Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-dimensional dynamics of a pair of deformable bubbles rising
  initially in line. Part 1: Moderately inertial regimes   The buoyancy-driven motion of two identical gas bubbles released in line in a
liquid at rest is examined with the help of highly resolved simulations,
focusing on moderately inertial regimes in which the path of an isolated bubble
is vertical. Assuming first an axisymmetric evolution, equilibrium
configurations of the bubble pair are determined as a function of the
buoyancy-to-viscous and buoyancy-to-capillary force ratios which define the
Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. The
three-dimensional solutions reveal that this axisymmetric equilibrium is
actually never reached. Instead, provided $Bo$ stands below a critical
$Ga$-dependent threshold determining the onset of coalescence, two markedly
different evolutions are observed. At the lower end of the explored
$(Ga,\,Bo)$-range, the tandem follows a Drafting-Kissing-Tumbling scenario
which eventually yields a planar side-by-side motion. For larger $Ga$, the
trailing bubble drifts laterally and gets out of the wake of the leading
bubble, barely altering the path of the latter. In this second scenario, the
late configuration is characterized by a significant inclination of the tandem
ranging from $30^\circ$ to $40^\circ$ with respect to the vertical. Bubble
deformation has a major influence on the evolution of the system. It controls
the magnitude of vortical effects in the wake of the leading bubble, hence the
strength of the attractive force acting on the trailing bubble. It also governs
the strength and even the sign of the lateral force acting on this bubble, a
mechanism of particular importance when the tandem is released with a small
angular deviation.

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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph