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 L19: Surface Tension III |
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Chair: Buie Cullen, Massachusetts Institute of Technology Room: 28E |
Monday, November 19, 2012 3:35PM - 3:48PM |
L19.00001: Elastocapillary Flows in Flexible Tubes Theresa Hoberg, Emilie Verneuil, Anette Hosoi Interactions between capillary and elastic effects have sparked interest for a variety of applications, from micro- and nano-scale manufacturing to biological systems. In this work, we investigate capillary flows in extremely flexible, millimeter-scale cylindrical elastic tubes, and examine the interaction between surface tension and elastic effects. We present experimental results for capillary rise and evaporation experiments in different regimes, and demonstrate that surface tension effects on sufficiently flexible tubes can cause them to collapse and coalesce spontaneously through non-axisymmetric buckling. The deformations of the tube wall and their dynamic impact on capillary-driven fluid flow are measured in different regimes, and equilibrium states are characterized. Experiments are compared with theoretical predictions. [Preview Abstract] |
Monday, November 19, 2012 3:48PM - 4:01PM |
L19.00002: Sandwiched drops and magnified substrate deformations Jason S. Wexler, Howard A. Stone The Laplace pressure and contact line force of a wetting sessile drop (radius $R$) are strong enough to deform the surface of a soft elastic media ($\sim25$ kPa) by distances on the order of microns. If the drop, instead of being sessile, is squeezed flat in a gap ($h \ll R$) between two elastic substrates, the resulting forces are much stronger (by a factor $R/h \gg 1$). In fact, a similarly soft material will deform by distances that are orders of magnitude larger than in the sessile drop case. We present an analytical theory that predicts a relationship between drop volume and substrate displacement. In particular, unlike the sessile drop case, where larger deformations correspond to smaller drops, here we find that larger drops lead to greater displacements. We solve for the volume at which the two surfaces first come in contact, and test the predictions of our model with a series of experiments. [Preview Abstract] |
Monday, November 19, 2012 4:01PM - 4:14PM |
L19.00003: Capillary forces on elastic solids measured in molecular dynamics Joost H. Weijs, Antonin Marchand, Bruno Andreotti, Jacco H. Snoeijer The distribution of capillary forces that a liquid drop exerts on a solid substrate is still debated. While the force normal to the interface can be derived from a global argument, this is not the case for the tangential force component. Experiments in which the force is derived from the elastic deformation of the solid are difficult to perform and interpret, and have lead to different conclusions. To resolve this issue, we directly measure the force in Molecular Dynamics simulations of Lennard-Jones droplets in contact with a solid at varying contact angles. We find that the tangential force component is always pointed towards of interior of the drop, and can qualitatively be explained by density functional theory with the sharp kink approximation. This contradicts the classical view the that the capillary force on the solid acts parallel to the liquid interface. [Preview Abstract] |
Monday, November 19, 2012 4:14PM - 4:27PM |
L19.00004: An elastic meniscus Arnaud Antkowiak, Marco Rivetti A liquid surface touching a solid usually deforms in a near-wall ``meniscus'' region. In this study, we replace the free surface with a soft polymer and examine the deformation of this ``elastic meniscus,'' result of the interplay between elasticity and hydrostatic pressure. In particular we demonstrate both experimentally and theoretically the existence of a limit height of liquid tenable before collapse of this structure. As a side result, we show that the effort needed to pull an object deposited on a fluid surface is increased with its elasticity, as is common in adhesion phenomena. Finally we discuss the consequences of our results in terms of metrology and optimal tailoring of ``elasto-pipettes.'' [Preview Abstract] |
Monday, November 19, 2012 4:27PM - 4:40PM |
L19.00005: Contact angles on a soft solid: from Young's law to Neumann's law Jacco Snoeijer, Antonin Marchand, Siddhartha Das, Bruno Andreotti The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles different from that predicted by Neumann's law, which applies when the drop is floating on another liquid. Here we derive an elasto-capillary model for contact angles on a soft solid, by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of vanishing elastic modulus yields Neumann's law or a slight variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit (Young) to the soft limit (Neumann) appears when the length scale defined by the ratio of surface tension to elastic modulus $\gamma/E$ reaches a few molecular sizes. [Preview Abstract] |
Monday, November 19, 2012 4:40PM - 4:53PM |
L19.00006: Dynamics of ultrasound-driven two-dimensional microbubbles Cheng Wang, Bhargav Rallabandi, Sascha Hilgenfeldt Oscillating microbubbles driven by ultrasound are powerful actuators in microfluidics, with applications including mixing enhancement, particle manipulation, and cell lysis. The bubble dynamics is crucial towards the understanding of steady microstreaming flows. We experimentally characterize the oscillation modes and the frequency response spectrum of oscillating bubbles in 2D, driven by a pressure variation resulting from ultrasound in the range of 1\,kHz$\leq f\leq $100\,kHz. Using high-speed imaging, we analyze the oscillation modes of time-resolved bubble interface shapes. We find that (i) distinct, robust resonance patterns occur independent of details of the set-up, (ii) the position and width of the resonance peaks can be understood using an asymptotic theory approach, and (iii) the appearance of streaming flow patterns is governed by the {\em relative} amplitudes of bubble surface modes (normalized by the volume response). These results enable an understanding of streaming flow control through tuning of the driving frequency, with consequences for practical applications. [Preview Abstract] |
Monday, November 19, 2012 4:53PM - 5:06PM |
L19.00007: Oscillations of a cylindrical bubble attached to a wall Bhargav Rallabandi, Cheng Wang, Sascha Hilgenfeldt Sustained bubble oscillations in a liquid can result in steady streaming flows that may be exploited as a powerful tool of fluid manipulation at the micron scale. While the oscillations and the resulting streaming of a bubble in bulk fluid are well understood, the practically relevant case of a bubble attached to the wall of a microfluidic device has not been studied extensively, as additional complexity is introduced by the presence of the wall and the bubble contact lines. We provide here an asymptotic theory by which a long-wavelength ultrasound excitation is translated into shape oscillations of the bubble via its surface dynamics. We show that viscous effects near the contact lines entail a coupling mechanism between volume and surface mode oscillations, which governs the features of the frequency response curves obtained. The amplitudes and phases of the bubble oscillation modes are then used to calculate the streaming flow, which is a combined effect of wall-induced streaming and mode-interaction near the surface of the bubble. [Preview Abstract] |
Monday, November 19, 2012 5:06PM - 5:19PM |
L19.00008: Straight contact lines on a soft solid Laurent Limat Using a Stokes like approach of incompressible elasticity, I calculated the distortions induced by a straight contact line on a elastic substrate having a non-zero surface tension. The response is very similar to that of Shanahan and de Gennes, except that the short scale divergence of the Log profile is regularized by the elastocapillary length built upon shear modulus and substrate surface tension, and replaced by a Neumann balance of surface tensions. This method is extended to treat a substrate surface tension that differs in the dry and wetted regions, i.e. a contact angle that differs from 90 degrees, with the example of a infinite rivulet composed of two contact lines connected by a curved, cylindrical, liquid interface. The perhaps most surprising result is that the local slope of the substrate, very near contact line, is nearly inversely proportional to the substrate surface tension, each ``side'' (``dry'' or ``wet'') of the contact line being very close to support one half of the applied vertical force. This result has surprising implications for the approximate treatment of wetting hysteresis on substrates having both plastic and elastic properties, that seem to be ruled at small scales only by surface tension effects [Preview Abstract] |
Monday, November 19, 2012 5:19PM - 5:32PM |
L19.00009: Multiple equilibria and evaporation in elastocapillary systems Kiran Singh, Michele Taroni, Dominic Vella, Tae-Hong Kim, Ho-Young Kim In this talk we consider the coalescence of microscopic flexible beams caused by the surface tension of an intervening liquid. Our work is motivated by the coalescence observed in the manufacture of MEMS devices. We develop a model coupling the elastic deflection of the beams, lubrication-type flow and surface tension; we also investigate the role played by the evaporation of the liquid. In the absence of evaporation, multiple equilibrium states exist. We characterize these states and determine their stability. We consider the effect of evaporation and show that sufficiently high evaporation rates can suppress the tendency of beams to stick together. Finally, we consider some extensions of our models showing how the interaction between multiple beams may delay the rate of evolution and discuss the way in which heating the beams is even more effective in suppressing sticking. [Preview Abstract] |
Monday, November 19, 2012 5:32PM - 5:45PM |
L19.00010: Capillary rise of oil in an aqueous foam Keyvan Piroird, \'Elise Lorenceau Oil is usually known as an anti-foaming agent. Yet, it has been shown that oil droplets present in the foaming solution can have the opposite effect and stabilize a foam when unable to cross the air/water interface. In these previous studies, oil is first emulsified and then mixed with air to generate a foam. In this work, we report experiments where an aqueous foam is put in direct contact with a large oil drop. With the appropriate choice of oil and surfactants, oil spontaneously invades the liquid network of the foam without damaging it. We study the dynamics of penetration at the scale of a single Plateau border, that acts as a ``liquid capillary tube" in which oil flows in an unbroken stream. At the end of the experiment, a long and stable cylinder of oil is formed in the Plateau border. This cylinder breaks up into droplets when, following a rearrangement, oil is transferred from the Plateau border to a soap film. [Preview Abstract] |
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