On the lifetimes of evaporating droplets

Abstract

The complete description of the lifetime of a droplet on a solid substrate evaporating in a 'stick-slide' mode is obtained. The unexpectedly subtle relationship between the lifetime of such a droplet and the lifetimes of initially identical droplets evaporating in the extreme modes (namely the constant contact radius and constant contact angle modes) is described and summarised in an appropriate master diagram. In particular, it is shown that the lifetime of a droplet is not, in general, constrained by the lifetimes of the extreme modes.

On the lifetimes of evaporating droplets with related initial and receding contact angles

“…For values of θ 0 smaller than θ 0min (i.e., when 0 ≤ θ 0 ≤ θ 0min ), then (11) yields θ * = 0, so that the contact line never depins and the droplet evaporates in the CR mode, while for values of θ 0 larger than θ 0min (i.e., when θ 0min < θ 0 ≤ π), then (11) yields θ * = arccos( f p + cos θ 0 ) (0 < θ * ≤ π − θ 0min ), and the droplet evaporates in the SS mode. Stauber et al 16 ( Figure 2) showed that the theoretical predictions of the present model are in rather good agreement with the lifetimes extrapolated from 29 sets of experimental data for droplets evaporating in a SS mode in which the second slide phase is smaller than 10% of the lifetime of the droplet (so that the present idealised SS mode is likely to be an appropriate description of their behaviour) obtained by previous authors. Details of these sets of experimental data are given in Table I.…”

“…This mode of evaporation is sketched in Figure 1. Stauber et al 16 showed that the resulting theoretical predictions for t SS are not, as might naively have been expected, always constrained to lie between the lifetimes of the extreme (i.e., the CR and CA) modes, and, moreover, that they are in good agreement with the lifetimes measured experimentally by previous authors. In order to make this latter comparison, the values of θ 0 and θ * for each experiment (which, in general, depend of the nature of the substrate, the fluid, and the atmosphere) were taken directly from the experimental measurements.…”

“…Fluids 27, 122101 (2015) the analysis of Stauber et al 16 by proposing a physically credible relationship between them based on the unbalanced Young force and use this relationship to give a complete description of t SS . In particular, we show that the dependence of t SS on θ 0 is qualitatively different from that when the relationship between θ 0 and θ * is not taken into account.…”

“…[6][7][8][9][10][11][12][13][14] is one in which an initial stick phase is followed by a first slide phase with constant contact angle and a second slide phase in which both the contact radius and the contact angle vary. In practice, the second slide phase can be relatively short compared to the other two phases, and so Nguyen and Nguyen, 15 Dash and Garimella, 14 and Stauber et al 16 considered a simple but effective model for an idealised SS mode in which the second slide phase is entirely neglected and initially the droplet evaporates in a CR phase in which R = R 0 and θ(t) and V (t) decrease until θ(t) reaches the receding contact angle θ * (0 ≤ θ * ≤ θ 0 ), at which the contact line depins and subsequently the droplet evaporates in a CA phase in which θ(t) = θ * and R(t) and V (t) decrease to zero at time t = t SS , where t SS (which depends on both θ 0 and θ * ) denotes the lifetime of the droplet. This mode of evaporation is sketched in Figure 1.…”

Dissolution of a spherical cap bubble adhered to a flat surface in air-saturated water

“…Stauber et al (2014) name this behaviour as the 'stick-slide' mode, in which the droplet first evaporates in a constant contact radius phase, followed by a sliding phase at a constant contact angle. The advancing contact angle is referred to as the transition contact angle instead.…”