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Aleksei Vasil'evich Luikov was born in 1910 in Kostroma.
After his graduation from the Physicomathematical Department of the
Yaroslavl' Pedagogical Institute in 1930, he worked in Yaroslavl'
as a teacher at the Power Engineering Faculty for Workers, and then
as a research worker at the Drying Laboratory of the All-Union Heat
Engineering Institute. Here he conducted his first investigations
into the kinetics of drying and the development of methods of determining
the thermophysical characteristics of moist materials. In 1931 he
received his first inventor's certificate for his invention "Alternating-Pressure
Dryer" for work completed on the dehydration of moist porous materials
at alternating vapor pressure.
Beginning in 1931, A. V. Luikov developed rapid methods
for comprehensive determination of thermophysical characteristics
from one short experiment. They were used to discover and to study
the anisotropy of heat conduction of dispersed materials and polymer
solutions due to the flow. It was demonstrated that flowing systems
with a slowly obliterating or infinitely large mechanical memory that
contain extended elements (linear macromolecules, solid particles),
acquire tensor heat conduction as a result of flow. The components
of the thermal-conductivity tensor differ from their isotropic analog
by 200-300%.
As early as in 1932, to analyze the kinetics and dynamics
of the process of drying, A. V. Luikov conducted experiments to investigate
the moisture-content fields in convective drying of capillary-porous
bodies (filter paper disks). As a result he discovered the salient
points of the curves of distribution of the moisture content across
the thickness of the body that corresponded to the site of the location
of the evaporation surface. At the same time it was established from
the analysis of the moisture-content fields that there was no sharp
line of demarcation between the evaporation surface and the subsequent
layers similarly to the frost line of the ground in the Stefan problem.
Thus, one can say that the evaporation occurs not only on the deepened
surface but also over the entire thickness of the body. However, the
largest quantity of the evaporating liquid escapes from the evaporation
surface. In another method, to investigate the deepening of the evaporation
zone, use was made of the temperature fields experimentally obtained
in the process of drying of moist materials. If the temperature of
bodies is measured at several points, there is observed a salient
point of the curve (starting from this instant the temperature t
increases sharply) as the evaporation zone passes through the point
xi on the curve t = f(x). By recording
these salient points for each instant, Luikov obtained a relationship
between the thickness of the evaporation zone and the time and showed
that the evaporation zone deepens into the body approximately by a
linear law.
On the basis of the experiments conducted, A. V. Luikov
was the first to propose temperature curves for the analysis of the
kinetics of a drying process, including the study of the mechanism
of deepening of the evaporation zone.
In 1932, Aleksei Vasil'evich enrolled in the post-graduate
school at the Scientific-Research Institute of Moscow University,
where at that time worked well-known scientists - A. P. Mlodzeyevskii,
I. V. Luzin, A. S. Predvoditelev, I. E. Tamm, and others who had a
great influence on the formation of his creative abilities and further
scientific activities.
In 1932-1935, A. V. Luikov worked long and fruitfully
on the problem of transfer in colloidal and capillary-porous bodies.
He developed a new method to determine the thermophysical characteristics
of moist materials. In 1935, he discovered a new phenomenon -
thermal diffusion of moisture in capillary-porous bodies.
In nonisothermal transfer of moisture, when the regime
of heating of a moist material determines the appearance of a gradient
not only of moisture but also of temperature in it, the moisture inside
the material will move both due to the moisture gradient (the phenomenon
of moisture conduction, or concentration diffusion) and owing to the
temperature gradient (the phenomenon of heat and moisture conduction,
or thermal diffusion). This fundamental work by the young scientist
became widely known in the USSR and abroad. It was reported at a panel
of the London Royal Society and published in its transactions. In
the literature, the phenomenon of heat and moisture conduction is
known by the name of the Luikov effect. It is similar to the phenomenon
of thermal diffusion in gases and solutions (the Soret effect). In
1935, A. V. Luikov successfully defended his dissertation for a candidate's
degree (PhD thesis) on this subject.
The motion of moisture under the action of the temperature
gradient (heat and moisture conduction) in colloids and capillary-porous
bodies is a complex process that includes the following phenomena:
1) molecular thermal diffusion of moisture, basically in
the form of a molecular flow of vapor, which occurs due to the different
velocity of molecules of the heated and cold layers of the material;
2) capillary conductance determined by the change in the
capillary potential that is dependent on the surface tension which
decreases as the temperature increases, and since the capillary pressure
over the concave meniscus is negative, the decrease of pressure increases
the suction force, which causes the moisture in the form of liquid
to leave the heated layers of the body for the colder ones;
3) the movement of the moisture under the action of the
"entrapped" air, since during the heating of the material the air
in the pores expands and pushes the liquid toward the layers with
a lower temperature.
Heat and moisture conduction is the reason for the movement
of the moisture toward the heat flux. However, during convective drying
there develops a temperature gradient opposite to the moisture gradient,
which prevents the movement of the moisture from inside toward the
surface of the material. But if the directions of the moisture gradient
and the temperature gradient coincide, the directions of the corresponding
moisture flows coincide, too, yielding, on the whole, a total moisture
flow. The thermogradient coefficient introduced by A. V. Luikov shows
what moisture-content difference is created in the material at a temperature
difference of 1oC.
A. V. Luikov showed that the thermogradient coefficient
depends on the humidity of the material, i.e., on the thermal movement
of moisture, and, just as moisture conduction, is determined by the
form of the moisture's bond with the material.
Based on the phenomena of moisture conduction and heat
and moisture conduction, A. V. Luikov revealed the mechanism of the
shrinkage and cracking of the material in the process of drying as
well as of the transfer of water-soluble substances and showed that
the main obstacle to fast drying of many materials is their cracking.
The reason for the appearance of cracks (local fracture) as well as
of total destruction (loss of structural integrity) is the development
of the volume stressed state of the dried material above the maximum
permissible level determined by the strength of the material. This
stressed state is created by inadmissible shrinkage that, in turn,
appears as a result of the nonuniform distribution of the moisture
content and temperature inside the material. Hence, the main cause
of cracking in the process of drying is the presence of the moisture-content
and temperature fields with significant differences of these quantities.
Using these phenomena, A. V. Luikov introduced the criterion
of crack formation. Knowing the permissible value of the criterion
of crack formation, it is always possible to obtain dried material
of high quality.
The theory of transfer of water-soluble substances, developed
by A. V. Luikov, makes it possible to control this process. The liquid
in many materials contains soluble substances that, as the liquid
moves, are transferred with it and concentrate on the surface of the
material due to the evaporation of the liquid. It should be noted
that this is undesirable for some materials, whereas it is an indispensable
condition for other technological processes.
The change of the temperature gradient inside the material
is a particularly efficient method of control over the transfer of
a substance. By changing the magnitude and direction of  t,
it is possible to create diverse conditions for the transfer of moisture
and by doing so to act upon the physicochemical and biological properties
of the material.
A. V. Luikov created experimental methods to determine
the specific mass capacity, the moisture-transfer potentials, and
the coefficients of moisture conductivity and thermal and moisture
conductivity.
All the experimental and theoretical material on the mechanism
of the process of drying accumulated in the pre-war period was systematized
by A. V. Luikov and was published in 1938 in the monograph "The Kinetics
and Dynamics of the Processes of Drying and Moistening."
While working on general problems of heat and mass transfer,
Aleksei Vasil'evich, in particular, devoted himself to the theory
of heat conduction and to the development of efficient methods of
solving problems of nonstationary heat conduction by the Laplace
- Heaviside operational method. He obtained a number of important
new relationships in the operational calculus. They make it possible
to solve complex problems of the theory of heat conduction by using
the simple algebraic apparatus and elements of mathematical analysis
alone. In particular, he derived a Heaviside expansion formula for
the case of multiple roots without using the notion of a contour integral
in the region of complex variables.
