The sessile drop work of adhesion revisited

Work of adhesion per unit area of the interface to separate two distinct phases, and creating new interfaces. For the case of sessile drop, the Young-Dupre equation is usually used to express the work of adhesion, but it assumes the newly formed drop preserves its shape after detachment, which is not correct. Also, initial and final drop shapes cannot provide the work of adhesion. We argued that the work of adhesion depends on the path (despite the internal energy), and suggest a methodology to calculate the work of adhesion, based on calculating the mechanical work during the detachment, i.e. integration of drop centroid displacement times the external resistive forces. To put things into perspective, a 4 $\mu l$ sessile water drop was studied with initial (advancing) and receding contact angles of 79.7° ± 0.9°, 60.2° ± 0.8°, respectively. The direct calculation of work of adhesion using the developed methodology in this paper gives 0.03 J/m², while Young-Dupre gives 0.085 J/m², and calculating the work of adhesion based on initial (sessile) and final (full sphere) states of the drop gives a negative value, i.e. −1.49 J/m². So, neither Young-Dupre relation nor the initial and final energy states of drop can be used to calculate the work of adhesion, and detachment path should be considered in the calculation of work of adhesion.