Asian Journal of Physical and Chemical Sciences
3(3): 1-11, 2017; Article no.AJOPACS.36523
ISSN: 2456-7779
On the Anniversary of the Phenomenon of "Solid
Flame" about Some Features of Modern Practice of
the Theoretical Description of Combustion
Processes
G. B. Brauer1*
1
Institute of Structural Macrokinetics and Materials Science (ISMAN), Chernogovka, Russia.
Author’s contribution
The sole author designed, analyzed and interpreted and prepared the manuscript.
Article Information
DOI: 10.9734/AJOPACS/2017/36523
Editor(s):
(1) Victor G. Zavodinsky, Physics, Institute of Materials Science, Russia.
(2) Stanislav Fisenko, Department of Mathematics, MSLU, Russia.
(3) Thomas F. George, University of Missouri- St. Louis One University Boulevard St. Louis, USA.
Reviewers:
(1) Rakesh Choure, Shri Vaishnav Institute of Technology and Science, India.
(2) Meshack Hawi, Jomo Kenyatta University of Agriculture and Technology, Kenya.
(3) Imdat Taymaz, Sakarya University, Turkey.
(4) Obiekea Kenneth Nnamdi, Ahmadu Bello University, Nigeria.
Complete Peer review History: http://www.sciencedomain.org/review-history/21350
th
Mini-review Article
Received 30 August 2017
th
Accepted 7 October 2017
Published 12th October 2017
ABSTRACT
This paper is devoted to a review of the widespread practice of the combustion processes
description using the so-called classical combustion theory equations without proper clarification of
the real kinetics mechanisms of physical processes under consideration. The «vitality» of this type
theoretical description is related to the mathematical properties of the functions used. Below some
various examples and historical facts, illustrating the idea, are presented, in particular, connected
with emergence and development of the "solid flame" science or SHS (Self propagating High
temperature Synthesis), being partially a result of a large policy, associated with the collapse of the
USSR.
Keywords: Arrhenius equation; classical combustion theory; solid flame; self-propagating hightemperature synthesis (SHS).
_____________________________________________________________________________________________________
*Corresponding author: E-mail: gbr@ism.ac.ru;
Brauer; AJOPACS, 3(3): 1-11, 2017; Article no.AJOPACS.36523
the redemption of taxes and this led him to the
guillotine of the French Revolution.
1. HISTORICAL INTRODUCTION
1.1 The Phlogiston
The mention of the phlogiston theory is given in
view of certain analogies with the current
situation that has arisen with the modeling of
combustion processes. Now, unlike the times of
Lavoisier, the level of understanding of the
processes occurring during combustion is much
higher. However, I will try to demonstrate, that
the so-called Arrhenius equation became an
analogue of "phlogiston theory" of the 20th
century.
The combustion processes (in general sense)
played a major and specific role in the history of
civilization. In ancient Greece, Heraclitus taught
that everything in the world arises from
constantly changing fire, and in ancient Chinese
natural philosophy, fire is one of the five
fundamental elements of the universe. The role
of fire in the development of methods of
transformation of matter (from cooking to
metallurgy and the production of ceramics) is
enormous. And it is no coincidence that one of
the first theories that can be considered scientific
from the point of view of modern man was
dedicated to burning. This is the so-called
phlogiston theory (from the Greek φλογιστοζ combustible) associated with the names of
German chemists Johann Joachim Becher and
Georg Ernst Stahl. Phlogiston is a hypothetical
fluid, according to the authors of the theory,
contained in all combustible bodies and
possessing a negative mass. According to this
hypothesis, combustion is represented as an
expansion with the release of phlogiston, which
is scattered in the air, forming a visible fire.
Despite the absurdity of such views from the
point of view of modern science, the phlogiston
theory simply and adequately described the
experimental facts, was internally consistent,
creative, etc. With its help many correct
predictions were made and practical results were
obtained. The theory was owned by the minds of
scientists for more than a century, and its
development played a great role in the evolution
of science in general and in the creation of a
special science of thermodynamics that laid the
foundations of all modern science and theoretical
physics, in particular (from the Boltzmann Htheorem in statistical physics to the Gibbs
potential in chemistry). As an illustration, we can
cite the case of the famous chemist Antoine
Laurent, whose name is associated with the
"oxygen" theory of combustion. Although
Lavoisier himself used mainly the theory of
phlogiston, he substantiated the successful
method of bleaching sugar with activated
charcoal on the grounds that the yellowish shade
of sugar crystals is given by the phlogiston,
which can be removed by making it switch to
coal. This successful decision brought the
scientist a lot of money (for the sake of justice,
he and before that was one of the richest people
in France). Then Lavoisier began to participate in
1.2 The Arrhenius Equation
As a child, watching his father work with columns
of numbers, Svante August Arrhenius acquired a
unique arithmetic ability and, already becoming a
scientist, enjoyed the fact that he had to look
briefly at the experimental data to suggest a
formula of regularity. In 1889, he published an
article "On the rate of inversion of cane sugar
under the action of acids," which is associated
with the introduction to physics and chemistry of
the famous equation. This equation was not
inferred, but suggested, selected from several
variants to describe the speed of a specific
chemical reaction: the decomposition of cane
sugar under the action of acid. In the article of
Arrhenius 7 empirical equations from the works
of different authors were cited, among which at
number 5 there was an equation from the work of
Van't Hoff and Schwab 1984, which is close to
the modern Arrhenius equation, namely, lg k =
5771 / T +11.695 for the decomposition of
chloroacetic acid In an aqueous solution. The
equation was obtained by biggest number of
pluses in the correspondence table with the
experimental results of other authors, and the
corresponding justifications are also given. At
that time, there yet were no modern ideas about
atoms and molecules, and the kinetic reasoning
of scientists of that time is not always easy to
understand. Rejecting a possible decrease in
internal friction with increasing temperature as
the cause of such temperature dependence of k,
Arrhenius writes that "there is only one way" - the
existence of some hypothetical reaction
component, which he called "active cane sugar,"
the rest of the matter is passive cane sugar. In
the other words, he suggested that the
concentration of the active sugar is exponentially
increasing with the temperature rise. Later, as
leaders of the Nobel Committee, both Vant-Goff
(1901) and Arrhenius (1903) received their Nobel
Prizes, but not for these works. Arrhenius was
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awarded for the theory of "electrolytic
dissociation," which was also very revolutionary
at that time, and in this connection Arrhenius had
to survive many attacks from colleges. Nobody
believed in the existence of ions in solution, and
Arrhenius himself said that this is only a
"convenient hypothesis," explaining the observed
facts. Simple calculations using Coulomb's
formula can show how huge forces are required
for to separate cations and anions. For example,
according to the memoirs of the Congress of the
British Association, physicist Fitzgerald pestered
everyone with one question, where do these
forces come from? (They did not know about
hydration at that time). Another funny case from
the life of Arrhenius: a young man was asked to
dispose of the liquid in the laboratory, without
warning about its properties. The flask contained
mercaptan, a substance with one of the odors
most unpleasant to humans, and Arrhenius did
not know about it at the time. Arrhenius lightly
threw it on the road when he was riding home on
a bicycle, and most of the city began to smell like
a sewer. The Special Commission, after several
weeks of discussion, concluded that mercaptan
was formed due to unique meteorological
conditions and it is unlikely that this will ever
happen again.
dissertation was devoted precisely to the
"comparison" of the so-called statistical and
kinetic reaction rate constants. Many works
connected with this equation concern the
nonequilibrium of real processes, the presence of
several temperatures and generally different
constants in one elementary act, the concepts of
Arrhenius and non-Arenius kinetics.
However, the "phlogistic" essence of the
Arrhenius equation is much simpler: this
equation, paraphrasing the name of one famous
article by E. Wigner ("The Incomprehensible
Efficiency of Mathematics in the Natural
Sciences") it is an "inconceivably effective
mathematical" object, making possible to close
almost any system of macrokinetic equations or
formally "simulate" almost any "burning"
experiment. In fairness, other functions with a
strong temperature dependence (for example, a
power law or a polynomial one), can be used as
closing functions that describe the chemical
interaction in combustion, the main thing is the
presence of coefficients that can be varied to "fit"
to the experimental data. But the Arrhenius
exponent unlike these functions seems to have a
physical and chemical meaning and the "fit" turns
into "modeling", as if based on the laws of
nature.
At the beginning of the 20th century the profound
changes in the atoms and molecules structure
understanding took place, and a modest article
by Arrhenius on a rather narrow study results
"fitting" became a revolutionary milestone in the
development of chemistry and other sciences. It
made it possible to describe quantitatively the
most complicated physicochemical processes.
The Arrhenius equation began to be derived both
from the point of view of the molecular-kinetic
theory and more complex mathematical
constructions, for example, inverse Laplace
transforms, using various theoretical approaches:
thermodynamic, collision theory, transition state
theory, stochastic approaches. The modern
bibliography on the Arrhenius equation is
extensive. It turns out that the "rate constant"
used in chemical kinetics is called a constant
only by tradition and only formally. In fact, it is a
very complex parameter, which includes many
physicochemical parameters of the systems
under study. This was paid special attention in
the 60-70-ies of the last century (especially in
connection with the study of plasma-chemical
and radiation-chemical processes). In this
connection, it is interesting to note that the
Chancellor of Germany, Angelina Merkel, was
engaged in radiation chemistry, and her doctoral
1.3 Semenov
A few words about the origin and development of
the macrokinetics of combustion historically. In
the late 1920s and early 1930s, Nikolai Semenov
published several papers with the opposite
content: a chain theory based on tracking the
multiplication and death of active radical
particles, and the theory of a thermal explosion
based on the fact that combustion occurs in the
same laws as the breakdown of dielectrics. He
dedicated the work on chain reactions to
members of the Swedish Nobel Committee, and
one of the first Nobel Prize winners chemists
Arrhenius and Van Hoff - his "great distance
teachers", for which he was persecuted for
«idolatry before the West», but was also
awarded a corresponding Prize (1956). Another
series of works led to the development of the socalled thermal theory of combustion by
Zel'dovich, Frank-Kamenetsky, and Todes. The
term "thermal" is associated with emphasizing
the
main
mechanism
for
maintaining,
accelerating the physicochemical process - due
to the Arrhenius temperature dependence, in
contrast to the so-called "chain" mechanism
associated with taking into account the real
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elementary reactions responsible for the
combustion of gases. The fact is that the
reactions
between
the
valence-saturated
molecules have enormous activation energies in
comparison with the reactions involving free
atoms and radicals (by tens of kcal / mole more)
and the real mechanism of interaction is
determined by the fast reactions of the chain
carriers and by how they multiply and perish.
Meanwhile, the desire to simplify the
consideration of the systems of equations for the
physical and chemical combustion processes,
and sometimes even analytically solve these
systems (simplified methods of integrating
exponentials, narrow-band methods) led to the
use of expressions for the reaction rate with the
chemical part of the process the Arrhenius
exponents for the zero or first order reactions,
ignoring the real dependencies on reagent
concentrations, with meaningless activation
energies and pre-exponential factors chosen to
be satisfactory to the experimental data. This
approach now is very widespread under the
name of global kinetic mechanism. For example,
in [1], an empirical kinetic scheme is used for the
single-stage combustion of methane with
oxygen. The kinetic parameters are chosen from
the experimentally measured flame velocity, and
this allowed calculations of two- and threedimensional flows, including turbulent ones.
specific heat, U is the combustion rate, Q is the
thermal effect of the chemical reaction, Φ is the
rate of the chemical reaction, η is the reaction
depth, k0 is the rate constant of the chemical
reaction, Φ (T, a) is the kinetic exponential
function, E is the activation energy, R is the gas
constant, T0 is the initial temperature, and Tb is
the combustion temperature).
Heat and mass transfer consists in heat
conduction and diffusion, the fields of which are
similar, and chemical kinetics in the exponential
dependence of the reaction rate on temperature.
For the combustion of gases according to the
scheme of the simplest first-order reaction (the
burning rate is proportional to the concentration)
using various assumptions, as well as the
original approximate calculation methods, an
analytical solution was obtained: the burning
propagation velocity turns out to be in the
"Arrhenius" dependence on the combustion
temperature.
U ~ exp (-E/2RT)
where E is the activation energy; R is the gas
constant; T is the temperature.
The results obtained for the simplest reactions in
the gaseous medium have been used for to
study of many various systems (condensed,
homogeneous,
heterogeneous,
explosive
substances, etc) burning. It is necessary to note
the real importance of many results obtained with
the help of these approaches: a correct
qualitative understanding of the various moments
of the propagation of combustion waves, the
theory of limits, stability of combustion regimes,
etc.
2. THERMAL THEORY OF COMBUSTION
Returning to history, it must be said that in the
30s and 40s of the last century the works of
Zel'dovich,
Frank-Kamenetskii
and
other
researchers had created a classical combustion
theory, which was a continuation of the
Semenov’s of the thermal explosion theory,
based on the assumption that combustion takes
place according to the same laws as the
breakdown of dielectrics.
3. CRITICISM OF THERMAL THEORY
But the main property of the equations under
consideration and their ability to describe the
combustion waves quite accurately is due to the
presence of power and exponential dependences
in the formulas and the ability to vary the values
of the coefficients.
Originally, the theory was developed with
reference to the combustion of gases and was
based on a joint examination of the system of
equations [2]:
d dT
dT
QФ(T , ai ) 0
cU
dx dx
dx
d
U
k 0 ( ) exp( E / RT )
dx
x→ -∞: T=T0 ; x→: T=Tb
(4)
(1)
As already mentioned, the mathematical essence
of the problem is quite trivial. Models based on
the equations of conservation of energy, matter,
components and the Arrhenius conjecture can be
written in the following form:
(2)
(3)
Σ Fphys = Σ Fchem (exp(-E/2RT)
(where x is the coordinate, λ is the thermal
conductivity, T is the temperature, c is the
4
(5)
Brauer; AJOPACS, 3(3): 1-11, 2017; Article no.AJOPACS.36523
where on the right side the functions responsible
for the chemical processes and containing the
Arrhenius exponential for the rate of chemical
reactions are summed up, and in the left – the
functions responsible for the physical processes:
thermal conductivity, diffusion, convection,
radiation, etc. It turns out that the mathematical
properties of the functions used make it possible
to describe practically any experimental data in
the field under consideration. Indeed, if the right
and left parts of such expression are
logarithmized, this operation, without changing
the essence of the relationship, so "smoothes
out" the features of functions that did not initially
contain an exponential, which they can often be
neglected. In other words, the exponent is so
"strong" function for adjusting the results, that
using it in such equations, you can "no bother"
how accurately it was possible to describe the
actual physical processes, so, paraphrasing a
well-known expression, we can say that the
exponent "throws out with the bathwater the
baby "- a reality.
Alexandrov is credited with defending and
deflecting the threat of repression from many
scientist-burners.
Continuing on the existing practice of
mathematical
description
of
combustion
processes: such fitting modeling is usually
discernable: important physical processes, the
pre-exponent and the activation energy in the
laid-down chemical equations are ignored, the
various parameters differ in order of magnitude
from the meaningful ones: the dimensions of the
combustion zone, the characteristic times take
unrealistic values. Similar situations, when
theoretical models are fundamentally different
from what is happening in reality, are very
widespread in combustion theory.
4. THE EXAMPLE OF "THEORETICAL"
WORK
As an illustration, one of the works [4]: titanium is
poured into the boat and covered with quartz
glass (Fig. 1). Titanium is ignited in air, which
passes through a narrow slit. Vibrational
combustion is observed. But what is really
happening? As the ignition begins, an impurity
gas begins to emanate from the titanium, which
is there (0.1-0.3% of the mass) due to the
peculiarities of its production from the titanium
sponge and interferes with the supply of air, the
combustion decays and the impurity gas
becomes smaller. It flares up again. With powder
titanium, you can come up with other variants of
the "Chinese" smoker. What do the theorists do:
ignore everything that has been said above
about impurity gas evolution. A standard system
of equations of the type (1-3) is written and the
observed oscillations arise due to the properties
of the exponentials. Thus, there are quite certain
processes, but in the formulas laid down a very
different process, but the result seems to be the
same.
It should be said that Semyonov himself tried not
to participate in the development of the thermal
theory, and was included only when it was
possible to show the chain nature of the chemical
part of the macrokinetic process. However,
Semenov was seriously criticized by the less
educated politicians from science, who were then
not only in biology (Lysenko), but practically in all
areas of science in Soviet Union. Ironically, these
figures from the burning: Akulov, Frost and
others tried to seem even more supporters of a
chain theory than Semenov himself. When the
clouds over the scientist-burners were already
heavily condensed and they were threatened
with real repression, a "bomb" (nucler) came to
the aid, our contribution to the theory of
explosion of which consisted of thermal theory,
and, of course, ... the Nobel Prize. Uneasy
stories of the lives of these people can be
learned from various published memoirs. The
apotheosis of history with Semenov, in my
opinion, is a change in his point of view on the
nature of the third limit of hydrogen burning with
oxygen. According to one version, presented in
Semenov's monograph [3], he suddenly believed
Frank-Kamenetsky's
calculations that
the
constants taken from the experiment (the globalkinetic mechanism) describe combustion at high
pressures well. Meanwhile, among the scientists
retells the story of how exactly the then president
of the Academy Alexandrov made Semenov
write that hydrogen with oxygen explode at the
third limit by the thermal mechanism. In addition,
As already mentioned, the boom of these
equations usage is associated with the
development of a computer account. For a few
decades, a lot of works on this subject have been
written, and many are connected with the
calculations of military and space technology. It
can be said that a whole theoretical branch of
science has appeared or even several such
sections that solve various problems related to
combustion: stationary, nonstationary, onedimensional,
two-dimensional,
threedimensional, with a different number of chemical
reactions and various kinetic functions;
Instabilities, pulsating regimes, spin, the
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Fig. 1. 1 - Ignition spiral, 2 - Quartz glass, 3 - Initial powder layer,
U - Front velocity [4]
development of fingers, etc. In other words, the
characteristics of certain hypothetical objects that
are far from the physical and chemical processes
occurring in reality are studied.
5. SELF-PROPAGATING HIGH
PERATURE SYNTHESIS (SHS)
processes, something is always melting,
gasifying, there are no "auto-braking" reactions,
their experimental establishment and other things
contained in the text of the discovery. The peak
of the development of the subject fell on the 80s,
the time of the collapse of the USSR. According
to ISMAN-inform, several scientific papers were
published per day, work from 47 countries of the
world was recorded. In several universities there
appeared the chairs of SHS (many of them still
exist), were reported on successful introduction
to production. Recently, the Institute of the
Russian Academy of Sciences ISMAN was
named after Academician Merzhanov in honor of
the anniversary of the SHS. The best way to
understand the phenomenon of SHS is to refer to
the memoirs of the participants in the events and
their surroundings. For example, the American
participant John Kaiser turned out to be a prolific
writer and for his part himself published a book
[6] in which he told how the government
concluded an agreement with him on relevant
activities in Eastern Europe, whose aim was to
try to use the results of socialist science in the
United States, and the arrangement of various
"mousetraps" for the USSR. («We helped
industry to put Russia and Eastern Europe on the
map as places to seek better or cheaper
mousetraps, and acted as midwives in the
process»).To the exact sciences after the USSR,
John Kaiser no longer touched, but switched to
TEM-
5.1 History SHS
Another example of the application of the
classical theory of combustion is the so-called
"solid flame" story. By the way, this year's
anniversary, 50 years of SHS, "self-propagating
high-temperature synthesis" (still synonymous
with "solid flame", "gasless burning", "Russian
process"). Quotation from the text of the
"discovery": "It is experimentally established that
the phenomenon of wave localization of selflocking solid-phase reactions, unknown earlier,
consists in the fact that the chemical interaction
between solid dispersed components without
melting and gasification of reagents and
products", etc. About how this formulation arose,
writes in detail Academician Merzhanov in his
memoirs [5], it was necessary to fulfill the
requirements of the patent service agent, who
helped to issue the documents. And why 50
years? - the discovery was recorded in hindsight
with the priority of 1967. In fact, in all these
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writing texts about Islam and the Islamic threat
long before all the current tragic events in Iraq
and Africa. Now he grows pigs in France,
everything can be read on the Internet. A good
support for the emergence of the SHS project in
the USSR was the published in 1980 report Joey
F. Crider, US Army Foreign Science and
Texnology
Center
Charllottesville,
then
immediate supervisor John Kaiser. And the idea
to write this document belonged to Jimmy
McCollie, the head of the Crider. The report
spoke about the Americans' anxiety about the
fact that the "reds" invented a miracle - "solid
flame", "gas-free burning", "Russian process",
new technologies and materials. So, funding is
allocated, the Institute is being built. This was
one of the last investments of the Soviet Union in
science before the collapse. Namely, Gorbachev
[7]
spoke
about
these
"inconceivable
technological breakthroughs" in 1985, when he
allocated funding for the project. For the past 30
years, several ISMAN laboratories and many
scientists around the world, although not without
much success, have been engaged in
fundamental and applied research of SHS.
