d-square law

The d-square law or $d^2$-law is a relationship between diameter and time for an isolated, spherical droplet when it evaporates quasi-steadily, which was first observed by Boris Sreznevsky in 1882, and was explained by Irving Langmuir in 1918. If $d(t)$ and $t$ are the droplet diameter and time, then $d^2$-law pertains to the relation

$d_0^2-d^2=K(t-t_0),$

where $t_0$ is the initial time, $d_0=d(t_0)$ is the initial droplet diameter and $K$ is called the evaporation constant.

Crespo–Liñán correction

Crespo–Liñán correction refers to a small correction of the order $1/\sqrt{\epsilon }$ to the d-square law in terms of the small parameter $\epsilon ={\rho }_g/{\rho }_l\ll 1$, the ratio of gas to liquid density. Antonio Crespo and Amable Liñán showed that the quasi-steady approximation is correct in the inner zone having the size on the order of droplet diameter, but becomes invalid in an outer zone with a size larger than the droplet diameter by the factor of $1/\sqrt{\epsilon }$, where the unsteady terms cannot be neglected.