ISSN 0010-5082, Combustion, Explosion, and Shock Waves, 2018, Vol. 54, No. 3, pp. 345–349.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
On the Theory of Ignition, Combustion,
and Detonation of Micro- and Nanoparticles
A. V. Fedorov
Published in Fizika Goreniya i Vzryva, Vol. 54, No. 3, pp. 104–108, May–June, 2018.
Original article submitted September 27, 2017.
Abstract: A review of some investigations performed in the ﬁeld of mechanics of reacting hetero-
geneous media with micro- and nanostructures at the Khristianovich Institute of Theoretical and
Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences is presented. Some
new results are also reported.
Keywords: mathematical modeling, nanoparticles, molecular dynamics, heterogeneous detona-
tion, detonation suppression, mixture of a gas and reacting/inert particles.
Various issues of physical and mathematical mod-
eling of melting of Al and Fe nanoparticles were success-
fully studied at the Khristianovich Institute of Theoret-
ical and Applied Mechanics of the Siberian Branch of
the Russian Academy of Sciences. Methods of molecular
dynamics were used to describe the process. The numer-
ical data on the melting temperature, speciﬁc heat, heat
transfer coeﬃcient, and some other parameters of melt-
ing nanoparticles were found to agree well with exper-
iments. Later on, new phenomenological physicomath-
ematical models were proposed to describe the process
of melting of metal nanoparticles. The corresponding
initial-boundary-value problems refer to the group of
nonclassical Stefan problems. These models take into
account the experimentally observed fact of reduction
of the melting temperature with a decrease in the par-
ticle radius. Two-front modes of melting for thermal
ﬁelds of plane, cylindrical, and spherical particles were
detected for the ﬁrst time. These fronts are formed be-
cause the melting point and the speciﬁc heat depend
Khristianovich Institute of Theoretical and Applied
Mechanics, Siberian Branch, Russian Academy of Sciences,
Novosibirsk, 630090 Russia; email@example.com
on the particle radius. One front propagates from the
outer surface of the particle, while the other front is
formed in the particle interior. The order of samples
with diﬀerent types of symmetry in terms of melting
time was found (plate, cylinder, and spherical particle
in decreasing order), and approximate dependences of
this parameter on the particle size were derived.
The paper also presents a hierarchy of models
used to describe ignition and combustion of micro- and
nanoparticles, which was composed from the viewpoint
of mechanics of reacting heterogeneous media. These
models made it possible to determine the times of ig-
nition and combustion of particles of diﬀerent sizes at
diﬀerent temperatures and pressures of the ambient
medium. Comparisons with some available experimen-
tal data revealed the adequacy of these models. Atten-
tion was also paid to the problem of detonation suppres-
sion by clouds consisting of inert solid particles of dif-
REMARK ON TWO TYPES
OF THE PARTICLE HEATING
Physicomathematical modeling of various processes
in nanoparticles during their heating is of considerable
interest because of some unique properties manifested
by these objects. There are several approaches to mod-
by Pleiades Publishing, Ltd.