Tanner's law in the case of partial wetting

Tanner's law in the case of partial wetting

Wisse, A.C. (TU Delft Electrical Engineering, Mathematics and Computer Science)

Gnann, M.V. (mentor)
Veraar, M.C. (graduation committee)
van Elderen, E.M. (graduation committee)

Delft University of Technology

Applied Mathematics

2020-07-07

This thesis considers the thin-film equation in partial wetting. The mobility in this equation is given by h³+λ^3-nhⁿ, where h is the film height, λ is the slip length and n is the mobility exponent. The partial wetting regime implies the boundary condition dh/dz>0 at the triple junction. The asymptotics as h↓0 are investigated. This is done by using a dynamical system for the error between the solution and the microscopic contact angle. Using the linearized version of the dynamical system, values for n when resonances occur are found. These resonances lead to a different behaviour for the solution as h↓0, so the asymptotics are found to be different for different values of n. Together with the asymptotics for h→∞ as found in [Giacomelli et al., 2016], the solution to the thin-film equation in partial wetting can be characterized. Also, via this solution, the relation between the microscopic and macroscopic contact angles can be analyzed. From the main result of this thesis, it can be seen that the macroscopic Tanner law for the contact angle depends smoothly on the microscopic contact angle.

thin-film equation
partial wetting
Differential Equations
dynamical systems
Fluid dynamics

http://resolver.tudelft.nl/uuid:c8015fab-bab9-4139-b1c2-8e12e2c7120d

Student theses

bachelor thesis

© 2020 A.C. Wisse