Expressions for the evaporation of sessile liquid droplets incorporating the evaporative cooling effect.

The evaporation along the surface of pinned, sessile droplets is investigated numerically by using the combined field approach. In the present model, the evaporative cooling at the droplet surface which leads to a reduction in the evaporation is taken into account. Simple, yet accurate analytical expressions for the local evaporation flux and for the total evaporation rate of sessile droplets are obtained. The theoretical analyses indicate that the reduction in the evaporation becomes more pronounced as the evaporative cooling number Ec increases. The results also reveal that the variation of total evaporation rate with contact angle will change its trend as the intensity of the evaporative cooling changes. For small values of Ec, the total evaporation rate increases with the contact angle, the same as predicted by Deegan et al. and by Hu and Larson in their isothermal models in which the evaporative cooling is neglected. Contrarily, when the evaporative cooling effect is strong enough, the total evaporation rate will decrease as the contact angle increases. The present theory is corroborated experimentally, and found in good agreement with the expressions proposed by Hu and Larson in the limiting isothermal case.