Regularities of formation of granules at granulation of powdered materials in drum devices Текст научной статьи по специальности «Химические науки»

ISSN 2522-1841 (Online) AZ9RBAYCAN KIMYA JU RNALI № 3 2018 ISSN 0005-2531 (Print)

UDC 661.099.2:631.841.1

REGULARITIES OF FORMATION OF GRANULES AT GRANULATION OF POWDERED MATERIALS IN DRUM DEVICES

G.LKelbaliyev1, V-M-Samedli1, M.M.Samedov2, A.B.Askerov2, G.M.Mamedova3,

A.A.Niyazova2

institute of Catalysis and Inorganic Chemistry, NAS of Azerbaijan 2Sumgait State University 3Azerbaijan State University of Oil and Industry

samedov-muxtar@mail. ru

Received 04.07.2017

The theoretical and experimental investigation of influence of moisture of granules on their formation, deformation and distribution on sizes at granulation of powdered materials in drum devices are considered. It has been noted that simultaneous proceeding of processes of granule formation and consolidation has a wave and damping character. The problem of forced convective transfer of binding agent in pores of granule during its consolidation is solved.

Keywords: granulation, mass transfer, distribution, wetting, deformation, porosity

Introduction

Granulation of powdered materials in the presence of binding agent is widely used in the most multi-tonnage productions of chemical, food, pharmaceutical, metallurgical and agrarian technology. Granulation of powdered materials with participation of liquid phase is carried out in screw, disk, plate-shaped and drum devices and also in devices with mixers (mechanical mixers with blade mixers) [1-4]. In all cases a formation and growth of granules takes place owing to wetting of separate particles of powder leading to agglomeration and coagulation of particles in their contact with each other. It is apparent that in early stage of granule formation a growth and formation of granules takes place owing to adherence of small particles and agglomerates to larger granules. The content of liquid phase owing to which are appeared adhesive, capillary and surface forces, keeping particles on surface of granule exerts an essential influence on process of granule formation. Besides composition of mixture, its moisture and physico-chemical properties of initial components a mixing frequency (rotation rate of the device), degree of filling and angle of inclination of the device, ratio of liquid and hard phases which defines finally qualitative (density, durability, fluidity, lump-forming capacity, internal friction coefficient) and quantitative (productivity) characteristics of

the process exert an essential influence on formation of granules as a result of agglomeration of particles of powder.

On measure of growth of granules in the process of their formation such phenomena, as consolidation under action of external pressures [5, 6], deformation of form and surface deterioration determining their form and sizes [6-8] are appeared. Owing to consolidation and deformation a density pg =pd(l-0) is increased

and granules porosity is decreased. In work [9] the various empirical formulas for calculation of density of granule in drum devices have been proposed. It should be noted that not only moisture but also character of scattering and properties of binding agent influences on formation of granules. In small sizes of drops of binding agent a possibility of preparation of a set of fi-ne-dispersed components of granules is appeared and in large sizes of drops a powder lamination on generated particles occurs and granules can be prepared sufficiently large sizes up to lumps. The increase of moisture demands additional expenses for their drying.

Thus, the mechanism of granule formation is sufficiently complex, multistage and many phenomena proceeding in this process have a stochastic character from time to time not giving to the description. In the process of

powder lamination on granules surface the pore structure with defined and accidental geometry of pore space, the parameters of which are not referred to a number of measured characteristics of porous medium is formed. Agglomeration and bonding of particles of powder in uniform system (granule) with participation of binding agent is determined by physical laws, although interaction between particles (collision, adhesion bond, crushing) has a stochastic character.

The aim of this work is the investigation of theoretical and experimental problems connected with mechanism and formation of granules and influence of moisture on this process.

Formation of granules in drum devices.