The wide use of operational methods made it possible to obtain
a solution in two forms: one convenient for calculations at small
values of the Fourier numbers, the other - for large values of
the Fourier numbers.
A link was established between the theory of similarity
(the theory of generalized variables) and the operational calculus.
Thus, the solutions acquire a concrete physical meaning.
The method of asymptotic evaluations based on the analytical
properties of the Laplace transform was developed. A unified sign
was established for the regular regime of heating or cooling of solids
that combines the existing signs of the regular regime of the first,
second, and third kind.
For the first time in the theory of heat conduction the
so-called boundary conditions of the fourth kind were introduced,
for which a number of problems were solved. In their works, A. V.
Luikov and his disciples showed that a rigorous formulation of problems
of convective heat exchange in the interaction of the bodies' surface
with the environment corresponds to the boundary conditions not of
the third kind, as was usually assumed earlier, but of the fourth
one. Thus, the boundary conditions of the fourth kind acquire quite
an important and topical significance in the theory of convective
heat exchange.
A. V. Luikov developed a new method of solving nonlinear
problems of the theory of heat conduction, when thermophysical characteristics
depend on the coordinates. This generalized method results as a particular
case in a number of well-known methods of solving this kind of problem.
This extensive cycle of works was generalized in A. V. Luikov's now
classical book "Theory of Heat Conductions," which went through two
editions in the USSR and was translated in many countries.
This strenuous creative work took its toll on A. V. Luikov's
health - he was taken seriously ill and put through a complicated
operation. Restricted to his bed but preserving moral tenacity, Aleksei
Vasil'evich continued to work fruitfully by hand; he wrote two monographs
- one on the kinetics and dynamics of drying processes (40 printed
sheets per volume), the other - on heat conduction and diffusion.
After recovering in 1939, A. V. Luikov defended a dissertation
for a doctoral degree at the Moscow Power Engineering Institute. In
1960 he was confirmed in the title of professor. Since 1942 he had
been in charge of the Department of Physics at the Moscow Technological
Institute for the Food Industry. Well-equipped research laboratories
for molecular physics and the theory of heat were established there,
as well as at the Department of Physics of the Moscow Institute of
Chemical Machine-Building that he also headed, combining these two
jobs. These laboratories performed extensive widely publicized research
into heat and mass transfer in dispersed and capillary-porous bodies
during phase and chemical transformations, as well as work on radiation
heat transfer and the phenomena of transfer in deep vacuum.
At the same time, Luikov's international authority as a
scientist also grew - on the presentation by Prof. V. Ostwald
Aleksei Vasil'evich, he was elected member of the international society
Kolloidgesellschaft.
In 1951, A. V. Luikov published the monograph "Theory of
Drying," and in 1956 he published a second monograph, also devoted
to problems of drying - "Heat and Mass Transfer in Processes
of Drying."
The basis of the "Theory of Drying" is the regularities
of an interrelated heat and moisture transfer in moist materials during
their interaction with heated gases and hot surfaces, as well as in
processes of irradiation with heat and electromagnetic waves in the
case of phase transformations.
The theory of drying is an important section of the science
on heat and mass transfer. However, the process of drying of moist
materials is, at the same time, a technological process during which,
as was indicated above, changes occur in the structural-mechanical,
technological, and biochemical properties of the material due to the
fact that in the process of drying a change in the forms of the moisture's
bond with the material and its partial removal through evaporation.
Therefore, the theory of drying, too, is based not only on the processes
of heat and mass transfer in the capillary-porous bodies but also
on the doctrine of forms of the moisture bond with moist materials.
A. V. Luikov divided all moist materials into three types,
depending on their basic colloidal-physical properties:
1. Typical colloidal bodies. As moisture is removed they
significantly change their size (shrink) but preserve their elastic
properties (gelatin, pressed flour dough).
2. Capillary-porous bodies. As moisture is removed they
become brittle, always incompressible, and can be turned into powder
(sand, charcoal).
3. Capillary-porous colloidal bodies that possess the properties
of the first two types. They include the majority of materials that
are subjected to drying.
