Simple analytical model of capillary flow in an evaporating sessile drop

Abstract

An analytical expression of hydrodynamic potential inside an evaporating sessile drop with pinned contact line is found. The problem is considered for a hemispherical drop (with the contact angle of 90°) at the very early stages of the evaporation process when the shape of the drop is still a hemisphere and the evaporation field is uniform. The capillary flow carries a fluid from the drop apex to the contact line. Comparison with the published calculations performed using lubrication approximation (very thin drop) suggests that qualitative picture of the capillary flow is insensitive to the ratio of initial drop height to the drop radius.