Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session H8: Drops VII |
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Chair: Sushanta Mitra, University of Alberta Room: 25A |
Monday, November 19, 2012 10:30AM - 10:43AM |
H8.00001: Coffee Stain Effect with Liquid Droplets Sushanta Mitra, Siddhartha Das We discuss the dynamics of immiscible bidispersed oil droplets that are suspended in an evaporating water sessile drop. Therefore, in contrast to classical coffee stain problem, the depositing ``particles'' are replaced by microscopic oil droplets -- hence, we discuss a liquid-droplet coffee stain phenomenon. We show experimentally that unlike colloidal particles in a classical coffee stain problem, liquid oil droplets cannot reach the three phase contact line (TPCL) due to the aversion of the oil droplets to form finite oil-air interface in water medium. Therefore, the oil droplets get positioned at a finite distance from the TPCL. We call this distance the ``enclosure'' distance, which being a function of the droplet size, triggers a spontaneous size-based oil droplet separation. In addition, the ``enclosure'' effect is a function of the surface energies of the oil droplet and the rate of evaporation. We develop a theory to describe this effect, and the results show excellent agreement with the experimental findings. [Preview Abstract] |
Monday, November 19, 2012 10:43AM - 10:56AM |
H8.00002: The dynamics of drops coating the underside of a flexible wall Craster Richard, Alex Wray, Demetrios Papageorgiou, Omar Matar Lister et al., 2009, showed that a thin fluid coating the underside of a ceiling (a model which extends in particular the works of Hammond, 1983, and Lister et al., 2005) can give rise to pendent drops. If these are fixed in place by boundary conditions, they drain to give drops of constant pressure surrounded by annular trenches. These authors also showed that, on larger domains starting from an initial perturbation, these drops will undergo a self-induced quasi-steady translation. This is driven by the release of gravitational potential energy as the fluid in the film falls into the drop. The speed and growth of these drops is accessible to analytical computation by the self-similar study of the thin trenches surrounding them, and matching to far external conditions. The subsequent dynamics are intricate, allowing for coalescence (not seen in 1 dimension) as well as complex drop-drop interactions. We extend this model to allow for the ceiling to be a flexible substrate, and also to account for inertial effects in the drops. We then investigate the effect this has on the dynamics of the drops. [Preview Abstract] |
Monday, November 19, 2012 10:56AM - 11:09AM |
H8.00003: Slip or not slip? A comparison of models applied to contact line motion Nikos Sawa, David Sibley, Serafim Kalliadasis The motion of a contact line is examined through the spreading of a thin two-dimensional droplet on a planar substrate to compare the contemporary model based on interface formation of Shikhmurzaev to more prevalent models in the literature. The implementation of the long-wave approximation for the droplet thickness in a quasistatic spreading regime affords an insight to the interface formation model behaviour, principally that the evolution of the droplet radius reduces to an equivalent expression for a slip model when the prescribed dynamic contact angle has a velocity dependent correction to its static value. This result is found both in the original interface formation model formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features, such as the pressure behaviour and rolling motion at the contact line, are critically analysed. [Preview Abstract] |
Monday, November 19, 2012 11:09AM - 11:22AM |
H8.00004: The Effect of Droplet Inertia on Combined Gravitational and Thermocapillary Interactions of Contaminated Spherical Drops Michael Rother The motion of two spherical drops under the influence of gravity and a vertical temperature gradient in the presence of bulk insoluble, nonionic surfactant is considered in the limit of an incompressible surfactant film. In this limit the surfactant coverage is nearly uniform. Thermal convection is negligible, and flow conditions are such that droplet inertia is important, while inertia due to the surrounding matrix fluid can be neglected. In terms of dimensionless parameters, these conditions imply that the Stokes number may be order unity or larger, while the Reynolds number remains small. Physically, such conditions generally mean that the density of the surrounding fluid is much less than the drop density and that the drop radii are typically in the range of 5 to 50 micrometers. In the case where both the Stokes and Reynolds numbers are small, closed and retrograde trajectories are observed. The effect of droplet inertia is to destroy symmetry in the trajectories and reduce the collision-forbidden region of the parameter space. Van der Waals forces are also taken into account. A practical application of this research is in the study of raindrop growth, where the collision efficiencies fall between those for clean drops and solid spheres. [Preview Abstract] |
Monday, November 19, 2012 11:22AM - 11:35AM |
H8.00005: ABSTRACT WITHDRAWN |
Monday, November 19, 2012 11:35AM - 11:48AM |
H8.00006: Effects of surface wettability and edge geometry on drop motion through an orifice Ankur Bordoloi, Ellen Longmire In geothermal energy recovery and CO$_{2}$ sequestration, drops move through a porous structure by displacing a surrounding liquid. Both the pore geometry and surface wettability influence the drop motion. We simplify the pore structure to a thin plate with a circular orifice. The plate is held horizontally inside a rectangular tank filled with silicone oil. Drops of water/glycerin with Bond numbers (Bo) of 1-10 are released above and axisymmetric to the orifice, encountering the plate after reaching their terminal speed. We use high speed imaging to examine the effects of orifice-to-drop diameter ratio (d/D), orifice surface wettability (hydrophilic/hydrophobic) and edge geometry on the passage of drop fluid through the orifice. We generate regime maps for d/D and Bo delineating domains of drop capture, passage, and passage with breakup. For d/D $<$ 1, sharp edges are observed to yield contact between the drop and orifice so that surface wettability influences the subsequent dynamics. On the other hand, rounded edges appear to prevent direct contact so that the dynamics are unaffected by the surface wettability. [Preview Abstract] |
Monday, November 19, 2012 11:48AM - 12:01PM |
H8.00007: A theory of wall-induced lateral migration of a drop in shear: effects of drop inclination and viscoelasticity Kausik Sarkar Recently, migration of suspended particles, drops, polymers and biological cells have assumed importance in microfluidic separation and filtration assays. A rigid sphere in shear does not move cross-stream due to the reversibility in a Stokes flow. Deformation, as well as inertia and viscoelasticity, breaks the reversibility and leads to lateral migration away from a nearby wall. There have been algebraically complex perturbative analyses of the moving boundary problem [e.g. Chan and Leal 1979, JFM 92,131] to determine the migration velocity. However, the underlying physics remains unclear. Here, we show that the migration is induced by the image stresslet field, as was also indicated earlier by Smart and Leighton [1991, Phys. Fluid A, 3, 21]. We relate the stresslet field to the Interface tensor, and investigate the effects of drop inclination. In contrast to a plausible notion asserted also in the literature, that reduced inclination (increased alignment with flow) decreases migration, it is shown here that reduced inclination increases the stresslet and thereby the migration velocity. A semi-analytical expression of migration velocity based on numerically computed stresslet will be compared against simulation and the results will be discussed. [Preview Abstract] |
Monday, November 19, 2012 12:01PM - 12:14PM |
H8.00008: Abstract Withdrawn
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Monday, November 19, 2012 12:14PM - 12:27PM |
H8.00009: Physics of Spreading and Arrest of Molten Liquid on Solid Substrates Faryar Tavakoli, Steven Davis, Pirouz Kavehpour The physics of non-isothermal spreading followed by phase change, unlike universal equations established for isothermal spreading, is still a mystery. A plethora of applications such as coating technology, rapid prototyping, 3D printing and plastic electronics involve molten droplets spreading on cold substrate surfaces. Better control of these processes requires fundamental understanding of heat transfer and fluid flow that transpire during the spreading and solidification of liquid droplets. The present work focuses on the dynamic and thermal characteristics of liquid spreading and subsequent arrest. Spreading of liquid was recorded and evolution of liquid spread diameter and liquid-solid contact angle were measured from the recordings of a high-speed digital camera. After solidification initiation at the basal plane, a liquid drop is pinned to a solid substrate showing fixed footprint and contact angle. Arrested contact angle ($\theta$*) and arrested base diameter (D*) are evaluated against two main contributing variables: fluid flow rate and Stefan number. We have developed a power law that indicates the arrested contact angle and base diameter are not single-valued for given substrate temperature, but are strongly dependent on flow rate and the surface characteristics. [Preview Abstract] |
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