On the basis of analysis of the forms of the moisture bond
with a material and of the classification of moist materials, A. V.
Luikov made an attempt to explain the shape of the drying-rate curves
from the point of view of the mechanism of moisture transfer in bodies.
Using the drying-rate curves, A. V. Luikov developed approximate
methods for calculating the duration of a drying process that establish
the relationship between the body's moisture content and time. This
relationship can be obtained by the solution of a system of differential
equations for heat and mass transfer, which makes it necessary to
know the relationship of the transfer coefficients with the moisture
content and temperature. The solution turns out to be analytically
complex; therefore, A. V. Luikov proposed a sufficiently reliable
equation that describes a drying curve with a minimum number of constants
determined experimentally.
For many years this method of calculation justified itself
well for different conditions of drying. The essence of the method
was that the actual drying-rate curves are approximated by a straight
line with a minimum possible error, thus resulting in a directly proportional
relationship between the rate of drying and the moisture being removed,
and in this case the drying-curve equation was significantly simplified.
At present there are numerous data on the drying coefficient that
are included in the approximate drying equation.
A further step in the development of the theory of the
kinetics of a drying process was the establishment of the interrelationship
between heat exchange and mass exchange using a dimensionless quantity,
which was called the Rebinder number in the basic equation of the
kinetics of drying.
Based on the experimental material on the dependence of
the Rebinder number on moisture content, approximate methods were
developed for calculating the average integral temperature of the
material, knowledge of which is necessary to create a drying technology
since the temperature of the material is in many cases a determining
factor.
A. V. Luikov paid a great deal of attention to the development
of the theory of sublimation drying. Certain materials require drying
at low temperature since an insignificant rise in it causes a sharp
deterioration of their technological properties. Low-temperature drying
at atmospheric pressure occurs very slowly. Therefore, to intensify
the process, vacuum drying is used. Reducing pressure sharply increases
the intensity of evaporation by raising the mass-transfer coefficient,
which as a first approximation is inversely proportional to pressure.
In sublimation drying the material is in a frozen state.
A. V. Luikov's theoretical and experimental works in the field of
external and internal heat and mass transfer during sublimation drying
allowed him to propose a hypothesis on the removal of ice particles
from the surface that evaporate and thus contribute to the increase
in the value of the heat- and mass-transfer coefficients.
A. V. Luikov's works created a unified theory of interrelated
heat and mass transfer in capillary-porous bodies. They established
the regularities of the diffusion and effusion transport of moisture
and proved the great influence of the molar transfer of moisture caused
by thermal and diffusion slip. As a result, a law was formulated for
mass transfer in capillary-porous bodies for nonisothermal conditions.
These regularities allow a rather strict substantiation
of the change in the thermophysical and hydrometric characteristics
as functions of the moisture content of the body. A. V. Luikov's system
of differential equations
is at present solved for a broad range of problems and
various boundary conditions. When these equations are derived it is
expected that the heat- and mass-transfer coefficients and the thermodynamic
characteristics do not depend on the coordinates. Furthermore, it
is considered that the temperature of the moisture in the capillaries
of the body equals the temperature of the capillaries' walls during
the entire process of heat and mass transfer, which is true only for
diffusion transfer.
Thus, A. V. Luikov laid the theoretical foundations of
interrelated heat and mass exchange of capillary-porous bodie
s with
the environment; he established criteria and similarity numbers of
these processes, and his numerous extensive investigations have served
as a basis for the contemporary theory of drying of moist materials.
A. V. Luikov was among the first to note that use of the
Newton law is unacceptable for the expression of the specific heat
flux q through the temperature head (Tw - Tinf)
and hence the heat-transfer coefficient  , too,
for pre-assigned variable conditions on the surface of the body (often
very close to the actual ones). He showed that the law of the dependence
of the wall's temperature on the coordinates and time cannot be assigned
a priori but must be obtained through a simultaneous solution of equations
of the propagation of heat in a liquid and in a solid together with
the equations of motion, with the temperature and heat fluxes being
equal at the solid-liquid boundary, i.e., the so-called conjugate
problem of heat transfer must be solved. In this formulation allowance
is made for the mutual thermal influence of the body and the liquid
which is not taken into account in a different formulation, resulting
in the heat transfer being independent of the properties of the body,
its thermophysical characteristics, dimensions, distribution of the
sources in the body etc., which contradicts the physical meaning.
It is especially important to consider the heat-transfer problems
as conjugate ones in nonstationary heat transfer. Indeed, even for
the case of maximum values of the thermal conductivity coefficient
of a solid body, the temperature of the body's surface cannot be considered
to be constant since, although it indeed does not depend on the coordinates
of the surface points, it changes with time. However, in contrast
to stationary heat transfer, even in this limiting case the law of
change in the surface temperature with time cannot be assigned in
advance, and, hence, practically all the problems of nonstationary
convective heat transfer must be formulated as conjugate ones.
The solution of conjugate heat-transfer problems involves
serious mathematical difficulties. One of them is that, for example,
for stationary problems one has to deal with differential equations
of various types: for a liquid one ends up with an equation in partial
derivatives of parabolic type, and for a solid body, of elliptical
type.
A. V. Luikov took an active and direct part in the development
of new analytical and numerical methods and operational techniques
of solving conjugate problems. At present, the conjugate formulation
of heat-transfer problems is a universally recognized approach toward
the solution of scientific and practical problems.
A. V. Luikov was the first to give a generalization of
the Prigogine principle on the rate of change in the entropy in a
transfer process. As a result, a new system of linear equations of
transfer was obtained that differed from the Onsager system in that
the flows depend not only on the thermodynamic driving forces but
also on the rate of their change and on the time derivatives of the
flows.
From this system of generalized relations follow transfer
equations with allowance made for the final velocity of propagation
of the substance, and after that as a particular case hyperbolic differential
equations of heat conduction and diffusion are derived.
In the last years of his life Aleksei Vasil'evich had,
among other things, a profound enthusiasm for a set of problems that
was conventionally referred to as "nonlinear thermodynamics." Included
here were questions of the thermomechanics and thermodynamics of media
with complicated properties: such as micropolar media, media with
memory of various types, first of all - the theory of heat conduction
with memory. In the latter he was above all interested in the generalizations
and the thermodynamic substantiation of the hyperbolic equation of
heat conduction.
A. V. Luikov and his followers were the first to prove
the compatibility of the hyperbolic equation of heat conduction with
the second principle of thermodynamics or, in other words, the thermodynamic
assumption of this equation. Later on, the technique of finding thermodynamic
limitations of the relaxation function was generalized to different
classes of media with memory, as well as to the case of taking account
of all types of relaxation, including the cross effects too. Thus,
for example, for a deformable heat-conducting medium with memory there
are three types of relaxation, by temperature, by the temperature
gradient, and by the deformation gradient, for three independent variables
(the internal energy, the heat flux, and the stress tensor). The combination
of all three types of relaxation for each of the three variables yields
nine relaxation functions Rnm, in which three additional
elements describe the main types of relaxation (internal energy
- temperature, heat flux - temperature gradient, stress tensor
- deformation gradient); the rest are cross types.
These results were later developed for the case of generalized
thermodynamic systems, and for the linear theory their sufficiency
for the feasibility of the second principle in standard formulation
was also proved. Thus, the problem of thermodynamic limitations in
the linear theory was fully solved.
During the more than 40 years of his scientific-research
work, A. V. Luikov published about 250 scientific papers and 18 monographs,
including "The Theory of Drying," "Transfer Phenomena in Capillary-Porous
Bodies," "The Theory of Heat Conduction," "The Theory of Energy and
Material Transfer," "The Handbook of Heat and Mass Transfer," etc.
His monographs were translated and were published in England,
Germany, France, Hungary, the USA, and other countries. In 1951, A.
V. Luikov was awarded a state prize of the first degree for his monograph
"The Theory of Drying" (1950), and in 1969 he was awarded the supreme
prize of the USSR in the field of heat engineering - an I. I.
