On the determination of the steady film profile for a non-Newtonian thin droplet

A shooting method is used to determine a solution to a third-order ODE modeling the steady profile of a non-Newtonian thin droplet. We compare a direct approach to an iterative approach using a secant method. We obtain a nonlinear relationship between the contact angle ϕϕ and the position of the contact line rr. From this nonlinear relationship we use curve fitting to obtain an empirical law of the form tanϕ∝rf(k)tanϕ∝rf(k) where kk is the power law coefficient and ff is a nonlinear function of kk.