Shape approximation of sessile droplet by the equivalence between vertical capillary force and hydrostatic pressure

Liquids are widely employed in the investigations of wetting in the form of droplets, especially for superhydrophobic surfaces. An accurate approximation for the shape of sessile droplets is of significance for facilitating the studies of surface wetting. Inspired by the principle of the drop weight method, we derived the equivalent relationship between the vertical capillary force at the contact line and the hydrostatic pressure of a sessile droplet on horizontal substrates. On the basis of the force equivalence, a new model using elliptical arcs to approximate the profile of actual droplets is developed. In addition to predicting the droplet shape, the proposed model enables the inverse estimation of the physical parameters according to the characteristic sizes of the droplet profile. The estimation results accord well with the measurements within a wide range of droplet volumes, which fully demonstrates the validity and application potential of our model. Moreover, the force equivalence has been utilized to explain the volume difference of evaporative droplets falling through the superhydrophobic holes present on different grades of mesh substrates. It is anticipated that the newly proposed force-based model will contribute to the deep understanding of sessile droplet-related phenomena, such as the Cassie-Wenzel transition and nondestructive transfer. • Equivalence relationship between vertical capillary force and hydrostatic pressure is applied to shape approximation of sessile droplet • Shape of the sessile droplet is affected by the vertical capillary force on the contact line • Contact angle and surface tension can be estimated according to shape sizes of sessile droplet • Force equivalence provides a reasonable explanation for evaporative pre-concentration on superhydrophobic manhole