Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mathematical model and mesh-free numerical method for contact-line
  motion in lubrication theory   We introduce a mathematical model with a mesh-free numerical method to
describe contact-line motion in lubrication theory. We show how the model
resolves the singularity at the contact line, and generates smooth profiles for
an evolving, spreading droplet. The model describes well the physics of droplet
spreading -- including Tanner's Law for the evolution of the contact line. The
model can be configured to describe complete wetting or partial wetting, and we
explore both cases numerically. In the case of partial wetting, the model also
admits analytical solutions for the droplet profile, which we present here.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
2
The categories of this paper are: math
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio