On the Evaporation of Raindrops in the Presence of Vertical Gradients of Temperature and Relative Humidity

By use of the time-dependent diffusion equation it is shown that a heat-balance equation for an evaporating raindrop based on the “quasi-stationary” assumption (∂//t = 0) is accurate. This equation is then used to obtain the expression T = θw + zRdθw/dz for the steady-state temperature T of an evaporating drop in an atmosphere having linear vertical gradients of temperature and relative humidity, where θw is the equilibrium drop temperature in a uniform atmosphere (approximately the environmental wet-bulb temperature), dθw/dz is its vertical gradient, and zR is the thermal relaxation distance of the drop (falling at terminal velocity). The term zRdθw/dz is the thermal lag in the drop's response to the varying environment. Computations show that the ratio of the drop evaporation rate with the tag term to the rate without the tag departs significantly from unity for large drops and high humilities.