A comprehensive analysis of the evaporation of a liquid spherical drop

Abstract

In this paper, a new comprehensive analysis of a suspended drop of a pure liquid evaporating into air is presented. Based on mass and energy conservation equations, a quasi-steady model is developed including diffusive and convective transports, and considering the non-isothermia of the gas phase. The main original feature of this simple analytical model lies in the consideration of the local dependence of the physico-chemical properties of the gas on the gas temperature, which has a significant influence on the evaporation process at high temperatures. The influence of the atmospheric conditions on the interfacial evaporation flux, molar fraction and temperature is investigated. Simplified versions of the model are developed to highlight the key mechanisms governing the evaporation process. For the conditions considered in this work, the convective transport appears to be opposed to the evaporation process leading to a decrease of the evaporation flux. However, this effect is relatively limited, the Péclet numbers happening to be small. In addition, the gas isothermia assumption never appears to be valid here, even at room temperature, due to the large temperature gradient that develops in the gas phase. These two conclusions are explained by the fact that heat transfer from the gas to the liquid appears to be the step limiting the evaporation process. Regardless of the complexity of the developed model, yet excluding extremely small droplets, the square of the drop radius decreases linearly over time (R2 law). The assumptions of the model are rigorously discussed and general criteria are established, independently of the liquid–gas couple considered.