Tanner's law in the case of partial wetting
Anouk C. Wisse (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M.V. Gnann – Mentor (TU Delft - Analysis)
Mark Veraar – Graduation committee member (TU Delft - Analysis)
E.M. van Elderen – Graduation committee member (TU Delft - Mathematical Physics)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
This thesis considers the thin-film equation in
partial wetting. The mobility in this equation is given by h3+λ3-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.