The d-square law or -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,Sreznevsky, B. I. (1882). About evaporation of liquids. Journal of the Russian Physical Chemistry Society, ZhRFKhO, 14(8). and was explained by Irving Langmuir in 1918.Langmuir, I. (1918). The evaporation of small spheres. Physical review, 12(5), 368. If and are the droplet diameter and time, then -law pertains to the relationWilliams, F. A. (2018). Combustion theory. CRC Press. Chapter 3Liñán, A., & Williams, F. A. (1993). Fundamental aspects of combustion. Oxford university press.
where is the initial time, is the initial droplet diameter and is called the evaporation constant.
Crespo–Liñán correction Crespo–Liñán correction refers to a small correction of the order to the d-square law in terms of the small parameter , the ratio of gas to liquid density. Antonio Crespo and Amable LiñánCrespo, A., & Linan, A. (1975). Unsteady effects in droplet evaporation and combustion. Combustion Science and Technology, 11(1-2), 9-18. 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 , where the unsteady terms cannot be neglected.Williams, F. A., Nayagam, V., & Dietrich, D. L. (2022). Discussion of likely causes of possible variation of the effective ambient environment during quasi-steady droplet combustion supported by cool-flame chemistry. Combustion and Flame, 239, 111659.
References