A new way of assessing droplet evaporation independently of the substrate hydrophobicity and contact line mode: A case study of sessile droplets with surfactants

Evaluating and predicting evaporation kinetics of a sessile droplet present challenging exercises because of its strong dependence on the substrate hydrophobicity (contact angle) and the evaporation mode at the three-phase contact line. For sessile water droplets containing surfactants, the existence of surfactant would not only change droplet's geometry during the evaporation course, but could also affect the liquid cohesive energy density; thereby interactively affecting the evaporation kinetics. Here we present a new analytical model for the Hildebrand solubility parameter, which represents the cohesive energy density, as a function of time, thus a function of surfactant concentration inside a drying droplet. This distinct expression for the solubility parameter is independent of the droplet's geometry, therefore can be used to assess the variation of cohesive energy density during the evaporation course independently of both surface hydrophobicity and the evaporation mode. Our model resolve conflicting effects of water-soluble surfactants like sodium dodecyl sulfate (SDS) reported in the literature. It is shown that SDS can alter the evaporation rate differently (significantly or insignificantly) depending on the closeness of the studied system to the theoretical droplet lifetime extremum at the contact angle of 90°. The presence of SDS, up to the critical micellar concentration, does not significantly ease the vaporization of water through the air-liquid interface; nor SDS lead to faster evaporation rate by preferentially oscillating and vibrating of the adsorbed SDS molecules at the free water surface. Our theoretical analysis also provides a new approach to calculating the Hildebrand solubility parameter to estimate the cohesive energy density of different solvents.