The stability of inclined sessile drops

The limits of stability are determined for sessile drops with fixed volume and attached at prescribed wetting lines to inclined solid surfaces. Finite element techniques developed in an earlier paper [Lawal and Brown, J. Colloid Interface Sci., 89, 332 (1982).] are used to calculate the critical points, defined in terms of inclination angle and gravitational Bond number, at which the sessile drop loses stability. For fixed Bond number, axisymmetric sessile shapes on horizontal surfaces lose stability at a drop volume that corresponds to a point of bifurcation to a family of asymmetric shapes. The asymmetric shapes develop toward decreasing volume and are also unstable. Inclining the drop disrupts the axial symmetry and ruptures the bifurcation point into a limit point that marks the maximum volume for existence of stable drop shapes. This mode for loss of equilibrium persists for all inclination angles and is not changed qualitatively by changing the shape of the wetting curve.