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Zbl 1228.76009
Momoniat, E.
On the determination of the steady film profile for a non-Newtonian thin droplet.
(English)
[J] Comput. Math. Appl. 62, No. 1, 383-391 (2011). ISSN 0898-1221

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 $\varphi$ and the position of the contact line $r$. From this nonlinear relationship we use curve fitting to obtain an empirical law of the form $\tan\varphi \cong r^{f(k)}$ where $k$ is the power law coefficient and $f$ is a nonlinear function of $k$.
MSC 2000:
*76A05 Non-Newtonian fluids
65L10 Boundary value problems for ODE (numerical methods)
76A20 Thin fluid films

Keywords: thin film; secant method; contact angle; contact line

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