A model for the evaporation of droplets from sand

An analytical model is presented for predicting the evaporation behaviour of individual droplets from sand surfaces in atmospheric wind fields. The model describes the evaporation process exclusively in terms of mass transfer and is applicable to persistent liquids that have low volatilities. The model is based on a one-dimensional treatment of the problem, and describes the impinged droplet evaporation process via a receding evaporation front hypothesis. The evaporation rate is dictated by the rate at which vapour is transported from the submerged liquid front through the sand pores and into the atmospheric boundary layer. Transport of vapour in the sand is described by molecular diffusion, using an effective diffusivity to account for transport through the pore network. Transport of vapour into the atmospheric boundary layer is assumed to be passive, and both smooth and rough surfaces are considered. The effect of molecular diffusion in the interfacial sublayer adjacent to the surface is included. Vapour transport into the atmospheric sublayer is described by invoking similarity, and takes into account the atmospheric stability conditions. The model is compared with experimental data for the evaporation of diethyl malonate droplets from sand surfaces in an aerodynamically smooth wind tunnel. The droplet evaporation rate dependence on droplet size, wind speed and temperature are well represented by the model. In addition, the transient decline in the evaporation rate is well modelled by the receding evaporation front hypothesis.