Polzunov prize.
Having a highly developed feeling of the new and an exceptional
industriousness and self-discipline, Aleksei Vasil'evich appreciated
these qualities in people - colleagues and disciples. He invited
talented young people to participate in the solution of complex problems,
contributing to their creative development, trusting them, and bravely
promoting them to the leadership of important sections of work. He
kept reminding them of his view that critical analysis of the main
notions lying at the foundation of a theory is always beneficial and
necessary, that even a seemingly absurd idea must not be immediately
and categorically rejected since only the presence of a plurality
of new ideas borne by "mental experiments" is the greatest condition
for the development of science and engineering.
The Department of Thermal Physics that he set up at the
Belarusian State University prepares highly qualified specialists-researchers
in various fields of the science on heat and mass transfer. For 40
years Aleksei Vasil'evich taught at higher educational establishments
and supervised the work of full time and part time post-graduate students.
He prepared 130 Candidates of Sciences (PhD degree holders), and 27
of his disciples became Doctors of Sciences.
A. V. Luikov's work in his position as Director of the
Institute of Heat and Mass Transfer (IHMT) of the BSSR Academy of
Sciences, of which he became head in 1956, was exceptionally fruitful.
Within a short period of time a small team of 30 people grew to become
a major thermophysical scientific center. The IHMT of the BSSR Academy
of Sciences branched into the Institute of Nuclear Power Engineering
of the BSSR Academy of Sciences, the Institute of Water Problems of
the Ministry of Water Resources of the USSR, and the Belarusian Branch
of the A. M. Krzhizhanovskii Power Engineering Institute. In 1969,
the Institute was awarded a high Government award - the Order
of the Red Banner of Labor for great scientific achievements and success
in the preparation of scientists.
In 1958, at A. V. Luikov's initiative, the "Inzhenerno-Fizicheskii
Zhurnal" was set up, and he remained its editor-in-chief till the
end of his life. In 1959, Luikov was appointed editor of the "International
Journal of Heat and Mass Transfer" on behalf of the USSR; he was Deputy
Chairman of the Soviet National Committee on Heat and Mass Transfer.
A. V. Luikov's great contribution to thermal physics enjoyed
deserved recognition. In 1956 he was elected Member of the BSSR Academy
of Sciences, in 1957 - full Member of the USSR Academy of Construction
and Architecture, in 1957 he was awarded the title of Honored Man
of Science and Technology of the RSFSR, in 1967 he received the highest
decoration of the country - the Order of Lenin, and in 1970
- the Order of the Red Banner of Labor.
A. V. Luikov attached great importance to the international
cooperation of scientists and constantly sought its strengthening.
At the Institute, he initiated the All-Union Conferences on Heat and
Mass Transfer, which have been held every four years here since 1961.
Since 1988 they have been International Forums, which are attended
by hundreds of scientists from different countries. It is not by accident
that the IVth International Forum on Heat and Mass Transfer held last
May was dedicated to the 90th anniversary of A. V. Luikov's birth.
A. V. Luikov's services to the strengthening of international
ties between scientists have been recognized in many countries of
the world. In 1969, he was elected Honorary Foreign Member of the
Society of Mechanical Engineers of the Polish Academy of Sciences,
in 1971 the Government of the Czechoslovak Republic decorated him
with the gold medal "For Services to the Development of Friendship
and Cooperation with the CzSSR," and in 1973, he was decorated with
the Gold Medal of the French Institute of Fuel and Energy.
His distinctly original talent, devotion to science, respect
and love for people, the scientific integrity of a scientist -
all this taken together, won wide recognition for Aleksei Vasil'evich
Luikov as a public and political figure and one of the leading scientists
in thermal physics.
At present, the name of A. V. Luikov has been conferred
on the Institute of Heat and Mass Transfer of the Academy of Sciences
of the BSSR, which has been turned into a widely known scientific
center by his work and the work of his followers.
O. G. MARTYNENKO
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