Drop retention force as a function of drop size

The force, f, required to slide a drop past a surface is often considered in the literature as linear with the drop width, w, so that f/w = const. Furthermore, according to the Dussan equation for the case that the advancing and receding contact angles are constant with drop size, one can further simplify the above proportionality to f/V^1/3 = const where V is the drop volume. We show, however, that experimentally f/V^1/3 is usually a decaying function of V (rather than constant). The retention force increases with the time the drop rested on the surface prior to sliding. We show that this rested-time effect is similar for different drop sizes, and thus the change of f/V^1/3 with V occurs irrespective of the rested-time effect which suggests that the two effects are induced by different physical phenomena. The time effect is induced by the unsatisfied normal component of the Young equation which slowly deforms the surface with time, while the size effect is induced by time independent properties. According to the Dussan equation, the change of f/V^1/3 with V is also expressed in contact angle variation. Our results, however, show that contact angle variation that is within the scatter suffices to explain the significant force variation. Thus, it is easier to predict contact angle variation based on force variation rather than predicting force variation based on contact angle variation. A decrease of f/V ^1/3 with V appears more common in the system studied compared to an increase.