Modeling evaporation of a small drop on a horizontal substrate

The evaporation of a small liquid drop on a solid substrate is not only a fundamental phenomenon in our daily life, but also of particular importance in a number of applications, such as particle synthesis, DNA/RNA arrangement and disease diagnosis. This phenomenon has been extensively discussed by many researchers, however, most of these studies considered only drops that are smaller than the capillary length (e.g., 2.7 mm for water droplets), and the gravity effects were thus neglected. So we attempt to make a detailed investigation of the gravity effects on the liquid drop evaporation on a horizontal substrate using the lattice Boltzmann method. In order to account for the variation of evaporation flux along the drop interface, an evaporation scheme is introduced into the framework of the multiphase lattice Boltzmann method. Our code is validated by some simple cases, and the simulated values agree well with analytical values. Then the drop shape changing rules and inside flow patterns of drops with or without gravity during evaporation at different contact angles are studied. The results show that the gravity impact decreases as the drop size decreases. When the drop size is lower than a critical value, the gravity impact is negligible, which is in accordance with our common sense. However, these critical values for water droplets with different wetting properties are found at least 25% lower than the value given by the classical theory of capillary. Therefore, many previous studies may need to be reconsidered.