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октябрь, 2022 г.
IMPACT ON THE INTERNAL STRUCTURE OF MATERIALS TO DRYING PROCESS
Rasuljon Tojiyev
Doctor of Science, Fergana Polytechnic Institute, Republic of Uzbekistan, Fergana E-mail: rasuljon1945m@il.ru
Nargizaxon Rajabova
Graduate Student, Fergana Polytechnic Institute, Republic of Uzbekistan, Fergana
ВЛИЯНИЕ ВНУТРЕННЕЙ СТРУКТУРЫ МАТЕРИАЛОВ НА ПРОЦЕСС СУШКИ
Тожиев Расулжон Жумабоевич
д-р техн. наук, проф., Ферганский политехнический институт, Республика Узбекистан, г. Фергана
Ражабова Наргизахон Рахмоналиевна
соискатель ученой степени доктора философии, Ферганский политехнический институт, Республика Узбекистан, г. Фергана E-mail: n. rajabova@ferpi.uz
ABSTRACT
So far, drying processes have been studied mainly by macro-processes and sectors, the individual phases were treated as continuous models, represented as a continuously distributed medium, and body size and, accordingly, the analysis of the transfer processes in them is based on phenomenological ideas.
Molecular physics related to the significant progress achieved at the atomic-molecular level, as well as the wide use of new physics, deeper penetration into the essence of micro-processes in the building processes and the consideration of corpuscular models depending on the atomic-molecular structure, molecules that form wet materials, atoms, it is recommended to take into account the interaction forces between ions and bodies.
Such an approach to the study of drying processes is said to give positive results in the analysis of the processes developing inside the material. It has been written about the interaction of moisture with the dry skeleton of the body, the effect of surfactants on the wet material, and also led to the introduction of special methods of delivery of various energies to the drying areas.
АННОТАЦИЯ
До сих пор процессы сушки изучались в основном по макропроцессам и секторам, отдельные фазы рассматривались как непрерывные модели, представленные в виде непрерывно распределенной среды, размера тела и, соответственно, анализ процессов переноса в них основан на феноменологических идеях.
Молекулярная физика связана со значительным прогрессом, достигнутым на атомно-молекулярном уровне, а также широким использованием новой физики, более глубоким проникновением в суть микропроцессов в строительных процессах и рассмотрением корпускулярных моделей в зависимости от атомно-молекулярной структуры, молекул, образующих влажные материалы, атомов, рекомендуется учитывать силы взаимодействия между ионами и телами.
Говорят, что такой подход к изучению процессов сушки дает положительные результаты при анализе процессов, развивающихся внутри материала. Было написано о взаимодействии влаги с сухим скелетом тела, влиянии поверхностно-активных веществ на влажный материал, а также привело к внедрению специальных методов доставки различных энергий в зоны сушки.
Keywords: molecule, atom, ions, body, process, energy, momentum, glassy, micro, macro, polycrystalline surface, plastic deformation, dislocation, metal, lattice, adsorption, oxygen, thermal expansion, chemical corrosion, defects, electron, particle, crystal, vacancy, block, grain, microscope, evaporation zone, drying.
Ключевые слова: молекула, атом, ионы, тело, процесс, энергия, импульс, стекловидность, микро, макро, поликристаллическая поверхность, пластическая деформация, дислокация, металл, решетка, адсорбция, кислород, тепловое расширение, химическая коррозия, дефекты, электрон, частица, кристалл, вакансия, блок, зерно, микроскоп, зона испарения, сушка.
Библиографическое описание: Tojiyev R.J., Rajabova N. IMPACT ON THE INTERNAL STRUCTURE OF MATERIALS TO DRYING PROCESS // Universum: технические науки : электрон. научн. журн. 2022. 10(103). URL: https://7universum.com/ru/tech/archive/item/14458
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Introduction
Drying is an energy-intensive process involving a complex combination of heat and mass transfer processes.
The drying process depends on the strength, shape, properties, hardness or softness of the materials, the number of defects and the design and types of drying devices, and has a significant impact on the formation of the product structure, its final properties, the possibilities of further technological processing and storage stability.
For a systematic analysis of drying processes, five levels of the hierarchy of physicochemical effects and events can be distinguished, these processes develop interdependence and are studied by their level [1].
