Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable and unstable capillary fingering in porous media with a gradient
  in grains size   We present a theoretical and experimental investigation of slow drainage in
porous media with a gradient in the grains size (and hence in the typical
pores' throats), in an external gravitational field. We mathematically show
that such structural gradient and external force have a similar effect on the
obtained drainage patterns, when they stabilise the invasion front. With the
help of a newly introduced experimental set-up, based on the 3D-print of
transparent porous matrices, we illustrate this equivalence, and extend it to
the case where the front is unstable. We also present some invasion-percolation
simulations of the same phenomena, which are inline with our theoretical and
experimental results. In particular, we show that the width of stable drainage
fronts mainly scales with the spatial gradient of the average pore invasion
threshold and with the local distribution of this (disordered) threshold. The
scaling exponent results from percolation theory and is -0.57 for 2D systems.
Overall, we propose a unifying theory for the up-scaling of dual fluid flows in
most classical scenarii.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
2
The categories of this paper are: math