However, the followers of Merzhanov [8]
compare him with Columbus, who was looking
for a way to India ("solid flame"), but discovered
America ("new technologies").
propagating high-temperature synthesis" (SHS).
So, whatever Merzhanov wrote about the need
for the discovered discovery formula for patent
purity, the text of the "discovery" fully
corresponds to this theoretical model. As a
scheme of reactants interaction, a reaction
diffusion model was adopted. The process of
stationary combustion of a model system
consisting of ordered layers of reacting
components is considered, with mutual contact of
the initial components a product is formed, the
rate of heat release is determined by the speed
of transport of the reagents through the product
layer. The conclusions drawn from the
consideration of the model layer system are
transferred to the case of combustion of real
media consisting of particles. On the basis of
numerous approximations, it turns out that the
propagation of a stationary combustion wave in
heterogeneous condensed media is described
practically by the same system of equations of
chemical kinetics and heat balance as for
combustion in homogeneous media and
practically the same for the mass combustion
rate U ~ exp (-E / 2RT) (E is the activation
energy, T is the temperature, R is the gas
constant). There is a typical picture, when,
frankly speaking, the incorrect results obtained
for the simplest reactions in the gaseous
medium, based on the so-called classical
combustion theory [2], are used for combustion
of many systems, condensed, homogeneous,
heterogeneous, explosive substances, deserves
a separate discussion. Here we note that the
presence of [2] was one of the grounds for the
appearance of the "solid flame" predicted "at the
tip of the pen" by the theorists of combustion.
The theory of the solid flame Merzhanov-Khaikin
[10] is an illustration of the incident when the
model is completely untrue: the determining
processes are ignored, the combustion and
heating zones in the model are an order of
magnitude larger than those observed in the
experiment, which in principle forbids continuum
mechanics equations usage for the mathematical
description of the combustion process, and many
other inconsistencies.
5.2 Theoretical Description of Combustion Processes
5.2.1 Classical theory of SHS
So far, the most common description of the "solid
flame" with the help of an example of application
of the so-called classical theory of combustion
[2]. It arose as a consequence of the classical
theory of the propagation of combustion, the
theorists have a "solid flame" model, when in the
combustion front there is no melting and
gasification, which greatly simplifies the physical
model. Here we note that the presence of was
one of the grounds for the appearance of the
"solid flame" predicted "at the tip of the pen" by
the theorists of combustion. The search for socalled "gas-free burning" started in the postwar
years, led to the fact that Merzhanov [9] with the
employees announced the discovery of systems
obtained from mixtures of certain substances, in
the combustion of which there is no melting and
gasification or gas evolution and the presence of
the liquid phase is so insignificant that they can
be neglected in the modeling of the process.
Later these studies were formalized as a
discovery of the phenomenon of "self-
5.2.2 Microheterogeneous model (CCM) by
Rogachev
For the sake of justice, in addition to the classical
theory of SHS due to its obvious inadequacy,
other models of the description of "solid flame"
appeared during this time. For example, this is
the
so-called
microheterogeneous
theory
proposed by Rogachev and co-authors [11]. This
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theory explains the features of the propagation of
a "solid" flame observed as a result of the highspeed video recording as a result of
inhomogeneities in the reacting medium. The
powder mixture is represented as a set of
identical reaction cells, each containing a fuel
and an oxidizer in the same proportions as the
initial mixture, the temperature and other
parameters inside the cell are the same, and the
process is spread due to heat exchange between
the cells - combustion sites. Many experimental
results cannot be explained with the help of this
model, since it, like the theory of MerzhanovKhaykin, does not take into account the actual
processes of melt flow and gas evolution. For
example, from the point of view of this theory,
like the classical theory of Merzhanov-Khaikin,
such methods of action as blowing a burning
sample with an inert gas in different directions,
thermovacuum treatment (drying), various minor
(~ 1% by mass) gasifying additives (borax, soda ,
humidity), should not have a significant effect on
the combustion of samples. However, it turns out
that the speed of the combustion front can vary
very much under these effects [12].
according to the classical theory of SHS and the
"convective" component associated with the
assumption that there is an impermeable or
poorly permeable piston in the combustion zone
from the liquid melt that moves under the action
of the gas pressure drop before and behind the
combustion zone, and also due to the capillary
forces δ/r (δ is the surface tension coefficient, r is
the pore diameter). For example, along with the
influence of the pressure of impurity gases on the
motion of the melt, the determining effect is
exerted by thermocapillary forces. Estimates
show that the change in the coefficient of surface
tension in the combustion zone due to
temperature changes is of the order of 0.1 n/m.
