Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thin films flowing down inverted substrates: Three dimensional flow   We study contact line induced instabilities for a thin film of fluid under
destabilizing gravitational force in three dimensional setting. In the previous
work (Phys. Fluids, {\bf 22}, 052105 (2010)), we considered two dimensional
flow, finding formation of surface waves whose properties within the
implemented long wave model depend on a single parameter,
$D=(3Ca)^{1/3}\cot\alpha$, where $Ca$ is the capillary number and $\alpha$ is
the inclination angle. In the present work we consider fully 3D setting and
discuss the influence of the additional dimension on stability properties of
the flow. In particular, we concentrate on the coupling between the surface
instability and the transverse (fingering) instabilities of the film front. We
furthermore consider these instabilities in the setting where fluid viscosity
varies in the transverse direction. It is found that the flow pattern strongly
depends on the inclination angle and the viscosity gradient.

30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th