Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coalescence of Liquid Drops   When two drops of radius $R$ touch, surface tension drives an initially
singular motion which joins them into a bigger drop with smaller surface area.
This motion is always viscously dominated at early times. We focus on the
early-time behavior of the radius $\rmn$ of the small bridge between the two
drops. The flow is driven by a highly curved meniscus of length $2\pi \rmn$ and
width $\Delta\ll\rmn$ around the bridge, from which we conclude that the
leading-order problem is asymptotically equivalent to its two-dimensional
counterpart. An exact two-dimensional solution for the case of inviscid
surroundings [Hopper, J. Fluid Mech. ${\bf 213}$, 349 (1990)] shows that
$\Delta \propto \rmn^3$ and $\rmn \sim (t\gamma/\pi\eta)\ln [t\gamma/(\eta
R)]$; and thus the same is true in three dimensions. The case of coalescence
with an external viscous fluid is also studied in detail both analytically and
numerically. A significantly different structure is found in which the outer
fluid forms a toroidal bubble of radius $\Delta \propto \rmn^{3/2}$ at the
meniscus and $\rmn \sim (t\gamma/4\pi\eta) \ln [t\gamma/(\eta R)]$. This basic
difference is due to the presence of the outer fluid viscosity, however small.
With lengths scaled by $R$ a full description of the asymptotic flow for
$\rmn(t)\ll1$ involves matching of lengthscales of order $\rmn^2, \rmn^{3/2}$,
\rmn$, 1 and probably $\rmn^{7/4}$.

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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con