Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive interaction of multiple surface nanobubbles and nanodroplets:
  shrinkage, growth, and coarsening   Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on
immersed substrates which are stable, even for days. After the stability of a
{\it single} surface nanobubble has been theoretically explained, i.e. contact
line pinning and gas oversaturation are required to stabilize them against
diffusive dissolution [Lohse and Zhang, Phys.\ Rev.\ E 91, 031003 (R) (2015)],
here we focus on the {\it collective} diffusive interaction of {\it multiple}
nanobubbles. For that purpose we develop a finite difference scheme for the
diffusion equation with the appropriate boundary conditions and with the
immersed boundary method used to represent the growing or shrinking bubbles.
After validation of the scheme against the exact results of Epstein and Plesset
for a bulk bubble [J. Chem. Phys. 18, 1505 (1950)] and of Lohse and Zhang for a
surface bubble, the framework of these simulations is used to describe the
coarsening process of competitively growing nanobubbles. The coarsening process
for such diffusively interacting nanobubbles slows down with advancing time and
thus increasing bubble distance. The present results for surface nanobubbles
are also applicable for immersed surface nanodroplets, for which better
controlled experimental results of the coarsening process exist.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex