When does gravity actually influence the macroscopic contact angle in partial wetting problems?
Controversy still exists as to whether the contact angle of a liquid on a solid is affected by drop size or gravity. Long time ago, Pethica and Pethica (1957) and Leja and Poling (1960) have suggested that the contact angle is affected by gravity. In contrast, Herzberg and Marian (1970) have suggested experimentally that the change in the contact angle with drop size was produced by hysteresis rather than the effect of gravity. Good and Koo (1979) have introduced the concept of line tension to explain the change in the contact angle with drop size. Thus some researchers have concluded that the contact angle is not affected by gravity, but nobody as yet has proved this theoretically.
Therefore, the aim of the present work is to understand whether gravity can influence partial wetting configurations. Indeed, in a gravity field when the drop volume is such that its size becomes greater than its capillary length, then its liquid-fluid interface deviates from a spherical cap. So, what happens to the macroscopic wetting angle? Does it depend on the volume of the drop (the Bond number), or does it remain independent of it? We have implemented two complementary approaches: one experimental and the other from modeling. The creation of a sessile drop on a horizontal substrate is achieved by injecting distilled water via a motorized syringe through a 1 mm hole drilled in the PMMA substrate, in an ambient air environment. In parallel, an axisymmetric macroscopic model has been developed, whose equations model the shape of the drop in static equilibrium, accounting for the thermodynamic equilibrium and the total energy conservation equation. This model leads to an algebraic-differential system comprising four first-order differential equations in space, and two algebraic constraint equations. As this system is highly non-linear, it is solved numerically using the numerical asymptotic method. This set-up emphasizes the gravity influence on macroscopic wetting angle and the developed model enables us to understand how, as well as the role of three-phase-zone energy in its evolution, both in advancing and in receding contact lines.