Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session L33: Drops XI: Levitation and Propulsion on Surfaces |
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Chair: Shreyas Mandre, Brown University Room: 404 |
Monday, November 25, 2013 3:35PM - 3:48PM |
L33.00001: Dynamic levitation of droplets Anais Gauthier, Christophe Clanet, David Quere We discuss how levitation can be induced for a liquid sitting on a plate in movement. In order to create the motion, we use a polished aluminum plate with a controlled rotational speed. As the surface reaches a critical velocity (between 1 and 10 m/s depending on the nature of the fluid), a drop gently deposited on the plate does not wet it but instead keeps a quasi-spherical shape, flying above the plate. We investigate experimentally the parameters that affect the value of the threshold speed between wetting and levitation, such as the nature of the fluid or the radius of the droplets. We also present a simple model to explain the existence of the levitation threshold. [Preview Abstract] |
Monday, November 25, 2013 3:48PM - 4:01PM |
L33.00002: Levitation of a drop over a moving surface Henri Lhuissier, Yoshiyuki Tagawa, Tuan Tran, Chao Sun We investigate the levitation of a drop gently deposited onto the inner wall of a rotating hollow cylinder. For a sufficient velocity of the wall, the drop steadily levitates over a thin air film and reaches a stable angular position in the cylinder, where the drag and lift balance the weight of the drop. Interferometric measurements yield the three-dimensional air film thickness under the drop and reveal the asymmetry of the profile along the direction of the wall motion. A two-dimensional model is presented which explains the levitation mechanism, captures the main characteristics of the air film shape and predicts two asymptotic regimes for the film thickness $h_0$: For large drops $h_0\sim\mbox{Ca}^{2/3}\kappa_b^{-1}$, as in the Bretherton problem, where $\mbox{Ca}$ is the capillary number based on the air viscosity and $\kappa_b$ is the curvature at the bottom of the drop. For small drops $h_0\sim\mbox{Ca}^{4/5}(a\kappa_b)^{4/5}\kappa_b^{-1}$, where $a$ is the capillary length. [Preview Abstract] |
Monday, November 25, 2013 4:01PM - 4:14PM |
L33.00003: Bouncing and rolling motions of capillary Leidenfrost drops on a micro-ratchet Kyra Stephanoff, Paul Steen, Henri Lhuissier, Detlef Lohse Capillary drops falling onto a micro-ratchet that is heated to temperatures 275 C $\le $ T $\le $ 350 C, bounce off a layer above the ratchet multiple times before settling down to the motion typically observed when the Leidenfrost effect is present. The deformation of the drops is asymmetrical about the y-z plane through the center of the drops as the drops move in the x direction. The magnitude of the asymmetrical deformations varies with ratchet temperature as does the number of bounces. Videos show that, when a drop settles down to its ``rolling'' regime, the fluid within a drop moves in a counter-clockwise direction. The counter-clockwise internal motion and the asymmetric deformations of a bouncing drop indicate, albeit indirectly, that the fluid in the ratchet cavities is moving clockwise. A simple model that correlates well with the experimental observations is presented. [Preview Abstract] |
Monday, November 25, 2013 4:14PM - 4:27PM |
L33.00004: Propulsion on a superhydrophobic ratchet Philippe Bourrianne, Guillaume Dupeux, Christophe Clanet, David Quere As shown by Linke in 2006, an evaporating Leidenfrost drop self-propels on a hot ratchet. Indeed, the vapour flow below the drop can be rectified by the asymmetric teeth of the ratchet and, therefore, entrain the levitating drop by viscosity. This motion is usually observed above the Leidenfrost temperature. We show how the use of a super-hydrophobic ratchet allows us to extend self-propulsion down to the boiling point of water, and even below. We discuss a possible explanation for this ``cold regime'' of propulsion. [Preview Abstract] |
Monday, November 25, 2013 4:27PM - 4:40PM |
L33.00005: Surfing on a herringbone Dan Soto, Guillaume Lagubeau, Christophe Clanet, David Quere Liquids in the Leidenfrost state levitate on hot solids, owing to the formation of a cushion of vapor. Without contact, drops glide with negligible friction on their substrate. The conjunction of vapor production and frictionless motion can be exploited to self-propel liquids when placed on hot horizontal ratchets. It was proposed to understand the effect as follows: the asymmetric teeth of the ratchet rectify the vapor flow below the levitating liquid, which is entrained by the viscous vapor. In our presentation, we propose to induce similar effects by geometrical means, hence achieving new designs for self-propelling Leidenfrost liquids. We force a directional flow of vapor by etching a herringbone pattern in the hot substrate. We show how this design can be tuned to optimize the propelling force and the drop speed, which is quantitatively analyzed. We eventually extend these principles to self-propel plastic levitating cards at room temperature, using patterned hockey tables. [Preview Abstract] |
Monday, November 25, 2013 4:40PM - 4:53PM |
L33.00006: The Walking Droplet Instability Joshua Bostwick, Paul Steen A droplet of liquid that partially wets a solid substrate assumes a spherical-cap equilibrium shape. We show that the spherical-cap with a mobile contact-line is unstable to a non-axisymmetric disturbance and we characterize the instability mechanism, as it depends upon the wetting properties of the substrate. We then solve the hydrodynamic problem for inviscid motions showing that the flow associated with the instability correlates with horizontal motion of the droplet's center-of-mass. We calculate the resulting ``walking speed.'' A novel feature is that the energy conversion mechanism is not unique, so long as the contact-line is mobilized. Hence, the walking droplet instability is potentially significant to a number of industrial applications, such as self-cleansing surfaces or energy harvesting devices. [Preview Abstract] |
Monday, November 25, 2013 4:53PM - 5:06PM |
L33.00007: Propelling a water drop with the vapor-mediated Marangoni effect Seungho Kim, Ho-Young Kim We show that a water drop on solid surfaces can be propelled just by placing a volatile alcohol drop nearby. It is found to be because the water-air interface near the alcohol drop mixes with alcohol vapor, thereby locally lowering the surface tension. The surface-tension-gradient induces the motion of the water drop, enabling the trajectory control of water drops through the motion of remote alcohol drops. This vapor-mediated Marangoni effect also gives rise to other interesting interfacial flow phenomena, such as nucleation of holes on a water film and ballooning of a water drop hanging from a syringe needle with the approach of an alcohol drop. We visualize such interfacial dynamics with a high-speed camera and rationalize their salient features by scaling analysis. [Preview Abstract] |
Monday, November 25, 2013 5:06PM - 5:19PM |
L33.00008: Thermocapillary-driven motion of a droplet on an inclined substrate: contact line dynamics, and non-monotonic dependence of surface tension on temperature George Karapetsas, Kirti Sahu, Khellil Sefiane, Omar Matar We consider the two-dimensional motion of a droplet on an inclined, non-isothermal solid substrate. We use the lubrication approximation to obtain a single evolution equation for the interface, which accounts for gravity, capillarity, and thermo-capillarity, brought about by the dependence of the surface tension on temperature. For the latter, a nonlinear function is used, which exhibits a well-defined minimum. The contact line motion is modelled by coupling the contact line speed to the difference between the dynamic and equilibrium contact angles; the latter vary dynamically during the droplet motion through the dependence of the liquid-gas, liquid-solid, and solid-gas surface tensions on the local contact line temperature. Thus, the local substrate wettability also varies dynamically at the two edges of the drop. A full parametric study is carried out for constant substrate temperature gradients in order to investigate the interplay between Marangoni stresses, induced by thermo-capillarity, gravity, and contact line dynamics in the presence of local wettability variations, and non-monotonic dependence of the surface tension on temperature. The results of this study are presented together with comparisons against experimental data. [Preview Abstract] |
Monday, November 25, 2013 5:19PM - 5:32PM |
L33.00009: Pancake droplets on the grill: Thermocapillary motion of confined droplets in Hele-Shaw cells Marc Habisreutinger, Fran\c{c}ois Gallaire, Pierre-Thomas Brun, Mathias Nagel Assuming constant surface tension, the sphere is an equilibrium shape for a drop that is translating at low Reynolds number through an infinite domain of stationary fluid. Remarkably, this result still holds true for the thermocapillary motion of a drop in a fluid at rest, when a constant temperature gradient is imposed and convection effects are neglected (Young, Goldstein and Block [1]). On the contrary, we show analytically that such an ideal result no longer stands when constraining the surrounding geometry of the droplet. For instance, flattened cylindrical droplets in microchannels, so-called pancake droplets, do not represent an equilibrium shape of thermocapillary motion. Our numerical studies also enable to take into account the flow-induced temperature variations and could help building a scaffold towards the individual control of droplets in microchannels. \\[4pt] [1] N.O. Young, J.S. Goldstein and M.J. Block, The motion of bubbles in a vertical temperature gradient, J. Fluid Mech. 6, 350-6 (1959). [Preview Abstract] |
Monday, November 25, 2013 5:32PM - 5:45PM |
L33.00010: Thermocapillary flow induced by the optical irradiation of carbon nanoparticles J. Rodrigo Velez Cordero, Juan A. Hernandez Cordero Transport of discrete drops in micro-channels constitutes an essential operation in microfluidic devices. Due to the small characteristic size of micro-channels, the pressure drop necessary to induce motion can be produced by surface tension forces, according to Laplace law, and not only by the use of a mechanical pump. Thermocapillary motion is produced when one extreme of the drop is heated: since surface tension diminishes with temperature, the pressure difference on both extremes will be unbalanced and subsequent equilibrated by the motion of the drop. In this work we used thermocapillary pumping to induce the motion of drops by using a polymeric matrix embedded with carbon nanoparticles (PDMS-Cpart) capable to absorb radiative energy (delivered by an optical fiber) and operate as a heat source. Capillaries with different sizes were then coated with the PDMS-Cpart mixture. The observed motion of the drops, whose velocity is comparable to those achieved using metallic heaters, was analyzed under three important considerations: the dynamic angle hysteresis, optical depth of the PDMS-Cpart layer, and the optical power delivered by the optical fiber. [Preview Abstract] |
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