Evaporation of a freely floating droplet in an airstream: effects of temperature, humidity, and shape oscillations

Abstract

We present a comprehensive experimental and theoretical investigation of the evaporation dynamics of freely levitated water droplets in an upward airstream under varying temperature and relative humidity conditions, using a custom-designed wind tunnel that replicates natural rainfall scenarios. A high-speed imaging system captures the temporal evolution of morphology, shape oscillations, and size reduction of the droplet undergoing evaporation. Our observations reveal that larger droplets exhibit persistent shape oscillations due to the interplay between inertia and surface tension in the presence of convective airflow, which significantly alters the evaporation rate compared to that of a stationary spherical droplet in quiescent air. To quantify the effects of air convection, complex morphology, and shape oscillations of the levitated droplet at different temperatures and humidity, we develop a modified evaporation model that extends the classical $d^2$-law. This model incorporates (i) a generalized Sherwood number that accounts for the variation in Reynolds number, Schmidt number, temperature, and relative humidity and (ii) a shape factor that captures the time-averaged surface area of oscillating droplets. The model is validated against experimental findings across a wide range of droplet sizes and environmental conditions, showing excellent agreement in predicting the temporal evolution of droplet diameter and total evaporation time. Furthermore, we construct a regime map showing the variation in the lifetime of the droplet in the temperature-humidity space. The present study establishes a framework that integrates convective transport and morphological deformation, offering new insights into the microphysics of raindrop evaporation.

Figures (18)

• Figure 1: A schematic diagram of the experimental test section, where a droplet undergoing evaporation is levitated between a pressure plate at the top and a mesh at the bottom. The droplet is introduced using a dispensing needle. A photograph of the actual experimental setup is provided in Figure \ref{['RRF']}.
• Figure 2: A photograph of the state-of-the-art raindrop research facility, designed to simulate a wide range of atmospheric conditions by precisely controlling the temperature and relative humidity of the inlet air patent_RRF. It consists of: (a) an outdoor chiller unit, (b) a cooling unit comprising an air inlet section, cooling and humidification unit, dehumidification chamber, and control unit, and (c) a Z-type wind tunnel composed of a settling chamber, a converging dome with sieves and honeycombs, a test section, a diverging section, a sonic nozzle valve, and a vacuum pump.
• Figure 3: Illustration of the procedure for selecting major and minor diameters of non-spherical droplets in various orientations to estimate their volume ($V$) at different time instants. Here, $\alpha$ denotes the orientation angle of the major axis relative to the horizontal. Panels (a) $\alpha = 0^\circ$, (b) $0^\circ \leq \alpha \leq 45^\circ$, and (c) $135^\circ \leq \alpha \leq 180^\circ$ correspond to oblate droplets in different orientations. Similarly, panels (d) $\alpha = 90^\circ$, (e) $45^\circ \leq \alpha \leq 90^\circ$, and (f) $90^\circ \leq \alpha \leq 135^\circ$ represent prolate droplets in various configurations.
• Figure 4: Temporal evolution of the morphology of a levitated droplet undergoing evaporation in an upward airstream captured from two orthogonal views: (a) $yz$ - view and (b) $xy$ - view, using synchronized cameras as shown in figure \ref{['schematic']}. Here, $d_{0} = 4.0\pm 0.3$ mm, $RH = 10\%$ and $T = 30^{\circ}$C. The normalized time is given by $\tau = t/t_{80}$, where $t$ is the instantaneous time and $t_{80}$ denotes the time at which 80% of the initial volume of the droplet has evaporated. The corresponding combined video showing both views is provided as a Supplementary Movie.
• Figure 5: Temporal evolution of the normalized axis ratio ($\chi$) of the oscillating droplet at different temperatures ($T$) during the early and later stages of evaporation. The remaining parameters are $d_0 = 3.0 \pm 0.3$ mm and $RH = 50\%$. The time period ($t_p$) and the equivalent droplet diameter ($d_{eq}$) corresponding to the early and later stages are indicated in the respective panels.