Dallaston, Dmitri Tseluiko, Serafim Kalliadasis Heat transported from a surface by a thin coating film of liquid is greatly affected by instabilities on the free surface of the film. If the solid substrate is heated above the ambient temperature, the hydrodynamic instability of the flow at sufficiently large Reynolds number is exacerbated by Marangoni stresses that result due to the temperature gradient in the fluid. Most studies of this phenomenon assume constant temperature or heat flux at the wall. Here we discuss the less-studied but more realistic situation in which the heat flow within the liquid film is coupled to conduction within the solid substrate, which has a complicated effect on the stability of the free surface. Analytical progress is made possible by linear stability analysis and low-dimensional nonlinear evolution equations derived using a weighted residual method. [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M16.00010: On Pore Dynamics and Calcite Solubility in Carbonaceous Aquifers used in Energy Storage Applications BS Tilley, DS Brady, M Ueckert, T Baumann Geothermal energy harvesting applications use deep groundwater aquifers to store harvested energy. The impact of this additional energy to the aquifer chemistry is crucial for long-term operation. Gaseous CO2 is added to the injected water to compensate potential precipitates of carbonates and to prevent structural changes to the aquifer. Both of these effects affect the local chemical equilibrium of the aquifer, and we consider a long-wave model of this process for a single axisymmetric pore where gaseous CO2 concentration, temperature, fluid flow and hydrochemistry modify the pore radius in space and time. Substrates are composed of calcite and dolomite, whose composition evolution is part of the full pore problem. During oscillatory flow conditions, concentration levels of the dissolved species can be sufficient to overcome elevated temperature levels and promote pore closure for sufficiently thin pores. We identify the conditions under which this pore closure takes place. [Preview Abstract] |
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