TY - JOUR
T1 - A novel asymptotically-consistent approximation for integral evaporation from a spherical cap droplet
AU - Wray, Alexander W.
AU - Moore, Madeleine R.
PY - 2024/4/17
Y1 - 2024/4/17
N2 - 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, sim-ple 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.
AB - 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, sim-ple 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.
KW - evaporation
KW - approximate solutions
KW - droplets
KW - capacitance
U2 - 10.1007/s10665-024-10355-1
DO - 10.1007/s10665-024-10355-1
M3 - Article
SN - 0022-0833
VL - 146
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
M1 - 4
ER -