Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural break-up and satellite formation regimes of surfactant-laden
  liquid threads   We report a numerical analysis of the unforced break-up of free cylindrical
threads of viscous Newtonian liquid whose interface is coated with insoluble
surfactants, focusing on the formation of satellite droplets. The initial
conditions are harmonic disturbances of the cylindrical shape with a small
amplitude $\epsilon$, and whose wavelength is the most unstable one deduced
from linear stability theory. We demonstrate that, in the limit $\epsilon \to
0$, the problem depends on two dimensionless parameters, namely the Laplace
number, $La=\rho \sigma_0 \bar{R}/\mu^2$, and the elasticity parameter,
$\beta=E/\sigma_0$, where $\rho$, $\mu$ and $\sigma_0$ are the liquid density,
viscosity and initial surface tension, respectively, $E$ is the Gibbs
elasticity and $\bar{R}$ is the unperturbed thread radius. A parametric study
is presented to quantify the influence of $La$ and $\beta$ on two key
quantities: the satellite droplet volume and the mass of surfactant trapped at
the satellite's surface just prior to pinch-off, $V_{sat}$ and $\Sigma_{sat}$,
respectively. We identify a weak-elasticity regime, $\beta \lesssim 0.05$, in
which the satellite volume and the associated mass of surfactant obey the
scaling law $V_{sat} = \Sigma_{sat} = 0.0042 La^{1.64}$ for $La \lesssim 2$.
For $La \gtrsim 10$, $V_{sat}$ and $\Sigma_{sat}$ reach a plateau of about $3
\%$ and $2.9 \%$ respectively, $V_{sat}$ being in close agreement with previous
experiments of low-viscosity threads with clean interfaces. For $La<7.5$, we
reveal the existence of a discontinuous transition at a critical elasticity
$\beta_c (La)$, with $\beta_c \to 0.98$ for $La \lesssim 0.2$, such that
$V_{sat}$ and $\Sigma_{sat}$ abruptly increase. The jumps experienced by both
quantities reach a plateau when $La \lesssim 0.2$, while they decrease
monotonically as $La$ increases up to $La = 7.5$, where both become zero.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn