Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session PH: Drops VIII: Contact Lines |
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Chair: Marc Smith, Georgia Institute of Technology Room: 101H |
Tuesday, November 24, 2009 11:40AM - 11:53AM |
PH.00001: Capillarity driven contact line motion in cyclic bridge-drop grab-release events Henrik van Lengerich, Paul Steen Motivated by a reversible adhesion device which uses capillary forces to adhere to a substrate, we study the mechanical work done in a grab-release cycle. That is, the volume of a drop is increased until it grabs the substrate and forms a bridge and then shrunk until it goes unstable and releases from the substrate and forms a drop again. In the instant that a drop becomes a bridge (or vice versa) no work is done on the system, however, energy is dissipated due to the decrease in interfacial energy. This dissipation can be compared with the mechanical dissipation based on the fluid flow. For viscous fluids, a wedge model shows that most of the dissipation occurs in the vicinity of the contact line. The thermodynamic dissipation is compared with that expected in the fluid without the need of static contact angle or slip length. [Preview Abstract] |
Tuesday, November 24, 2009 11:53AM - 12:06PM |
PH.00002: Two dimensional droplets under partially wetting conditions: New analytical solutions J.M. Gomba, G.M. Homsy We present new analytical solutions that describe the static shape of a two-dimensional droplet in equilibrium with a surrounding thin film on a solid substrate. We model a partially-wetting liquid by a disjoining-conjoining pressure description of intermolecular forces between the liquid and solid substrate. The profile involves three regions: (i) a droplet core, (ii) a thin film region and (iii) an intermediate contact line region. The description of the droplet shape in these regions is usually carried out by series expansions or numerical solutions. In contrast, here we derive new fully- analytical solutions for the shape of the droplet, the cross sectional area, the half width and the maximum curvature. We also study the effects of the size of the droplet on the apparent contact angle. We find that for nanodroplets the contact angle follows a power law dependence with the cross sectional area, reaching a well defined value for larger droplets. [Preview Abstract] |
Tuesday, November 24, 2009 12:06PM - 12:19PM |
PH.00003: Modeling of dynamic wetting far from equilibrium Andreas Carlson, Minh Do-Quang, Gustav Amberg Moving contact lines in dynamic wetting phenomena have been studied extensively for several decades, nonetheless, the physics that drive such processes are not fully understood. Continuum mathematical models for such phenomena often rely on ad-hoc physical assumptions or simplifications. We present here numerical simulations of dynamic wetting far from equilibrium based on a free energy formulation. A direct qualitative and quantitative match with the experiments by [Bird, J. C., S. Mandre, and H. A. Stone, 2008, PHYSICAL REVIEW LETTERS 100(23)] is shown. To correctly capture the dynamics of rapid wetting, we demonstrate that it is crucial to account for non-equilibrium at the contact line. A term in the boundary condition at the solid surface, that naturally arises in the phase field theory, is interpreted as allowing for the establishment of a local structure in the immediate vicinity of the contact line. Besides one universal non-dimensional number, that is determined here, the model as presented has no free parameters. [Preview Abstract] |
Tuesday, November 24, 2009 12:19PM - 12:32PM |
PH.00004: Wall energy relaxation in Cahn-Hilliard model for moving contact lines Pengtao Yue, James Feng Contact angle in the Cahn-Hilliard model is determined by wall energy. The finite-rate relaxation of this wall energy results in a dynamic contact angle which differs from the static one. According to our numerical simulation, the wall energy relaxation is crucial to the successful fitting of experimental data with a numerically manageable slip length, which could be two orders of magnitude larger than the physical one. Through a simple analysis, we establish a relationship between the dynamic contact angle and the capillary number, which is verified by our numerical simulation. We further show that this relationship is consistent with Cox's hydrodynamic model. In a sense, the wall energy relaxation coarse-grains an area surrounding the contact line into a ``slip region'' while keeping the apparent contact angle outside the region unchanged. In the end, we show some new results on drop spreading. [Preview Abstract] |
Tuesday, November 24, 2009 12:32PM - 12:45PM |
PH.00005: Evolution of the Diffusive Precursor Film of a Wetting Fluid at the Vicinity of the Moving Contact Line Anna Hoang, Pirouz Kavehpour For wetting fluids, a microscopic film, which is known as the precursor film, exists at the front of the moving contact line. The structure of this thin film has been studied theoretically, but previous experimental investigations were limited by the resolution of the measurement system (lateral or vertical). We studied the evolution of the profile of a spreading droplet near the moving contact line using total internal reflection fluorescence microscopy (TIR-FM). Our technique provides the lateral resolution and dynamic range required to capture the features of the macroscopic drop (spherical cap), wedge region, and precursor film within a single experiment. The dynamic characteristics of the precursor film are in good agreement with the theoretical results. [Preview Abstract] |
Tuesday, November 24, 2009 12:45PM - 12:58PM |
PH.00006: Laser Speckle Drop Profilometry Validation and Measurement of Contact Angle Variation with Surface Roughness Jason Schmucker, Edward White, Joshua Osterhout A non-intrusive technique has been developed that measures full-field instantaneous interface shapes of unsteady droplets on rough surfaces. Illumination of a rough surface by a collimated laser forms a speckle pattern at the solid surface that is subsequently deformed by refraction at the drop interface, encoding information about the surface height and gradient. Computer algorithms analyze the resulting images to identify the interface shape, contact line location and contact angles about the contact line. This is achieved through a minimization of the mean-squared error between the measured speckle deformation and that of the reconstructed drop using simulated annealing. Extensive validation efforts demonstrate the technique's effectiveness on aluminum, copper, and stainless steel surfaces when the surface roughness is micron scale. Preliminary experiments provide data on how contact angle variations about a single drop's contact line and between different droplets depends on surface roughness on the various surfaces. [Preview Abstract] |
Tuesday, November 24, 2009 12:58PM - 1:11PM |
PH.00007: Investigating Contact Angle Forces with Traction Force Microscopy Elizabeth Jerison, Eric Dufresne Although the classic Young's relation indicates that the contact angle between a drop and substrate is a constant material property, observation of an evaporating water drop on solid PDMS reveals four phases of contact angle dynamics: spreading, pinning, isotropic contraction, and contraction with a decreasing contact angle. Only in the third phase does the contact angle remain constant. We use traction force microscopy to visualize the forces exerted by the drop contact line on the substrate, with the goal of explaining this contact-angle anomaly. [Preview Abstract] |
Tuesday, November 24, 2009 1:11PM - 1:24PM |
PH.00008: Oscillations of a viscous drop under spherical-belt constraint Joshua Bostwick, Paul Steen The motion of constrained liquid-gas interfaces is important in a variety of applications. We study the linear oscillations of a viscous liquid drop immersed in an immiscible fluid and constrained by an axisymmetric spherical ``belt.'' The belt is a rigid spherical band delimited by two latitudinal circles. Unlike the unconstrained(Rayleigh) problem, the liquid boundary is the union of a surface of support and two disconnected free surfaces, the latter coupled by the incompressibility condition and allowed to ``communicate'' across the constraint. A modified set of shear boundary conditions is introduced to address the transition from free to supported surfaces along the drop interface. This formalism allows mode shapes with discontinuous contact angle across a pinned circle-of-contact constraint, a limiting case which is consistent with observation. As the size of the constraint increases from a pinned circle of contact, the mode shapes are shown to qualitatively change their character by increasing the number of nodes of the corresponding eigenfunction, while preserving the numerical ordering of the eigenfrequencies at a critical belt size. [Preview Abstract] |
Tuesday, November 24, 2009 1:24PM - 1:37PM |
PH.00009: The Vibration of an Inviscid Incompressible Sessile Drop Marc Smith The fundamental frequencies and normal modes of vibration of a sessile drop supported on a horizontal planar surface are found using an integrated analytical and numerical technique. Spherical coordinates are used to describe the interface shape, but the potential flow field inside the drop is computed numerically using the finite element method. The numerical velocity potentials at the interface for both the fluid inside the drop and outside are fitted using a Legendre series. When these series are combined in the interfacial normal-stress balance the result is a linear eigenvalue problem that is solved numerically. Results will be presented for sessile drops with different contact angles without gravity and compared to experimental data. This technique can also be extended to sessile drops with gravity, in which the drop shape is flattened, and to substrate geometries that are not planar, such as a drop in a shallow cavity or hole. [Preview Abstract] |
Tuesday, November 24, 2009 1:37PM - 1:50PM |
PH.00010: The Shape of a Sessile Drop Bharadwaj Prabhala, Mahesh Panchagnula, Srikanth Vedantam, Venkat Subramanian Contact angle is an important parameter which characterizes the interaction between the liquid and solid surface. Based upon the contact angle solid substrates are primarily classified as hydrophilic, hydrophobic and super hydrophobic substrates. In this study, we investigate the dependence of the local contact angles on the configuration of the contact line shape of a sessile liquid drop on a solid substrate. We use the numerical algorithm `Surface Evolver' which is an interactive program for the study of surfaces shaped by surface tension, gravitational and other energies. The algorithm calculates the velocity at each vertex and the vertex is moved in the direction such that the surface evolves towards a minimum energy. The shapes and the energies of the drop are computed using the Surface Evolver. An analytical solution based on perturbation expansion is developed to predict the shape of the sessile drop for a given contact line description. The shape of the contact line is also varied in the same manner and the exact drop shape is computed in Surface Evolver. The Root Mean Square error is calculated by comparing the radius at all the vertices between the analytical and numerical approaches for varying contact angles and amplitudes of undulations. We show that the applicability of the analytical solution is quite widespread. [Preview Abstract] |
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