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Journal Article

Numerical solutions of thin-film equations for polymer flows


Bäumchen,  Oliver
Group Dynamics of fluid and biological interfaces, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Salez, T., McGraw, J. D., Cormier, S. L., Bäumchen, O., Dalnoki-Veress, K., & Raphael, E. (2012). Numerical solutions of thin-film equations for polymer flows. The European Physical Journal E: Soft Matter and Biological Physics, 35: 114. doi:10.1140/epje/i2012-12114-x.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-768C-A
We report on the numerical implementation of thin-film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus on two particular cases inspired by experiments: the leveling of a step at the free surface of a polymer film, and the leveling of a polymer droplet over an identical film. In each case, we first discuss the long-term self-similar regime reached by the numerical solution before comparing it to the experimental profile. The agreement between theory and experiment is excellent, thus providing a versatile probe for nanorheology of viscous liquids in thin-film geometries.