I-atom - research at the molecular level;
II-research of supramolecular and globular structures;
III-analysis of physical and physicochemical processes occurring in drying devices, in particular, phases in the field of energy and mass transfer;
Study of the processes that occur between the IV-drying chamber and the boundary layer areas;
Analysis of the set of processes that determine the macro-hydrodynamic and macro-energetic state of the V-device on a general scale. The first three levels of the hierarchy relate to internal heat and mass transfer, and IV and V to external exchange.
Currently, the calculation of drying processes and drying devices are mainly at the macroscopic level and are carried out at the III and IV hierarchy levels. However, clear data and future forecasts show that it is time to move to the atomic-molecular level, i.e., the 1st level hierarchy, and demand that research is conducted at this level.
Until recently, drying processes were mainly studied in terms of macro processes and drying areas, while individual phases were considered as continuous models represented as a continuous closed environment, the body volume and, accordingly, the analysis of transfer processes in them was based on phenomenological ideas.
Molecular physics related to the significant progress achieved at the atomic-molecular level, as well as the wide use of new physics, conditions of exposure to external fields, deeper penetration into the essence of micro-processes in drying processes and consideration of corpuscular models depending on the atomic-molecular structure of wet materials are recommended. the forces of interaction between forming molecules, atoms, ions, and bodies are taken into account.
This approach to the study of drying processes gives positive results in the analysis of the processes developing inside the material. It can be seen that the interaction of moisture with the dry skeleton of the body, the effect of surfactants on the wet material, as well as the introduction of special methods of supplying different energies to the drying areas.
At the current modern stage of development, drying of the material should be considered as a process of phase separation in heterogeneous systems under the conditions of the interaction of its external and internal parts, the initial stage of this movement has a decisive effect and is called the initial impulse.
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The concept of "impulse" is taken from mechanics, and in developing this analogy, it is also recommended to use the concept of "impulse force", which represents the time of the initial impact on the drying object, during its impact with the driving force of the drying process.
That is, it takes into account the duration of the application of the initial active force of the drying process.
According to Le Chatelier - Brown's universal physical principle, the stronger the external influence on the initial drying area, the stronger the internal processes tend to return the system to the equilibrium state [1].
Thus, in the design of drying devices, it is necessary to create conditions that provide a perfect environment, external heat and mass exchange in the drying chamber, and efficient flow of heat and mass transfer inside the devices.
The main part
The structure of materials means the distribution and interconnection of gaseous, vitreous (amorphous) and crystalline phases, their physicochemical nature and quantitative relations, the form of structure, and its micro and macrostructure. The microstructure is determined by the nature of the crystalline phase, the glassy phase and the combination with pores and their structural character. The macrostructure determines the size, structure, shape, and mutual arrangement of pores in materials.
The drying of materials is determined by the number of microcracks in them depending on the surface. It is impossible to immediately determine the reasons for their formation.
Their main reasons are:
a) Mechanical damage to the surface of the material in the process of obtaining the finished material;
b) Thermal expansion of polycrystalline materials at different coefficients in individual phases;
c) Chemical corrosion of the surface during the production of the material;
d) Connection of dislocation in the process of material plastic deformation [2].
The process of obtaining the finished material is always related to its primary mechanical processing. For raw materials, this is the process of mining, subsequent grinding and sorting, and for moulded materials, this is the process of mixing the initial compounds. At all these boundaries on the surface, the initial joints have a partial mechanical effect, which leads to the formation of not only micro cracks but also macro cracks. Here we are not talking about technological cracks in products, but about defects on the surface of individual compounds.
Often, the material is directed to heat treatment during the preparation process. The difference in the coefficient of thermal expansion is the reason for the formation of surface microcracks. Here we are talking not about technological thermal micro-cracks, but micro-cracks with a multi-phase structure formed between fireclay and clay particles.
It is known that the freshly exposed surface of many minerals has high chemical activity.
Adsorption of this surface by foreign ions or molecules leads to chemical corrosion and partial destruction of the surface layer. For example, the failure of quartz
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with Si-O bonds occurs with the formation of microcracks on the surface of the structure of the crystal itself. In this case, in cracks on the surface, Si and O ions are formed with unsaturated valence bonds. Such a surface has high energy and is characterized by a very reactive effect, on which oxygen atoms from the ambient air are immediately adsorbed, which leads to a decrease in surface energy.
