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On the determination of the steady film profile for a non-Newtonian thin droplet. (English) Zbl 1228.76009
Summary: 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 tanφr f(k) where k is the power law coefficient and f is a nonlinear function of k.
76A05Non-Newtonian fluids
65L10Boundary value problems for ODE (numerical methods)
76A20Thin fluid films (fluid mechanics)
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