Revisiting D2-law for the evaporation of dilute droplets

Abstract

In a wide range of applications, the estimate of droplet evaporation time is based on the classical D 2 -law, which, assuming a fast mixing and fixed environmental properties, states that the droplet surface decreases linearly with time at a determined rate. However, in many cases the predicted evaporation rate is overestimated. In this Letter, we propose a revision of the D 2 -law capable of accurately determining droplet evaporation rate in dilute conditions by a proper estimate of the asymptotic droplet properties. Besides a discussion of the main assumptions, we tested the proposed model against data from direct numerical simulations finding an excellent agreement for predicted droplet evaporation time in dilute turbulent jet-sprays.

Modelling the direct virus exposure risk associated with respiratory events

“…A graphical representation of these model parameters is provided in figure 1. From a mathematical point of view, the model formulation can be summarized as follows: the surface evaporation rate estimated by the thermodynamic properties of the droplet and environment [25]. The inertial Reynolds number of droplets with initial diameter D 2 d,0 is taken into account for the Stokes law with a fixed drag correction factor f. The initial height of the droplets away from the ground is defined as H d and U 0 is the velocity of a respiratory puff ejected from a mouth with characteristic size R 0 .…”

“…A similar evaporation model, the so-called D 2 -law, was introduced by Langumir's pioneering work [22] and then adopted in the Wells theory [17]. Recently, it has been revised by Dalla Barba et al [25] for the determination of k, where the asymptotic evaporation temperature of isolated, evaporating droplets is used instead of the initial one to calculate the evaporation rate. This revised D 2 -law provides more accurate predictions for the evaporation of dilute droplets (see electronic supplementary material for details and validations against experimental data); for additional details, readers are referred to Dalla Barba et al [25].…”

“…Therefore, the warm and humid exhaled vapour puff becomes supersaturated when entering the cold ambient air, so the droplets carried by the puff tend to experience vapour condensation before evaporating at long time. The colder the ambient air, the more important this nonmonotonic behaviour is [20,25]. To improve the accuracy of the evaporation model, especially for short time evolution, we propose here a minor improvement to the revised D 2 -law.…”

“…Specifically, the mean evaporation times seem to follow a D 2 -law-like scaling but with a different pre-factor. Inspired by this observation, a revised version of the D 2 -law has been recently proposed by Dalla Barba et al [25]: using a proper estimate of the asymptotic droplet temperature, the evaporation rate of dilute droplets in sprays, jets and puffs can be accurately determined. Even if more accurate than the classical formulation, it should be remarked that the performance of the revised D 2 -law is affected by low-temperature and high RH environmental conditions.…”

“…We start by assessing the accuracy of the revised D 2 -law [25] in evaluating the evaporation of respiratory droplets. Building on this, we propose a revision of the traditional Wells theory, including an effective correction to the classical Stokes drag needed for relatively large droplets.…”