Metals and alloys obtained in a normal environment are composed of a large number of crystals oriented in different directions in space, that is, they are formed in a polycrystalline state. These crystals are called particles and their shape is irregular. Each particle in the crystal lattice has its orientation, which is different from the orientation of the neighbouring particle.
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Electron microscope studies show that the structure of the materials, that is, the structure of the internal crystal particles of metals, is not properly formed. A solid metal crystal lattice contains various defects that disrupt the bonding of atoms and affect the properties of the metal. These defects in the lattice are the result of the incorrect arrangement of atoms in the lattice [3-7].
Structures whose location is not completely perfect differ from each other as follows:
Lattice defect v ~ 3 • 10-8 sm, which is small in all three dimensions; linear which is smaller in both dimensions; plane (two-dimensional, surface) is small in one dimension.
v
Figure 1. Atomic defects in the crystal lattice
a) vacant; b) atomic shift to an intermediate node; c) introduction of a foreign atom or ion into the lattice
Figure 1 shows three types of atomic defects. It is shown that they appear in the form of vacant nodes, atomic displacement to the interstitial node, and the introduction of a foreign atom or ion into the lattice. A dislocation is a special form of imperfection located
in the crystal lattice, and naturally, they are less different from other defects. Dislocation is a special arrangement of individual atoms. Figure 2 shows a micrograph of dislocation traces. At present, the direct presence of the dislocation has been proved.
Figure 2. Microphotography of dislocation traces
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For the first time about dislocation in 1934, physicists Orovan, Polyana and Taylor used the phenomenon of dislocation to prove that there is a big difference in the theoretical and practical strength of metals when it comes to the displacement of atoms under the influence of plastic deformation.
A dislocation is a one-dimensional (linear) type of defect. There are shear and screw types of simple dislocation. (Fig. 3, a) shows an ideal crystal structure of atomic formations parallel to each other.
Figure 3. Location scheme
a) ideal crystal structure; b) edge location; c) screw location
If one of them is broken in the crystal, a shear dislocation is formed in place of the broken place. At maximum close-up, lattice distortion is rapidly absorbed by the size of its loss (Fig. 3b).
In the case of a screw dislocation, there is no discontinuity in the atomic planes within the crystal, but the atomic planes themselves reflect a spiral staircase-like system. In practice, this single atom is twisted into a plane screw line. Disorientation blocks in a screw dislocation can be represented in the form of (Fig. 3, c). The area adjacent to the location axis is represented by two blocks, one of which moves forward one step about the neighbouring block. Distortion of a large portion of the lattice is known as nucleation. Any exact location is provided in the form of a screw and screw location. Two-dimensional (planar) defects include the boundary between the crystal grains of linear arrangement paths. The surface of a crystal can be considered a two-dimensional defect.
Vacancy-type point defects are present in each lattice, which disappear under the influence of thermal fluctuations and appear continuously. The equilibrium concentration of vacancy nv in the lattice at the temperature denoted by the letter T is determined according to the Boltzmann formula as follows:
For many crystals -Ev =1 eV. At room temperature RT= 0.025 ey, from which
n^-l/0.025 П
10
-14
= np-E*(RT)
(1)
where n is the number of atoms per crystal volume unit; -Ey - energy that creates vacancies; R- Boltzmann constant.
With increasing temperature, the relative concentration of vacancy increases rapidly and reaches 10-5 at T=600K and 10-2 at T=900K.
Applying similar considerations to relative concentration, the energy of Frenkel defects is 3+ -5 ey.
Even if the relative concentration of atomic defects is not very large, it can become large with changes in the physical properties of the crystal.
Even if the relative concentration of atomic defects is not very large, it can become large with changes in the physical properties of the crystal.
A dislocation is a displacement of crystal points, involving much larger knots than atomic defects. Dislocation energy is estimated as 4-10-19 Dj per dislocation length of 1 m. Such large energy to create dislocations puts them in an athermal state, practically independent of temperature. For the entire range of the substance in the crystalline state, the occurrence of dislocations from thermal fluctuations is less lost than in vacancies.
A dislocation in a real crystal is formed by its growth in a mixture or solution. From the study of the structure of real crystals, it can be seen that their structure is different from the structure of ideal crystals. Real crystals are made up of regular blocks that are closely parallel to each other. It should be said that real
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crystals have a mosaic structure. The size of the blocks ranges from 10-4 to 10-6. Figure 4 shows two blocks that are spread out at an angle 9 to each other and grow opposite each other. In addition, the crystal lattice has a
different orientation against the plane. Therefore, a transition layer occurs, in which a lattice source from one direction in a block leads to the accumulation of vacancies (Fig. 4).
Figure 4. A dislocation in a real crystal
a-blocks growing opposite each other; y - the angle between them; b- dislocation resulting from the displacement of blocks
Figure 5. The formation of displacement in the crystal
a- accumulation of vacancies in the crystal; b- the vacancies resulting from this accumulation
The formation of displacement in the crystal develops under the influence of external force, shows the effect of sliding on the formation and releases it to the surface of the crystal. If the displacement occurs only due to the release of dislocations, the plastic deformation will decrease and the crystal will turn into a perfect state.
It can be seen from the experiment that with the increase of the deformation, the disorder of the lattice increases, and the dislocation density also increases. For example, the dislocation density in well-burnt metals is 107...108 cm-2. After cold treatment, the dislocation density increases to 10n...1012 cm-2. In this dislocation, plastic deformation concentrates all the energy absorbed by the metal.
Currently, a dislocation appears in the process of creating a shift under the influence of external forces. On the other hand, it is known that according to the size of the development of plastic deformation, the amount of growth of crystal defects is strengthened. The essence of this strength is the interaction of dislocations in the lattice crystal with each other and with other lattice defects. A dislocation breaks the lattice tension, creates a force field around itself, and exhibits net stress and normal stress at each point. Forces are created from the
impact of another dislocation on it, which ensures that the dislocations move closer together or tend to each other. If the dislocation is located in one plane, then dislocations of the same direction repel each other, and those of different directions attract each other. According to the degree of dislocation filling in a given slip plane, the shear resistance increases and the crystal is strengthened. The difference between the theoretical and actual strength of solid bodies is caused by the formation of small cracks in them, resulting in strong concentrated stress.
In polycrystalline materials, grain sizes range from 1 to 1000 pm, more often 100 pm. The grains are directed in all directions relative to each other and are turned by 10°. Grain boundaries are considered the main defects in materials and are very complex and still not fully understood. At grain boundaries, atoms are misaligned. Here there is such a passage, the width of which is equal to the diameter of several atoms, and the lattice of one grain crosses the lattice of another grain differently. (Fig. 6).
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Figure 6. Scheme of the polycrystalline structure of the metal
Accumulation of the layer at the boundary causes the dislocation to pile up because neither can keep the slip field unchanged when crossing the boundary along the Burchere vector.
When studying the composition of grain using an electron microscope, it was found that the structure of crystals inside the grain is incorrect.
The action of a shear force on a crystal with a dislocation creates a linear gap between the top two rows of the plane. In the lower plane, there will be a row of redundant atoms at the boundary falling into the block section. There is an incredible amount of compression between two atoms packed into this space. (Figure 7) At some initial moment, the space between atoms 4 and 5 and atoms 41 and 51 are compressed. Under the influence of force F, rows 5 and 6 are moved into space.
Figure 7. Displacement scheme of an ideal crystal A crystal with a) and dislocation b)
All dislocations move to the right, and their movement continues in the same order until the dislocation leaves the boundary of the crystal. As a result, the displacement of an ideal crystal is the displacement of atoms along a series. In the second case, it is not necessary to prove that the shear force will be partially less. In the first case, it is necessary to prevent the interaction of the entire series, and in the second case, only the atoms. The movement of several dislocations in one plane, and their joining, leads to the formation of crack states. The distribution of all such constraints in the crystal leads to the distribution of the dislocations themselves.
We will explain this with the following example. We assume that the crystal has several dislocations in the shear plane, and with the inclusion of a foreign atom in the plane, the bond strength between neighbouring atoms in the crystal lattice becomes sufficiently large compared to the atomic bond in the crystal itself. In this case, the movement of the first dislocation is stopped by its exit from the crystal, and the movement of atoms is stopped by the attraction of a foreign atom. The displacement of the atoms of the second and third dislocations leads to the densification of the atoms on the left side of the crystal and the concentration of the voids on the right. Such restrictions in a real crystal are not only foreign atoms but also defects at the crystal boundary, which greatly hinder the free movement of
dislocations. The presence of such barriers leads to the strengthening of the crystal lattice and the formation of surface cracks. The distribution of such restrictions in the entire crystal leads to the distribution of dislocations, which are aligned with the direction of the dislocation lines. Thus, the initial mechanical damage to the surface, the difference in the coefficient of thermal expansion in the structure of separate solid phases, chemical corrosion and dislocation are the reasons for the formation of cracks.
