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 ? ? and the position of the contact line r r . From this nonlinear relationship we use curve fitting to obtain an empirical law of the form tan??rf(k) tan ? ? r f ( k ) where k k is the power law coefficient and f f is a nonlinear function of k k .
secant method contact angle contact line thin film