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 G18: Interfacial and Thin Films I |
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Chair: Roman Grigoriev, Georgia Institute of Technology Room: 206 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G18.00001: Linear Stability Analysis of Convective Flow in a Confined Layer of Volatile Liquid Driven by a Horizontal Temperature Gradient Roman Grigoriev, Tongran Qin Convection in layers of nonvolatile liquids with a free surface driven by a horizontal temperature gradient is a fairly well-studies problem. It is described by several nondimensional parameters: the Prandtl number $Pr$, the Marangoni number $Ma$, and the Rayleigh number $Ra$ (or the dynamic Bond number $Bo_D = Ra/Ma$). Previous studies mostly focused on characterizing the critical $Ma$ and the nature of the convective pattern (e.g., stationary rolls or traveling waves) as a function of $Pr$ and $Bo_D$. To understand convection in volatile liquids one also has to consider the transport of heat and mass in the gas layer above the liquid. In confined geometries, the composition of the gas phase plays a very important role, since air tends to suppress phase change at the interface and thereby the amount of latent heat released or absorbed at the interface as a result of evaporation or condensation. Linear stability analysis of the problem based on a two-sided model shows that, for $Bo_D=O(1)$, both the critical $Ma$ and the critical wave length of the pattern increase as the average concentration of air decreases. The predictions of linear stability analysis are found to be in good agreement with previous experimental and numerical studies of both nonvolatile and volatile fluids. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G18.00002: Experiments on elastohydrodynamics of a free particle on a soft substrate Baudouin Saintyves, Theo Jules, Thomas Salez, L. Mahadevan We present the results of experiments on the dynamics of a negatively buoyant cylinder in a viscous bath that sediments, rolls and slides close to a soft inclined wall. We show that an elastohydrodynamic lift force - not present in the hard-wall case - balances gravity, thus allowing for a fast steady-state sliding regime. Our results can be explained in terms of a recently published scaling approach. We also show that the cylinder displays other non-intuitive behaviors such as counter-clock wise rotation and an oscillatory behaviours, qualitatively consistent with some recent theoretical predictions. The work is a step in explaining aspects of phenomena that include the dynamics of cartilaginous joints, and motion of a cell in a microfluidic channel or in a blood vessel, and perhaps even some geophysical phenomena, all of which intimately couple elasticity and hydrodynamics. ~ [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G18.00003: Low-order modelling of films over arbitrary, highly curved substrates Alex Wray, Demetrios Papageorgiou, Omar Matar Low-order modelling of free surface flows typically relies upon careful and judicious consideration of various length scales intrinsic to a problem. In a planar geometry, this typically consists of a single ``aspect ratio'' comparing the characteristic length of typical waves to the thickness of the layer. This has given rise to classic ``thin-film'' or ``long-wave'' models. Curvature of the underlying substrate complicates the situation by incorporation of two additional length scales: the radii of curvature. In such situations, modelling has typically relied on some potentially prohibitive symmetry assumption (Craster \& Matar 2006), or the assumption that the substrate shape is slowly varying (even where that assumption is violated e.g. Kalliadasis, Bielarz, Homsy 2000). We show that even when substrate variations are not assumed to be small, a set of boundary-layer equations may be extracted under the assumption that the waves are long. We show that the resultant equations are soluble and that the models produced are highly accurate, providing exceptional agreement with solutions of the full Navier-Stokes equations. They are also shown to out-perform existing thin-film models by orders of magnitude. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G18.00004: Dynamic measurement of the evolving mechanical properties of thin drying films via induced wrinkling Manuela Nania, Giulia Ferretti, Omar Matar, Joao Cabral Surface patterning is important for controlled liquid spreading, adhesion and assembly of smart coatings. Patterns with feature sizes in the 100nm-100$\mu$m range can be achieved via wrinkling of bilayers, an inherently inexpensive, scalable and robust method. Conversely, measuring wrinkling of well-defined bilayers and multilayers represents a valuable way to measure mechanical properties of laminate thin films supported by well-defined substrates. We focus on the dynamic measurement of the elastic modulus of micrometer scale layers of ternary solutions during drying and film formation. Aqueous salt model solutions are cast on pre-stretched, oxidised polydimethylsiloxane, and allowed to dry under controlled environments, leading to thin film formation. Upon strain removal, different pattern morphologies are observed and mapped as a function of composition, drying time, temperature and relative humidity. Several classes of wrinkling behaviours are identified, from single frequency sinusoidal wrinkling to various complex modes involving stress localization and wrinkling cascades. Within sinusoidal wrinkling, we can infer dynamically the film elastic modulus evolution during drying from the pattern dimensions. The results are validated by AFM nanoindentation measurements. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G18.00005: Mathematical modelling of swelling-induced surface instabilities in deformable porous media Matthew Hennessy, Alessandra Vitale, Joao Cabral, Omar Matar The swelling of a deformable porous medium as it absorbs liquid can generate large compressive stresses which, in turn, can induce a rich variety of surface instabilities. When controlled, these instabilities can be used to drive the self-assembly of microscale structures that find practical applications in fields such as surface patterning, imprint lithography, optically-active surfaces, and flexible electronics. Recent experiments by our group have suggested that a swelling-induced instability can occur at a surface of crosslinked polymer gels exposed to a good solvent. In this talk, we present a mathematical model for a swelling porous medium and use it to describe spontaneous pattern formation on gel surfaces. The model is based on nonlinear poroelasticity and the flow of liquid is described by a generalisation of Darcy's law that accounts for the thermodynamics of mixing. A combination of linear stability theory and finite-element simulations is used to explore the surface morphologies in the linear and nonlinear regimes. We show that the model is able to accurately reproduce experimental observations. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G18.00006: Rupture of thin films of power law fluids on a substrate Vishrut Garg, Sumeet Thete, Osman Basaran Applications in coating, drying, foam stability and drop coalescence require an in-depth understanding of the dynamics of the rupture of thin films. A number of emerging applications in the field involve fluids that exhibit power law (deformation-rate-thinning) rheology. In a power law fluid, viscosity is not constant but is proportional to the deformation rate raised to the n$-$1 power, where 0$<$n$\le$1 is the power law exponent (n=1 for a Newtonian fluid). Previous studies by Vaynblat and co-workers (2001) and Zhang and Lister (1999) have focused on the rupture of free films and ones supported on a substrate, respectively, for Newtonian fluids. Here, we study the rupture of a thin film of a power law fluid on a substrate under the balance between destabilizing Van der Waals pressure and stabilizing capillary pressure. The power law scaling in time of the film thickness, the lateral length scale, and fluid velocity is determined analytically and confirmed by numerical simulations. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G18.00007: Modeling of liquid electrolyte films on non-uniformly charged solid substrates Mahnprit Jutley, Vladimir Ajaev We consider a thin electrolyte film on a solid substrate characterized by a space-dependent electrical charge density. Using the Debye-H\"uckel equation to model the electrostatic potential and the Navier-Stokes equations for fluid flow, we consider both steady-state interface shapes and their stability resulting from small perturbations of arbitrary wavelength. Calculations are carried out by two different approaches: Fourier expansion of all terms is used and the corresponding coefficients of the first order correction to the interface shape are found, and, secondly, an evolution equation is obtained within the framework of a lubrication-type model. Stability analysis of the linearized problem is conducted. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G18.00008: Experimental free-surface instability growth in gravity-driven film flows of Newtonian and non-Newtonian liquids Jeffrey Olander, Roberto Camassa, M. Gregory Forest, H. Reed Ogrosky We present experiments on the growth of free-surface instabilities for Newtonian and viscoelastic film flow in a tube. The liquids used were a Newtonian silicone oil and various concentrations of elastic Boger fluids. The test liquids were injected axisymmetrically into a vertical glass tube at constant volume flow rate and the evolution of the free surface was observed as the film flowed down the tube due to gravity. The range of film thicknesses which exhibited instability growth was smaller for Boger fluids than for silicone oil. Long-wave modeling studies of related problems will be compared with the experimental observations, and our test fluids' rheology and potential mechanisms for the observed instability growth will be discussed. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G18.00009: Long wave evolution of a two-fluid channel flow with surfactant and gravity David Halpern, Alexander Frenkel For a horizontal two-fluid channel flow (with top-to-bottom aspect ratio $n$ and viscosity ratio $m$ ) in the presence of surfactants and gravity, with no inertia, the lubrication approximation yields two coupled evolution equations for interface and the insoluble surfactant. Even for arbitrarily strong stabilizing gravity, there is a band of unstable wavenumbers for certain ($m$,$n$)-ranges. We show that gravity violates the significance of vorticity (Wei 2005) for the surfactant instability. The two types of normal modes are characterised in physical terms, in the spirit of Charru and Hinch (2000). We observe that the role of vorticity hinges on inertia. With no gravity, a small-amplitude saturation of the surfactant instability is possible in contrast to the semi-infinite case studied by A.F. and D.H. (2006). For certain ($m$,$n$)-ranges, the interface is governed by a decoupled Kuramoto-Sivashinsky equation, and it provides a source term for the linear convection-diffusion equation of the surfactant . When diffusion is negligible, the surfactant equation has an analytic solution consistent with numerics. The surfactant wave is as chaotic as the interface; however, the ratio of the two waves is just constant. Strongly nonlinear regimes are found at finite $n$ for $m<1$. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G18.00010: Dynamics of a flowing liquid column with an immiscible reactive micellar interface Zahra Niroobakhsh, Andrew Belmonte We experimentally investigate the instabilities resulting from the reactive formation of a thin layer of micellar material around a flowing liquid column. The material is produced when an aqueous surfactant solution (cetylpyridinium chloride) descends through a reservoir of oleic acid, a room temperature oil which can act as a weak surfactant. A variety of instabilities are observed, including connected and disconnected droplets, a straight cylindrical pipe which undergoes buckling, and various surface wave morphologies on the column. These states appear to be determined by a competition between surface tension and the growth of the interfacial material layer, as a function of imposed flow rate and surfactant concentration. Rheology provides evidence for the structural nature of the oleic/surfactant interaction, in the context of similar observations from other experiments. [Preview Abstract] |
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