A novel asymptotically consistent approximation for integral evaporation from a spherical cap droplet

The total evaporation rate due to a volatile capillarity-dominated droplet diffusively evaporating into the surrounding gas is a critically important quantity in industrial and engineering applications such as Q/OLED screen manufacturing. However, the analytical expression in terms of integrals in toroidal coordinates can be unwieldy in applications, as well as expensive to compute. Therefore, simple yet highly accurate approximate solutions are frequently used in practical settings. Herein we present a new approximate form that is both accurate and fast to compute, but also retains the correct asymptotic behaviour in the key physical regimes, namely hydrophilic and superhydrophobic substrates, and a hemispherical droplet. We illustrate this by comparison to several previous approximations and, in particular, illustrate its use in calculating droplet lifetimes, as well as approximating the local evaporative flux.