Infiltration of impacting droplets into porous substrates
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RESEARCH ARTICLE
Infiltration of impacting droplets into porous substrates D. J. Bouchard1 · S. Chandra1 Received: 5 August 2020 / Revised: 14 September 2020 / Accepted: 16 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The impact of water droplets on thin porous layers of glass beads held vertically between glass plates was photographed to observe simultaneous spreading and infiltrating of the liquid into the porous medium. Glass beads with diameters of either 100 µm or 500 µm were tested and micro-computed tomography was used to measure the porosities of the layers. The water drop diameter was kept constant at 2 mm while the impact velocity was varied from 0.06, to 1.9 m/s. High-speed videos of the advance of water into the porous structure were studied with image analysis software and the volume flow rate of liquid calculated. Increasing droplet impact velocity decreases droplet infiltration time because higher droplet inertia drives more liquid into the porous material and a larger droplet spreading diameter increases the area in contact with the substrate. Too high of an impact velocity results in droplet cleaving where a portion of the drop remains on the upper surface. A simple model is proposed to determine when inertia driven infiltration will be significant. Once droplet inertia is dissipated capillary forces draw liquid into the substrate and analytical models are compared to predict the rate of capillary driven flow. Graphic abstract
Water drops, 2 mm in diameter, impacting porous slices at 1.9 m/s. Drops mostly spread over 100 µm diameter glass beads (left) but penetrate into 500 µm diameter glass beads (right).
List of symbols Ao Open surface area of impact site AT Total surface area of impact site 𝜌gD 2 Bo Bond number—Bo = 𝜎 p C Material property of porous material D Droplet spread diameter Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00348-020-03056-9) contains supplementary material, which is available to authorized users. * D. J. Bouchard [email protected] 1
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada
D0 Initial drop diameter Db Diameter of glass bead Dp Pore diameter g Gravitational constant hp Height of liquid profile hp+ Dimensionless height of the liquid profile H Height of liquid front in capillary rise experiments L Gap width Leff Effective gap spacing m Mass of liquid N Number of samples P Pressure PR0 Pressure at the source of liquid profile PR1 Pressure at the advancing front of the liquid profile
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Ps Stagnation pressure R0 Starting radius of liquid profile in the porous slice R1 Radius of liquid profile R2 Profile principal radius of curvature—perpendicular to the plates R3 Drop radius 𝜌UD Re Reynold’s number – Re = 𝜇 p
reff Effective capillary radius rWCR Wasburn Capillary Rise radius t Time t+ Dimensionless inert
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