Profiles on Curved Surface Derivation of Governing Equations

Liquid Profiles on Curved Surface Derivation OF Governing Equations 

Excess free energy, O, of the liquid droplet on an outer surface of a cylindrical capillary of radius a is as follows  

The condition of equilibrium according to Section 2.2 (condition (1)) results in the following equation describing the liquid profile on the surface of the cylindrical capillary  

Note that the latter equation is different from Equation 2.23 in Section 2.2 not only due to the presence of the second curvature. 

FIGURE 2.46 Cross section of an axisymmetric liquid droplet on the outer surface of a cylinder of radius a. H is the maximum height of the droplet, is the thickness of an equihbrium film of uniform thickness. 

---