  Advancing and receding angles are physical quantities frequently measured to
characterize the wetting properties of a rough surface. Thermodynamically, the
advancing and receding angles are often interpreted as the maximum and minimum
contact angles that can be formed by a droplet without losing its stability.
Despite intensive research on wetting of rough surfaces, the gravitational
effect on these angles has been overlooked because most studies have considered
droplets smaller than the capillary length. In this study, however, by
combining theoretical and numerical modeling, we show that the shape of a
droplet smaller than the capillary length can be substantially modified by
gravity under advancing and receding conditions. First, based on the Laplace
pressure equation, we predict the shape of a two-dimensional Cassie-Baxter
droplet on a textured surface with gravity at each pinning point. Then the
stability of the droplet is tested by examining the interference between the
liquid surface and neighboring pillars as well as analyzing the free energy
change upon depinning. Interestingly, it turns out that the apparent contact
angles under advancing and receding conditions are not affected by gravity,
while the overall shape of a droplet and the position of the pinning point is
affected by gravity. In addition, the advancing and receding of the droplet
with continuously increasing or decreasing volume is analyzed, and it is showed
that the gravitational effect plays a key role on the movement of the droplet
tip. Finally, the theoretical predictions were validated against line-tension
based front tracking modeling that seamlessly captures the attachment and
detachment between the liquid surface and the solid substrate.