All solids have external and internal defects. Existing defects develop and new ones are formed when the body is loaded, causing tension and plastic deformation. The pattern of small cracks on the surface of the material can be considered a pinhole. Both sides of the slit mouth will have all the surface properties of the surface energy a. At the end of the free surface to the depth of the micro-notch, the surface energy is lost [8,9,10]
The presence of microcracks ensures the penetration of the external environment into the surface layer of the material. If the external medium is liquid, it forms a thin layer in the cracks with sufficient excess free energy. In this case, the free energy increases due to the decrease in the thickness of the layer. The cracks in the layer can be shallow or deep, and the cracks are short and long.
To reduce the free energy, the liquid layer tries to thicken in the microcracks and exerts pressure on the walls of the cracks. This pressure is maximum at the end of the crack, where it can penetrate the liquid. The impact
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of the liquid is important and is determined by the heat energy of the liquid surface of the given body. Capillary pressure Rk is characterized by swelling force as follows:
PK = 2a^cos6/n
Here: 0 is the shear angle;
h is the width of the slot (crack).
Together with the kinetics, the shrinkage n depends on the viscosity of the liquid material:
dl dt
2
r2p
gh
Pk
[pi- gsin(p]
Here: l-the column length of the liquid in the capillary; t-breathing time; p-liquid density; a angle of inclination of the capillary to the horizon.
In order to enhance this effect, it is necessary not to hold back the effect of impact and the absorption of liquid into narrow micro-cracks should not be complete, it should be removed quickly.
Point defects can interact with each other and other foreign defects as a result of their intra-crystal migration. Dislocations are formed as a result of the interaction of the mixture of atoms with vacancies, point defects and line defects.
Removal of moisture from defects (capillaries, micro- and macro-cracks and dislocations) located in the internal structure of the material discussed and analyzed above is a somewhat complicated process.
Therefore, when choosing a drying method and construction for the drying process, it is appropriate to take into account the state of defects in it, in addition to the properties of the material. It is also important to minimize drying time and energy consumption.
Drying is a mass transfer process, when the moisture accumulated in the material being dried is more than the equilibrium one, the evaporating moisture flows from the solid phase to the gas phase according to the equilibrium law, Figure 8 shows the movement of moisture from the solid phase to the gas phase [11,12, 13,14].
At the initial time t0 , the moisture in the body of the material is uniform and it is equal to C0.
At moments t1,t2—Tn, as a result of the evaporation of moisture in the material, evaporation on its surface decreases and gradient moisture is formed in the body of the material, as a result of which moisture moves from the centre of the material to the surface of the upper surface, evaporates, and in the centre of the material, a nucleus of the gas phase is formed in the form of vapour.
According to the theory of evaporation zone inwardness developed by A.V. Lykov, during the drying process of a wet body, changing evaporation and moisture zones are formed over time [2].
Evaporation occurs not only on the surface of the
material (x = ^ — but also on the full layer thickness 5 of the material. Evaporation of liquid occurs more on the surface of the wet zone, (x = ^ ) evaporation slowly decreases as it approaches the surface of the body.
Figure 8. Scheme of movement of moisture from the solid zone to the gas zone
In the evaporation zone, the adsorbent is dominated by moisture, and in the wet zone, the capillary liquid, where evaporation occurs on the surface of the liquid.
On the surface of the wet zone (x = - — 5) the gas is
fully saturated; and in the evaporation zone, the moist gas is in the same equilibrium with the material.
Dehumidifying the material changes its energy state. Academician P.A. Rebinder, taking into account the change in the energy state, proposed the method of energy description technology, which represents the form of moisture connection with the material. Based on this description, he mentioned that there are three types of bonds between moisture and material [3].
The first is the chemical bonding method, in which the moisture penetrates into the crystal lattice of the material.
It takes a lot of energy to get the moisture out.
The second is that the material is physically and chemically connected with moisture, that is, the material is connected with moisture through adsorption and osmotic forces.
The adsorbent is the force of the field of molecules lying in a certain plane, which binds to the outer surface of the material and occupies it. The osmotic wet colloid penetrates into the capillary pore areas of the body due to the osmotic pressure in the form of diffusion through their walls. Although the physicochemical bond is more strongly bound to the wet material, it does not take much energy to separate them.
