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 R33: Drops: Wetting and Spreading III |
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Chair: Francois Gallaire, EPFL Room: Ballroom A |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R33.00001: Finite time singularity in a glass Francois Gallaire, Francesco Viola, Benjamin Dollet, Pierre-Thomas Brun Using a simple liquid-foam sloshing system as prototype, we demonstrate that nonlinear friction effects, resulting from the multiscale nature of moving contact lines, become predominant at low amplitude and result in a finite-time arrest of the oscillations. This result is in strong contrast with the classical exponential relaxation induced by linear damping. We proceed to derive a model for the oscillation of foam in a cylinder accounting for capillary effects near the container walls, which we solve using multiple scales analysis. These results help rationalize our experimental observations and reveal the importance of sublinear effects in perturbation theory. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R33.00002: Spreading of viscoelastic droplets Yuli Wang, Do-Quang Minh, Gustav Amberg We intend to gain new insights into the spreading dynamics of viscolastic droplets from a numerical perspective. Focusing on the the Giesekus droplet and the Oldroyd-B droplet, we simulated the viscous spreading and the spreading after impacting on a horizontal surface. The results qualitatively agree with some experimental observations on Boger fluids and shear-thinning fluids. We discuss how shear-thinning and elasticity influence the contact line motion, given detailed information on the flow field, the stress distribution and the contact line morphology in the near vicinity of the contact line. The results suggest that viscoleastic droplets can spread faster than their Newtonian counterparts. The spreading speed of the Oldroyd-B fluid shows dependence on elasticity while the one of the Giesekus droplet does not. [Preview Abstract] |
Tuesday, November 24, 2015 1:16PM - 1:29PM |
R33.00003: The inner region of the moving contact line - diffusive and nanoscale models Andreas Nold, David N. Sibley, Ben D. Goddard, Serafim Kalliadasis Much of the work within the Complex Multiphase Systems group [1] at Imperial College London for the last number of years has been to understand the moving contact line problem. In [2], it was shown that contrary to the classical asymptotic theory at the moving contact line, the intermediate region is in fact an overlap region between the inner and the outer regions. Here, we investigate the inner region independently for the Navier-Stokes/ Cahn-Hilliard (NS/CH) model for binary fluids, as well as dynamic density functional theory (DDFT) for a simple fluid. We show that in the NS/CH model, the overlap region is recovered in the sharp-interface limit, and we link the slip length to the mobility of the system. In contrast, DDFT, which is based on statistical mechanics of fluids, allows to incorporate nanoscale details. Results are presented for advancing and receding contact lines for a wide range of contact angles. The numerical method employs spectral methods in an unbounded domain along the surface. Advantages are discussed, both for differential and integral DDFT equations. [1] http://www3.imperial.ac.uk/complexmultiphasesystems. [2] Sibley, D.N., Nold, A. and Kalliadasis, S. J. Fluid Mech. 764, 445 (2015). [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R33.00004: Numerical study of liquid-gas flow on complex boundaries Sheng Wang, Olivier Desjardins Simulation techniques for liquid-gas flows near solid boundaries tend to fall two categories, either focusing on accurate treatment of the phase interface away from wall, or focusing on detailed modeling of contact line dynamics. In order to fill the gap between these two categories and to simulate liquid-gas flows in large scale engineering devices with complex boundaries, we develop a conservative, robust, and efficient framework for handling moving contact lines. This approach combines a conservative level set method to capture the interface, an immersed boundary method to represent the curved boundary, and a~macroscopic moving contact line model. The performance of the proposed approach is assessed through several simulations. A drop spreading on a flat plate and a circular cylinder validate the equilibrium contact angle. The~migration of a drop on an inclined plane is employed to validate the contact line dynamics. The framework is then applied to perform a 3D simulation of the migration of a drop through~porous media, which consists of irregular placed cylinders. The conservation error is shown to remain small for all the simulations. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R33.00005: Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder Dmitri Tseluiko, Te-Sheng Lin, Uwe Thiele We analyze the behavior of a partially wetting liquid on a rotating cylinder using the model of Thiele [1] that takes into account the effects of gravity, viscosity, rotation, surface tension and liquid’s wettability. Such a system can be considered as a prototype for many other systems with a spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition. Thiele [1] found that a partially wetting drop on a rotating cylinder undergoes a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids the behavior changes monotonically. We analyze in detail the transition in the bifurcation behavior for partially wetting liquids as the wettability of the liquid decreases, and, in particular, how the global bifurcation related to depinning of drops is created when increasing the contact angle. We employ various numerical continuation techniques that allow us to track stable and unstable steady and time-periodic states. We support our findings by time-dependent numerical simulations and asymptotic analysis of steady-state and time-periodic solutions for large rotation numbers. [1] U. Thiele, ``On the depinning of a drop of partially wetting liquid on a rotating cylinder," J. Fluid Mech. 671, 121-136 (2011) [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R33.00006: Drop spreading on under-liquid substrates: Inertial to Viscous Regimes Naga Siva Kumar Gunda, Surjyasish Mitra, Sushanta Mitra Spreading of liquid drops on a substrate placed in air medium is a well understood phenomenon from the theory of minimization of surface energy. This process has been studied rigorously over the past few decades due to its wide array of applications like printing, coating, microfluidic devices as well as it presents the challenging problem of contact line dynamics. However, many applications like oil recovery, emulsions, liquid-liquid displacement in porous media, etc. warrants the need to study this phenomenon in the presence of a surrounding liquid medium. In the present study, an experimental investigation of the spreading process of a laser-oil drop on an ITO-coated glass substrate submerged inside water has been conducted. The experimental investigation reveals two different regimes of under-liquid drop spreading, one which is dominated by inertia and a later regime, where viscous effects, with contributions from both the drop and surrounding liquid, takes over. In doing so, we have identified the characteristic time scales for each regimes and also the transition point from one regime to another. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R33.00007: Contact line moving over a sinking sphere Seong Jin Kim, Jim An, Kamel Fezzaa, Tao Sun, Sunghwan Jung Spreading dynamics of a contact line over a sinking sphere with a constant speed into a liquid reservoir are studied both experimentally and theoretically. A high-speed camera system with X-ray illumination is employed to accurately characterize contact line motions. Over a range of Reynolds number from 30 to 1000, the spreading speed of the contact line is linearly dependent on the sinking speed of the sphere. A simple scaling equation from the force balance between the drag-induced pressure and inertia agrees with the experimental results. In addition, the numerical solution of Navier-Stokes equation, showing pressure distribution and streamline near the sinking sphere, validates our scaling equation. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R33.00008: ABSTRACT WITHDRAWN |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R33.00009: Numerical simulations of the moving contact line problem using a diffuse-interface model Muhammad Afzaal, David Sibley, Andrew Duncan, Petr Yatsyshin, Miguel A. Duran-Olivencia, Andreas Nold, Nikos Savva, Markus Schmuck, Serafim Kalliadasis Moving contact lines are a ubiquitous phenomenon both in nature and in many modern technologies. One prevalent way of numerically tackling the problem is with diffuse-interface (phase-field) models, where the classical sharp-interface model of continuum mechanics is relaxed to one with a finite thickness fluid-fluid interface, capturing physics from mesoscopic lengthscales. The present work is devoted to the study of the contact line between two fluids confined by two parallel plates, i.e. a dynamically moving meniscus. Our approach is based on a coupled Navier-Stokes/Cahn-Hilliard model. This system of partial differential equations allows a tractable numerical solution to be computed, capturing diffusive and advective effects in a prototypical case study in a finite-element framework. Particular attention is paid to the static and dynamic contact angle of the meniscus advancing or receding between the plates. The results obtained from our approach are compared to the classical sharp-interface model to elicit the importance of considering diffusion and associated effects. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R33.00010: Non-isothermal spreading dynamics of self-rewetting droplets Dimitris Mamalis, Khellil Sefiane, Kirti Chandra Sahu, George Karapetsas, Omar K. Matar We study the spreading dynamics of droplets on uniformly heated substrates. More specifically, we consider the case of binary alcohol mixtures which exhibit a non-monotonic dependence of the surface tension on temperature; these systems are often referred in the literature as self-rewetting fluids. We show through experiments that the early-stage spreading exponents depend non-monotonically on the substrate temperature in contrast to the monotonic dependence of pure liquids. In addition, we observe through the use of IR thermography visualization the formation of spontaneous travelling waves which develop along and across the free surface of the evaporating droplet and influence the spreading behaviour. Finally, we develop a theoretical model based on lubrication theory and derive an evolution equation for the interface accounting for capillarity and thermocapillarity. Using this model we investigate the effect of varying droplet wettability, which is linked to the temperature of the solid surface, on the spreading dynamics. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R33.00011: How to include the nonlinear Cox-Voinov law into sloshing dynamics? A weakly non linear approach Francesco Viola, Pierre-Thomas Brun, Francois Gallaire Fluid sloshing in a glass is a common example of damped oscillator, with the frequency derived in the potential flow limit. The damping rate is then evaluated considering the viscous dissipation at the wall, in the bulk and at the free surface, respectively. This classical theoretical result however differs from what is often seen in the laboratory when the attenuation of gravity waves happens in a small basin. In particular, the damping rate is found to increase as the sloshing amplitude decreases. Here we show that this enhanced damping is due to capillary forces at the contact line between the liquid and the container. The angle $\theta _{\mathrm{d}}$ made by the liquid interface with the container walls (contact angle) is modeled as a non-linear function of the interface speed U, (Cox-Voinov law $\theta^{3}_{\mathrm{d}}$ $\alpha $ U). We propose a multiple scale expansion scheme to consistently derive an amplitude equation using the Cox-Voinov law as boundary condition at the moving interface. The zero order problem reduces to the classical static meniscus problem, while the first order problem yields an eigenvalue problem defining the viscous sloshing modes. At an higher order, a compatibility condition has to be enforced, yielding an amplitude equation. Solving the later, we recover the expected increase of the damping rate as the sloshing amplitude decreases, an effect thus attributed to capillary effects. [Preview Abstract] |
Tuesday, November 24, 2015 3:13PM - 3:26PM |
R33.00012: Obtaining macroscopic quantities for the contact line problem from Density Functional Theory using asymptotic methods David Sibley, Andreas Nold, Serafim Kalliadasis Density Functional Theory (DFT), a statistical mechanics of fluids approach, captures microscopic details of the fluid density structure in the vicinity of contact lines, as seen in computations in our recent study [1]. Contact lines describe the location where interfaces between two fluids meet solid substrates, and have stimulated a wealth of research due to both their ubiquity in nature and technological applications and also due to their rich multiscale behaviour. Whilst progress can be made computationally to capture the microscopic to mesoscopic structure from DFT, complete analytical results to fully bridge to the macroscale are lacking. In this work, we describe our efforts to bring asymptotic methods to DFT to obtain results for contact angles and other macroscopic quantities in various parameter regimes. [1] A. Nold, D. N. Sibley, B. D. Goddard and S. Kalliadasis, ``Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory'' Phys. Fluids 26, 072001 (2014). [Preview Abstract] |
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