title: Transient volume of evaporating sessile droplets: 2/3, 1/1, or another power law?
abstract: The transient shape and volume of evaporating sessile droplets are critical to our understanding and prediction of deposits left over on the solid surface after droplet evaporation. The 2/3 power law of scaling, (V/Vo)(β) = 1 - t/tf with β = 2/3, has been widely used. The 1/1 power law of scaling with β = 1 was also obtained for vanishingly small contact angles. Here we show that β significantly deviates from 2/3 and 1 when the droplet base is pinned: β depends on both initial and transient contact angles. The 1/1 power law presents the upper limit of β = 1, while β = 2/3 is the lower limit if contact angles are smaller than 148°. Unexpectedly, β can be smaller than 2/3 if contact angles are larger than 148°. We also present a semianalytical approximation for β as a function of the initial contact angle.
authors.affiliation: School of Chemical Engineering, The University of Queensland , Brisbane, QLD 4072, Australia.
authors.forename: Tuan A H
authors.initials: TA
authors.lastname: Nguyen
authors.forename: Anh V
authors.initials: AV
authors.lastname: Nguyen