There are other problems with CCM. For
example, the scheme of this model and all the
basic equations were formulated in [15], to which
the author of the CMC does not refer. It studied
the combustion of samples from a mixture of
titanium and soot under an argon atmosphere
under conditions of a pressure drop along the
sample. It turned out that as the pressure drop
increased from 0 to 30 atm, the burning rate
increased in proportion to the pressure and a
stop was created that interfered with the gas
flow. To explain the results obtained, it was
suggested that in the combustion front a melt
layer appears that moves under the action of a
pressure drop, a scheme and equations
completely coinciding with the scheme and
equations of the CCM are given. Because the
experiment took place in a thick-walled steel tube
where the studied composition was injected,
there was great doubt that the stopper interfering
with the passage of gas was created by the melt,
and that the combustion front was flat enough. In
addition, no other experimental work, describing
such a piston-shaped melt movement, was not
later presented and the authors of [15] in the
future practically do not refer to the results of this
work.
5.2.2 Convective-conductive model (CCM) by
Seplyarsky
Another model for explaining the mechanism of
propagation of the combustion front in SHS
processes was proposed by Seplyarsky [13,14]
and is called convective-conductive model
(hereinafter referred to as CCM). This name is
due to the fact that in this model it is assumed
that the propagation, why do finer samples burn
at a faster rate than thick ones. Indeed, in those
samples where the impurity gases that are
formed in front of the melt piston and thus inhibit
the combustion front, the thicker the sample, the
more difficult it is for gases to escape through the
lateral surface and is slower more strongly. Also,
the above-mentioned effects associated with
blowing a burning sample and the like were
explained
more
or
less
satisfactorily.
Nevertheless, many things that are assumed in
this model are not true. Namely, there is no
continuous melt layer, nor that the combustion
zone would have an increased resistance to gas
blowing: usually the permeability of the products
is higher than that of the initial charge, and the
resistivity in the combustion zone has some
intermediate value. In addition, the concept of
capillary forces in the form δ/r also appears to be
incorrect. In fact, in the processes of a "solid"
flame velocity of the combustion front is a sum of
the classical "conductive" velocity, determined
5.2.3 Focal model by Brauer
The author proposed a mechanism explaining
the observed phenomena of the "solid flame" and
the scheme of the process [16,17], according to
which the process is determined by the motion of
the droplets of the melt that ignite the substance,
the behavior of the formed combustion sites
determines the character and speed of
propagation of the combustion front. The melt
moves under the action of thermocapillary forces
and forces of gas pressure. The diagram of the
propagation of combustion is shown in Fig. 2.
There is no continuous melt zone-there are
8
Brauer; AJOPACS, 3(3): 1-11, 2017; Article no.AJOPACS.36523
individual droplets of melt in the burning zone
with an average density ρm in the cross section of
the sample. The scheme is one-dimensional and
one-temperature: that is, in each section the melt
is at the same temperature T and the surface
temperature of the solid particles is also equal to
T. The velocity of the melt droplets Vm is
determined by the Darcy law temperature and
pressure gradients:
Vm
K ( )
( A grad T grad P)
(T )
,
this direction. This is due to the fact that as we
approach the boundary of the combustion front,
the temperature of the liquid heated in the
combustion zone decreases and its viscosity
increases. For example, the motion of foci of
combustion moving practically along the
boundary of the combustion front with velocities
of 8-20 times higher than the propagation
velocity
of
combustion
is
observed
experimentally. Far from the limits, a large
number of similar foci of moving along the
combustion front along a spiral (cylindrical
patterns) create a practically layer-by-layer
propagation of combustion, with high-frequency
pulsations, but as the limit approaches, this
combustion becomes pulsating, and at the limit,
spin, if such a regime in this system is possible.
