TY - JOUR
T1 - The shielding effect extends the lifetimes of two-dimensional sessile droplets
AU - Schofield, Feargus G. H.
AU - Wray, Alexander W.
AU - Pritchard, David
AU - Wilson, Stephen K.
PY - 2020/2/5
Y1 - 2020/2/5
N2 - We consider the diffusion-limited evaporation of thin two-dimensional sessile droplets either singly or in a pair. A conformal-mapping technique is used to calculate the vapour concentrations in the surrounding atmosphere, and thus to obtain closed-form solutions for the evolution and the lifetimes of the droplets in various modes of evaporation. These solutions demonstrate that, in contrast to in three dimensions, in large domains the lifetimes of the droplets depend logarithmically on the size of the domain, and more weakly on the mode of evaporation and the separation between the droplets. In particular, they allow us to quantify the shielding effect that the droplets have on each other, and how it extends the lifetimes of the droplets.
AB - We consider the diffusion-limited evaporation of thin two-dimensional sessile droplets either singly or in a pair. A conformal-mapping technique is used to calculate the vapour concentrations in the surrounding atmosphere, and thus to obtain closed-form solutions for the evolution and the lifetimes of the droplets in various modes of evaporation. These solutions demonstrate that, in contrast to in three dimensions, in large domains the lifetimes of the droplets depend logarithmically on the size of the domain, and more weakly on the mode of evaporation and the separation between the droplets. In particular, they allow us to quantify the shielding effect that the droplets have on each other, and how it extends the lifetimes of the droplets.
UR - https://doi.org/10.1007/s10665-019-10033-7
U2 - 10.1007/s10665-019-10033-7
DO - 10.1007/s10665-019-10033-7
M3 - Article
SN - 0022-0833
VL - 120
SP - 89
EP - 110
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
ER -