Tanner's law in the case of partial wetting

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.