(171r) Exploring the Influence of Evaporation on Respiratory Droplet Dynamics in Ventilated Indoor Environments

Infectious diseases, such as COVID-19, can be transmitted by the exhaled virus-laden respiratory droplets. In indoor environments, ventilation systems are widely used to dilute or remove such droplets. To improve their performance and lower the infection risk, investigations on droplet transport under different ventilation systems are of great importance.

Respiratory droplets in indoor environments constitute a complex multiphase system. The sizes of droplets, affecting the balance between aerodynamic and gravitational forces acting on them, play an important role in their trajectories. In addition, the respiratory droplets are multicomponent, containing volatile and non-volatile substances. They can evaporate, which causes changes in size and significantly affects droplet transport. Computational fluid dynamics (CFD) provides a powerful tool to investigate the droplet transport. To consider the effect of evaporation, a zero-dimensional (0D) evaporation model for the salt-water droplets, which assumes salt is homogeneously distributed inside a droplet, is widely used to resemble the respiratory droplets. However, the salt is found to be not homogeneously distributed inside the droplets [1]. A salt shell may form due to the enrichment of salt in the droplet surface, resulting in the droplet residue larger than the prediction of the 0D model. Therefore, the one-dimensional (1D) evaporation model, considering the salt diffusion inside the droplets, was adopted by some researchers [1, 2]. This, however, increases the computational costs.

In this study, the reaction engineering approach (REA) model [3] is adopted for the evaporation of respiratory droplets. It is a 0D model owning lower computational costs and it can consider the non-homogeneous salt distribution by establishing the REA curve. To obtain the REA curve, the factors affecting salt distribution inside the droplets are analyzed first using a validated 1D model. Based on the results, the REA model is established by relating the most influential factors with the REA curve [4]. Finally, the REA model is coupled with the Eulerian-Lagrangian approach to trace the transport and evaporation of respiratory droplets in ventilated indoor environments.

Some obtained information is shown as follows. First the factors affecting droplet evaporation are investigated. Samples with changing initial droplet diameter , initial droplet salt mass fraction , initial droplet temperature , ambient temperature , relative humidity , and relative velocity are simulated with the validated 1D model. The evaporation rate , evaporation time , equilibrium diameter after evaporation , and salt non-uniformities (the salt mass fraction ratio between surface and center , and that between surface and average ) of each sample are calculated. Fig. 1 presents their correlation coefficients. It can be seen that is the most important factor for evaporation rate and non-uniformity because increasing significantly reduces the evaporation rate and the small evaporation rate alleviates the surface enrichment of the salt.

Since plays an important role in droplet evaporation, the REA model will be established based on it. Fig. 2 presents the REA curves under different . The REA curves present the relationship between the dry basis of the moisture content and the relative activation energy of evaporation . Increasing , the REA curve moves to the right and upper regions. This indicates that the droplets under high have higher activation energy and thus lower evaporation rate. The REA curve can be fitted by an exponential function as shown in Fig. 3. The REA model is established by expressing the relationship between the parameters for the exponential function and the using the 8th-order polynomials.

Finally, the REA model based on is validated with droplets under changing , , , , and . Fig. 4 compares the size changes obtained using the 1D model and the REA model. Good agreement can be observed. The REA model established based on is reasonable and can be used to trace droplet evaporation under different ambient conditions.

Acknowledgement:

Computational resources provided by hpc@polito (http://www.hpc.polito.it)

References:

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[2] Feng Y, Li D, Marchisio D, Vanni M, Buffo A. A computational fluid dynamics—Population balance equation approach for evaporating cough droplets transport. International Journal of Multiphase Flow, 2023, 165, 104500

[3] Chen X, Xie G. Fingerprints of the drying behaviour of particulate or thin layer food materials established using a reaction engineering model. Food and Bioproducts Processing, 1997, 75 (C4), 213–222.

[4] Al Zaitone B, Al-Zahrani A, Al-Shahrani S, Lamprecht A. Drying of a single droplet of dextrin: Drying kinetics modeling and particle formation. International Journal of Pharmaceutics, 2020, 574, 118888.