title: Spreading of a droplet over a nonisothermal substrate: multiple scaling regimes.
abstract: We envisage the spreading behavior of a two-dimensional droplet under a thin-film-based paradigm, under a perfect wetting condition, while the droplet is placed over a nonisothermal substrate. Starting from the onset of thin-film behavior (or equivalently beyond the inertia-dominated initial stage), we identify the existence of mutually contrasting multiple scaling regimes defining the spreading behavior at different time scales. This is attributable to the time-stage-wise upsurge of capillarity or thermocapillarity over the other. In particular, the spreading behavior is characterized by the foot-width (w) evolution with time (t) in a power-law fashion w ∼ t(α), with α being the spreading exponent, defining the rate of spreading. Following pertinent thin-film and subsequent similarity analysis, we identify different asymptotes of α over disparate temporal scales, leading to the characterization of different scaling regimes over the entire spreading event starting from the inception of thin-film behavior. Reported literature data are found to correspond well to the present interpretations and estimations.
authors.affiliation: Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
authors.forename: Kaustav
authors.initials: K
authors.lastname: Chaudhury
authors.affiliation: Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
authors.forename: Suman
authors.initials: S
authors.lastname: Chakraborty