(6)
where K is the permeability coefficient in Darcy's
law, η is the degree of chemical transformation, μ
is the viscosity depending on the melt
temperature, and A is the coefficient.
6. THE ATTITUDE OF WORLD SCIENCE
TO SHS
Now, a few words about the applied aspects of
the usefulness of products obtained by the SHS
method and SHS-technologies. Periodically it is
reported that some unique and necessary
materials have been received, but it usually does
not go beyond statements. The problem is that
the SHS is a nonequilibrium and poorly repeated
process and reports that as a result of SHS the
materials and products that the modern science
is working on create always cause doubts about
their reliability. The world science in the SHS
issues moved in the waterway and with an eye to
the Soviet and then to the Russian science,
many Soviet and Russian scientists left abroad
and some manage to get financing there and
support the myth of SHS. In fairness, it should be
noted from the memoirs of Merzhanov [5] that
such famous American experts as Professors
Rice, Holt, Munir have reacted to the idea of
SHS-technologies with great caution (especially
Rice). In his memoirs Merzhanov [5] is described
as at a seminar in Monterrey, California, by
obtaining insider information about the contents
of Rice's critical report, the Russians rebuilt their
speeches so as to soften criticism and thereby
"defeated" Rice polemically. But the technology
of this, of course, did not become better. As
already mentioned, other Americans helped the
Russian SHS financially and organizationally.
Edward Michael organized an international
journal
"Self-propagating
high-temperature
synthesis," SHS, which exist to this day. It is
characteristic that this magazine did not become
formally recognized. And this reflects the attitude
of the world science to SHS.
Fig. 2. Scheme of propagation of "solid
flame": 1 - initial mixture; 2 - zone of
combustion containing melt drops; ρm is the
density profile of the melt drops; Pg is the gas
and pressure profile [17]
Thus, according to this model, the fact that
systems based on refractory components burn at
a relatively high speed, which was one of the
reasons to call a "solid" flame the discovery, is
related to the properties of the melt formed,
drawn from the hot regions into the cold in the
direction of the propagation of combustion due to
thermocapillary forces. The actual process of
melt flow is three-dimensional and depends on a
number of parameters: the amount of liquid
phase, physical and chemical properties of a
solid porous medium and melt, and the topology
of the porous medium. Very important are the
conditions of ignition and the peculiarities of the
development of the foci of combustion. It often
happens that the droplets of the melt do not
move in the direction of the propagation of
combustion, but are practically perpendicular to
9
Brauer; AJOPACS, 3(3): 1-11, 2017; Article no.AJOPACS.36523
7. POLEMIC ISSUES AND CONCLUSION
Why are there few such critical publications with
an alternative point of view. Unfortunately, the
topic of «solid flame» and the description of
various combustion processes with the help of a
global-kinetic mechanism and thermal theory
among scientists and experts is quite popular
and it is quite difficult to publish works
criticizing these approaches. It is also difficult to
publish
articles
criticizing
the
thermal
theory of combustion and the global-kinetic
mechanisms in general. The author knows
several articles with formulas, where the
right and left parts have different dimensions or
with frankly fabricated results. If this is
interesting, author can write a special article
about such works. In the meantime, many editorin-chiefs do not want to publish such materials,
they say, give positive results, do not just
criticize.
2.
The main question is: how did such problems
arisen in the theory of combustion? Is the matter
really connected with the above-described
properties of mathematical functions used? It
turns out that in order to understand how the
situation in the field was formed is not enough to
read only scientific books and authors' articles.
One must also look at the histories of their lives
and study the relevant moments in the history of
the country and the world, at a time when certain
theoretical constructions arose. Thus, the
author's hypothesis is that for to understand the
situation in modern science it is not enough to
study only physics, chemistry, mathematics, etc.
The “total history” of any scientific field
development must include also an "additive"
story, related to the philosophy and sociology.
The real political conditions of the scientific
researches, their aims and researchers destinies
can strongly influence the very science and
content of scientific theories and therefore must
be taken into account.
7.
3.
4.
5.
6.
8.
9.
10.
11.
COMPETING INTERESTS
12.
Author has declared that no competing interests
exist.
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The peer review history for this paper can be accessed here:
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