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d-square law

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The d-square law or d 2 {\displaystyle 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 ) {\displaystyle d(t)} and t {\displaystyle t} are the droplet diameter and time, then d 2 {\displaystyle d^{2}} -law pertains to the relation

d 0 2 − d 2 = K ( t − t 0 ) , {\displaystyle d_{0}^{2}-d^{2}=K(t-t_{0}),}

where t 0 {\displaystyle t_{0}} is the initial time, d 0 = d ( t 0 ) {\displaystyle d_{0}=d(t_{0})} is the initial droplet diameter and K {\displaystyle K} is called the evaporation constant.

References

  1. Sreznevsky, B. I. (1882). About evaporation of liquids. Journal of the Russian Physical Chemistry Society, ZhRFKhO, 14(8).
  2. Langmuir, I. (1918). The evaporation of small spheres. Physical review, 12(5), 368.
  3. Williams, F. A. (2018). Combustion theory. CRC Press. Chapter 3
  4. Liñán, A., & Williams, F. A. (1993). Fundamental aspects of combustion. Oxford university press.


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