The third is a physical-mechanical connection that fills the macro- and micro-capillaries of the wet material. Macrocapillary - capillaries with a radius of 10-5cm are filled with moisture only after contact with water, but cannot absorb moisture from the air
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The relationship between the material and the moisture is that due to the binding of water vapour at a partial pressure higher than the partial pressure of the moisture in the outside air, the material transmits the moisture contained in it to the air. If the water vapour on the surface of the product is lower than the humidity of the outside air at a partial pressure, it will absorb moisture from the air.
The physical model of wet material is presented in Figure 9. The material is presented in the form of a solid body 1, the micro 2 and macro 3 capillaries located in it are filled with moisture. 4 air bubbles are trapped inside the capillaries.
In order to study the mechanism of moisture movement in the material during the drying process, we will take a piece of the material from the surface of the capillary surface.
During drying, there is more evaporation on the surface of the material, and after a while, evaporation on its surface decreases and gradient moisture is formed on its body. The gradient causes a new formation in
J
3
4
Figure 9. Physical model of wet material 1-solid body; 2-micro capillary; 3-macro capillary; 4-air bubbles
To find out the mechanism of the formation of excess pressure in the material, let's look at the bubbles of the aggregate that have penetrated into the material (Fig. 10). Let the temperature of the agent bubble in the material at the initial state t0 be Tt, the relative humidity 9 < 100% and the pressure of the atmosphere 0.1 MPa, the accumulated pressure from the partial pressure p^ and the partial pressure of water vapour pjn. The bubbles in the material cool down a lot, its temperature Tm, relative humidity ^ increases, but its value is not 100%.
We write down t0 in the case where the pressure pn does not reach the atmospheric pressure as follows.
Pn(to)=Pt+Pbn*0,1MPa
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the moist layer, that is, the surface of the layer expands to a gel state, and the layer hardens as a result of absorbing moisture from the inner layer.
The increase in the size of the particle causes the narrowing of the capillaries in it and, in turn, the redistribution of moisture.
There is always a redistribution of moisture in the material, capillary radii are reduced, and moisture, air and gases move. This means that in any material there is a phase change in solid, liquid and gaseous states, which changes every minute in terms of quantity.
The pores inside the drying material are freed from moisture, and an agent consisting of heated air and water vapour takes its place, moving against the flow of moisture moving inside the material in the form of bubbles. The relative humidity ^ of the agent is much lower than the condition entering the material. Bubbles in the capillaries of the material are trapped with moisture, and the relative humidity ^ of its surface is 100%.
Figure 10. Schematic of high-pressure gas-water bubbles
formed inside the material 1- the skeleton of the material (solid phase); 2-gas bubble; 3-considered gas bubble; 4- moisture; the directions of evaporating moisture are indicated by arrows
By time t±, the moisture around the air bubbles begins to evaporate. Moisture will continue to evaporate until the relative humidity (p reaches 100%. At one time, the amount of moisture evaporation is .
Pn(ti) = Vi + P& + ApJn « 0,1 MPa + Apln
As a result, it exceeds the atmospheric pressure by pln, the material continues to heat up during drying, its temperature rises in places where there are bubbles, and the bubbles also heat up. The moisture in the bubbles evaporates and the relative humidity reaches 100% again.
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This process can be written as follows.
pn (±2) = pi + pL + kpln + kplh
As the process continues, the high pressure in the bubble increases even more. As the temperature in the material increases, the pressure in the bubbles increases again and becomes much higher than the atmospheric pressure [3].
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Because the air bubbles and agents in the material are at different distances from the surface of the material, they are at different temperatures. As a result, the pressure inside the material drops.
As a result of repeated exchanges and repetitions of such situations, moisture in the body of the material and in the capillaries continuously evaporates, the material becomes dehydrated, and as a result of drying (shrinkage) deposition, it hardens and becomes stronger.
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3. Ахунбаев А.А., Ражабова Н.Р. Высушивание дисперсных материалов в аппарате с быстро вращающимся ротором //Universum: технические науки. - 2021. - №. 7-1 (88). - С. 49-52.
4. Ахунбаев А.А., Ражабова Н.Р., Вохидова Н.Х. Исследование гидродинамики роторной сушилки с быстро-вращающимся ротором //Экономика и социум. - 2020. - №. 12-1. - С. 392-396.
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