Wed June 25th 2014
16:00 – 17:00
Seminar A Granular Rotor and dynamic surface tension measurements
Erik-Jan Staat, Loreto Oyarte


1. A Granular Rotor in the Non-Brownian Regime

The attempts to challenge the second law of the thermodynamics have been many throughout history. In 1912, Marian Smoluchowski devised a prototype designed to convert Brownian motion into work, but 50 years later Feynman showed unambiguously why at thermal equilibrium this device cannot actually do this. However, far from equilibrium the behavior of a rotor which rectifies motion of randomly moving molecules in their surroundings, is still an active matter of study. These molecular motors are responsible for tensing and relaxing the muscles of the body, for numerous cellular and intracellular transport process, photovoltaic and photorefractive effects, among many others.[1] We study experimentally and theoretically the movement of a granular motor, consisting of a horizontal rotor with four vanes immersed in a granular bath. The vanes in the rotor are precisely balanced around an axis, which in turn is connected to the container wall by a low-friction ball bearing. The angle is measured by an optical angle encoder.[2] We studied the rotor in the independent-kick regime. In this regime, the rotor is in rest for most of the time. Only occasionally a particle-vane collision sets the vanes into motion. Therefore the time between particle-rotor collisions is longer than the time the rotor needs to be stopped by friction (TC >> TS). This regime is dominated by ball-bearing friction. We calculate the angular velocity distribution (AVD), wich consists of a singularity corresponding to the time during which the motor is at rest, and a regularpart corresponding to the relaxation after kicks[3]. From the experimental study, we observed a non-linear relaxation velocity, implying that the dynamic friction of the rotor is not constant in this regime. We used this observation in our model to obtain the regular part of the AVD. With the goal of understanding the behavior of the granular rotor, we injected more energy to the granular gas and, as a result, the time between particle-rotor collisions becomes comparable to the time the rotor needs to be stopped by friction (TC ~ TS). In this case, our model turns into in an integral equation wich we solve using the corresponding eigenvalue problem. The rotor can be symmetric or not. In the non-symmetric case, the rotor favors one of the two directions, which is known as the ratchet effect. We adapted our models to both regimes and compared with the experimental results, like in the symmetric cases. Our models fit precisely to the experimental results in both regimes and for symmetric and non-symmetric conditions. [1] P. Reimann, Phys. Rep. 361, 57 (2002). [2] P. Eshuis, K. van der Weele, D. Lohse, and D. van der Meer, Phys. Rev. Lett. 104, 248001 (2010). [3] J. Talbot, R. D. Wildman, and P. Viot, Phys. Rev. Lett. 107, 138001 (2011)

2. Dynamic surface tension measurements from midrodroplet oscillations

In modern drop-on-demand inkjet printing, the jetted liquid is a mixture of solvents, pigments and surfactants. In order to predict the droplet formation process, it is of importance to know the liquid properties. Surface tension is not constant at the timescale of droplet formation for a liquid that contains surfactants, making it non-trivial to determine the surface tension of the ink directly. Therefore we developed a technique to measure the surface tension of liquids during inkjetting. We use high speed imaging to record the shape oscillation of a microdroplet within the first few hundred microseconds after droplet pinch-off. The frequency of oscillation depends on the surface tension, so by determining the oscillation frequency, we can measure the surface tension. The decay of oscillation amplitude is set by the viscosity, so we can also determine the viscosity with this technique.
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing