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

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Abstract

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 ϕ and the position of the contact line r. From this nonlinear relationship we use curve fitting to obtain an empirical law of the form tanϕrf(k) where k is the power law coefficient and f is a nonlinear function of k.

Keywords

Thin film
Secant method
Contact angle
Contact line

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