Running droplets in a random medium |
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| Institution: | 1. School of Science, Huzhou University, Huzhou 313000, PR China;2. Department Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran;3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;4. Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran;5. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;6. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran;1. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, China;2. School of Civil Engineering, The University of Sydney, Australia;3. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an, China;4. Department of Mechanics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden;5. The University of Sydney Nano Institute (Sydney Nano), The University of Sydney, NSW 2006, Australia |
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| Abstract: | We consider droplets of radius R injected in a porous medium with a pore size d Ř. The droplets react chemically with the surface of the pores, and make it less wettable. They should acquire a velocity V which is, in most cases, independent of R. For R ~ d, we expect the trajectory to be a random walk. For R > > d, however, it should be ballistic. These effects should be visible when gravity effects are negligible: either by using very small pores (d < d* ~10μm), or saturating the porous medium with a passive fluid of matched density. Various transport problems associated with this process are discussed here at the level of scaling laws. |
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