The formation and growth of granules from powdered medium is determined by the mechanism of process and conditions of proceeding of granulation process, i.e. by the character of scattering (quantity and sizes of drops) and properties of binding agent (viscosity, density, surface tension), conditions of mixing in apparatus, fractional (disperse) and chemical composition of powder, etc. If in the initial stage of nucleation and granulation, the formation of granules is carried out by simple sticking of powder particles to the isolated nucleus due to surface tension forces and capillary forces then the further granule growth is carried out by a powder lamination of particles on granule surface. At intensive mixing on the early stage of granule formation a change of mass of an individual granule for time by analogy with law of acting masses can be presented as

d t

(1)

where m - granule mass, K - sticking frequency of powder particles to surface of forming granules depending on properties and quantity of binding agent. It should be noted that in closed devices the condition is always supported: mtN < mp (where

mi - individual granule mass, N - total number

of granules in closed volume, mp - total mass of

powder). Due to this condition a size of each granule can reach only limit size.

In drum devices a formation and growth of

granules is determined by granule formation rate and consolidation rate of granules under action of external tensions. The various models and mechanisms of consolidation of granules under action of external deforming tensions as friable medium, including also dislocation mechanism of consolidation are presented in works [7-10]. Granule-formation rate as a result of lamination is determined according to the equation [1,6] da _ 2Rg>X (

at 7w

where R - radius of drum device, co - rotation frequency of drum device, X - lamination thickness of powder on granule surface depending on moisture of surface, a - current size of granule.

As a result of displacement of granules in drum device their consolidation takes place under action of external deforming tensions consequence of which are decrease of size and granule porosity and increase of their density. At consolidation of granule the fine-disperse component of hard powder phase of a porous medium flows into pores, compressing porous liquid and displacing it on continuous and non-closed system of pore channels. If the closed ensembles of closed pores are included in low-permeable or the impermeable environment then a volume flow leads to increase of liquid pressure in pores, to deformation of internal structure up to granule destruction. Mass of the individual generated granule we will present as

Ka /1 a\

(3)

differentiating which for time of granulation we will prepare [5]

dm 7xa3 d0 7ia2 ,, da

-dT-—p'dT+—"'('"V <4>

where pd - density of particles of powdered

material, 9 - granule porosity. On the other hand, a decrease of granule mass as a result of its consolidation in time At can be determined as

Am = --

p As

.(i-o)

sAV.

(5)

Herein. - shift viscosity coefficient, aD-deforming tension, § - granule surface, A F -change of granule formation rate in time At. Having divided (5) into At and passing to a limit at At —» 0, we will receive

p£s dV dt ^(1-0) dt

P As

(1-0) dT (6)

Comparing (4) and (6), and considering

that [5]

d0

(l-O)d/ ^

after elementary transformations, we will definitively receive the equation describing consolidation of granule as

d 2a da ,

—-- + bn--I-b.a = 0

dt2 0 ^ 1

Here

b = ' o

(it (1-0)2

(7)

A =

(i-0)

CTn

The private solution of the equation (7), under the stipulation that a characteristic number

(i-0)2

1-0

2 3

<0

for any 0 < 0 < 1, will be as

a (f ) = — exp [ ——I sin (—

(8)

a<2

2 2 } ^ 2, In principle, a characteristic number v, depending on parameters of consolidation v^jjg^), can be estimated using experimental

data as function from rotation frequency of drum device and moisture.

Then a total solution of formation problem (lamination and consolidation) of granules in dram device due to solutions (2) and (8) can be presented as

' vt "

a

(t) = (a0 + yt) + a0 exp (~b0t ) sin I —

(9)

Here y =

2 RcoX

K

in Figure 1 the character of granule formation as a result of lamination and consolidation is presented. The process of granules formation

has a wave and on measure of its growth -damped character. It is obvious that a wave character is determined by alternation of processes of lamination and size growth and decrease of size as a result of their consolidation. Powder lamination on granule surface is as consequence of its consolidation whereas as a result of consolidation and compression, a binding agent containing in pores squeezed out to a surface, which increases a possibility and probability of further sticking of dry particles of powder. In all cases the further growth and completeness of form of granule is determined by distribution of concentration of binding agent in volume of granule, i.e. moisture content or moisture of granule surface.

Fig.l. Change of sizes of granules as a result of powder lamination and consolidation at various values of lamination thickens, y.

Forced convective mass transfer at consolidation of granules. In the process of formation of individual granule the content, distribution and concentration of binding agent on a surface, favoring the further powder lamination exert an essential influence on its completeness, stabilization and structure formation. In work [6] the solution of problem of binding agent transfer in porous granule taking into account its deformation and change of porosity has been proposed. In this investigation the problem of forced convective mass transfer of binding agent in porous granule as a result of its consolidation under action of external tensions is considered. Considering cylindrical pore of granule a liquid flow tension value can be presented as

<T„=P + 2ti

dK

dz

(10)

Here gzz - tension in liquid, P - pressure of liquid in pore, K - liquid rate in cylindrical pore in direction z, r\- liquid dynamic viscosity. Integrating the expression (10), we'll prepare

K =

Gzz-P

zz_

2r|

(11)

Considering granule as individual friable system formed from small particles of powder and pores filled by liquid we'll make the following assumptions: a) forced motion of liquid in pores is carried out due to external tension oD « gzz ; h) physical properties are determined

by granule density and shift viscosity^.

Then in the first approximation an average flow rate of binding agent in granule volume in a radial direction by analogy with (11) can be defined as

(12)

V = ■

■a.

Consolidation of granules as a result of their balling occurs under action: a) centrifugal force arising as a result of rolling of drum device; b) weight of super stratums of granules in volume of device; c) impact forces arising in fall of granules as a result of their displacement. A character of these forces is accidental as all of them depend on the size of granules, on disposition and displacement of granules in a layer. The experimental measurement of these forces or total force is impossible. However, using experimental measurements of average sizes of granules or granules distribution on sizes a value g/;/c,_v can be estimated by solution of reverse

incorrect problem. In work [11] for a case of granulation in devices with blade stirrers a consolidation tension is bonded with sizes of granules, drop of binding agent and rotation rate as la 2

It follows from equation (12) that if if od>P, then granule is consolidated with extrusion of binding agent to surface with calculation rate V. In a case, if od<P (in particular for closed pores), then under action of internal

pressure in granule cracks are formed and takes place its destruction and crushing. The equation of mass transfer of binding agent in forced flow in radial direction of spherical granule can be presented as

dt dr r dry dr J

t = 0, C(t,r) = C0(r)

dC

r^O, -47ir2D— = J. (13a)

dr

For solution (13) let's enter new variables

C(r,i) = f/exp(|ir + cpO, (14)

Using these variables, we will rewrite

(13) as

dU _D d f 2 dU" dt r2 dr\ dr _

(15)

Considering (14) and regional conditions (13a), the solution (13) and (15) will be presented as [10]

C(r,/) = C0(r) +

J

4%Dr

I-erf

Pe '' „"I«

--m

2 a

.(16)

Here

(aD-P)2a2t Dt yj 2r? t

m = --t^-= Pe — = PeFo—,

4 a2 tg

<sn-P a n , , ^ Dt —--- Peclet number, Fo = —^—

2E,S D a2

Fourier number, J - mass flow of liquid to sur-

a

face. On surface of granule at r = — the concentration of binding agent will be determined as

Pe =

C{Rj) = C0{r) + -

J

1-

er/(Pe»T1/2)]. (17)

27iDa

In the dimensionless form we will define the following expression for Sherwood number Sh

f

exp

Sh = -

Pe2Fo —

A

I-erf

iFo

-1/2 >

\-erf(?QrnV2)

Here Sh = ■

J

- Sher-

\_C(R,t)-C~\ATiDa

wood number for forced flow. At small values a number Pe < 1 can be written

Sh:

l-®/(Pem '"2)] ' (19)

In Figure 2 the theoretical calculations of dependence of Sh number on time at various values of Pe number are presented. As it follows from this graphic with increase of granule formation time, external deformation tension and Pe number, the concentration of binding agent on surface of granule goes to zero which determines conditions of completeness of granule formation. Granule surface moisture is the main factor, determining a degree of completeness and formation of granules. Granule moisture characterizes a friability of its structure, the basic characteristics of which is a shift or volume viscosity.

Fig.2. Dependence of Sh number on granule formation time for various Pe number equal: 1 - 2.0, 2 - 1.5, 3 - 1.0,4 - 0.5.

Experimental investigation of influence of moisture on granule formation

The investigation of influence of moisture on formation of superphosphate granules was carried out in closed drum devices with definite rotation frequency determining degree of stirring in a layer of material. In this case the sizes of forming granules depend on ratio liquid: hard phase (superphosphate powder), on duration and stirring rate which are established by selection of geometric parameters (length, diameter, angle of inclination) of device.

The experimental investigations were carried out as follows: the powdered superphosphate was wetted to given level of moisture by solution of composition: 8-10% K2S04, 4-6% NH4OH, 85-88% H20 . The ratio liquid-

hard phase in wetting of powdered material was varied so that the total moi sture of mixture was optimal and necessary for preparation of granules by sizes 4-6 mm. For this 200g powdered superphopshate and given quantity of binding agent for each experiment was mixed for 0-1.5 min. The moist blend was transferred into rotating closed drum device with diameter 12 cm, length 80 cm and with rotation angle rate 30 min"1. In this case the granulation time for various moisture was 1 15 min depending on granules completeness. The conditions of granulation were selected depending on moisture of material so that in a final stage the content of granules by sizes 1-6 mm was the most significant. Granules prepared in each experiment were dried in thermostat at temperature T= 90-95°C for 1-1.5 h. After drying the sieve analysis was carried out as a result of which for each experiment the distribution of mass composition of granules of various sizes on fractions has been prepared (Table 1).

Table 1. Mass part of granule fractions depending on moisture of material

Average size of granules, a, nun Moisture in powdered material w, %

14 18 22 28

< 1.0 0.45 0.21 0.115 0.055

1.0-2.0 0.35 0.20 0.140 0.090

2.0-3.0 0.20 0.22 0.160 0.180

3.0-4.0 0.07 0.21 0.170 0.200

4.0-5.0 - 0.14 0.195 0.240

5.0-6.0 - 0.08 0.230 0.300

As it follows from this table with increase of moisture of material a quantity of fractions with large sizes of granules grows and on the contrary with decrease of moisture a fi-ne-disperse component of granules is increased. In optimal interval of moisture of material the formation of spherical granules and their average size growth with granule formation growth to 12 min was observed. The experimental data of dependence of average size of granules on granule-formation time are presented in Figure 3.

Fig.3. Dependence of sizes of granules depending on moisture of material: 1 - №'=12%; 2 - №=18%; 3 -w=22%; 4 - №=26%.

Using the equation (1), for spherical granules we'll prepare the equation of change of sizes as

~ = K()(w)a. at

(20)

Here KJw) K 3 granule formation coefficient. The solution (20) on condition t= 0, a=a$ we'll prepare as

a(t) = a0 exp[^T0 (w)t]. (21)

Here a0 =a0(w)-initial size of moistened

nucleus of granulation depending on content of moisture or size of drop of binding agent. In Figure 4 the calculation curves of granule sizes growth defined on formula are presented (21).

Fig.4. Calculating curves of deformation factor at: I-is =0.8, p = 8xl(T4; 2 -/„ 2 10 P = 0.5; 3 - xs = 0.01, p = 4.5 x 1(T3.

Using experimental data (Table 1), the unknown coefficients in equation (21) depending on moisture have been estimated as follows

K0(w) = 0.00353w2 — 0.10355w +1.0743, aQ (w) = -0.00175w2 + 0.0849w - 0.786, with corresponding correlation coefficients for the first and second equations: r2 =0.9999 and r2 =0.9975.

Granules deformation in drum device

In practical applications the granules are characterized by non-sphericity of form. In actual fact, the realization of form of granules is determined by symmetry of two factors: geometry of dynamics of granule motion in the process of its balling concluding in rotary and progress motion and geometry of anisotropy of properties of granule (friability, strength), i.e. its resistance to deformation, destruction and surface abrasion.

In works [4, 12] for estimation of degree of deformation it is proposed Stokes number (St)

St =

2cr.

(22)

being analog of

p cU2a

Weber number (We) We = for deforming bubbles and drops (il-

liquid density of drop, U - flow rate, g - liquid surface tension coefficient). In equation (22) gt characterizes wet granule strength and is determined as

_ 9 (1-е)2 9 4CK

(23)

8 0- 16 a where Vg - granule motion rate.

At granulation of powdered materials in drum devices Stokes deformation number can be presented as

St =

Peö

V

2<x,

J

In literature there are various data of values of St numbers, characterizing granule deformation in devices with mechanical mixing. So, it is confirmed in work [12] that a deformation and destruction of granules in devices with mixers comes at St = 0.04, in work [13] -St = 0.01, and in works [4, 14] - St = 0.7 .

As the parameter characterizing deformation of a granule, the factor of deformation equal to the relation of the minimum and maximum axes of a granule is taken

a

Here a,b— minimum and maximum size of axes of granule. It should be noted that at a = b we have % = 1, i.e. granule has absolutely spherical form. Then by analogy with theory of elasticity can be written as

1 AX

= -KsAa.

(24)

Here Ks - plasticity coefficient of structure of granule, vg - volume of granule, %s -

parameter, characterizing limiting change of granule deformation to ellipsoid form. Passing into the equation (24) to a limit, we have

J^f^'M*-*.)- <25>

The solution (25) under condition that

71

u = — a3 and y = 1 at Aa = 0, will be as

8 6

X = X5+(l"X5)exp(-pa4) (26)

where P = (71/24) Ks. Than there is more coefficient value P = / (St) and strength of granule,

than there is less probability of their deformation and destruction. An absence of serious experimental data on granules deformation in drum devices allows to make only theoretical conclusions. In Figure 4 the characteristic curves on granules deformation calculated on formula (26) are presented. As it follows from this graphic with increase of P, inversely proportional to a number St, granule deformation is increased.

With the aim of increase of granules strength the various chemical components which as a result of chemical and physical conversions in volume of granule reinforce bonds between particles of powder are added into composition of binding agent. In this experimental investigation as such components were used the following substances: K2SO4 and NH4OH, an addition of

which to binding agent gives defined elasticity to mechanical bonds between particles of powder as a result of which at deformation of granules these bonds are not destroyed. A formation of hard bonds between particles of powder takes place as a result of crystallization K2S04 from liquid phase in drying and chemical reaction between free phosphorous acid and ammonia water NH4OH, containing in water. Below in Table 2 an influence of quantity of addition on granules strength is presented.

Table 2. Dependence of granules strength on quantity of additives

CD,% 0 3.0 6.0 9.0 12.0 15.0 18.0

ctt, mPa 1.0 1.2 1.6 2.0 2.3 2.5 2.7

Here CD - total content of K2S04 and NH4OH in composition of binding agent.

Results and discussion

The granulation process of powdered materials in the first approximation seeming simple, conceals in itself rather difficult physical-mechanical phenomena consisting in formation of granules under the influence of various forces of the physical nature (adhesive, capillary, surface) and consolidation, deformation and surface deterioration under the action of mechanical forces. Naturally, in these processes the important role is played by capillary moisture capacity, surface moisture and sizes of drops of sputtering binding agent. The solution of joint problem of lamination and consolidation for time showed that the change of sizes of granules during its formation has a wave and damping character. The solution of problem of forced convec-tive transfer of binding agent in pores at consolidation of granule under action of external tensions has been considered and the view of function for Sherwood number has been determined (18). The experimental investigations of influence of moisture on its formation showed an essential scatter of sizes on fractions depending on moisture (Table 1). As it has been noted in works [5-7], such granules distribution on sizes and for time is described by the expression prepared by solution of Fokker-Planck equation

P(a) = B(w)am(w) exp(-n (w) a2). (27)

Here P[a)-function of granules distribution on sizes, B{w),m{w),n{w)- distribution coefficients depending on moisture of granule

B(w) = -736.981 (TV +485.4681 (TV + • 10.69ir • 7.90;

m(w) = 1549.48-10"-928.9010-4w + +19.0^-12.0,

w(w) = 106.7710"^ w3 -55.7810^w2 +0.830w--0.2628.

In Figure 5 the character of experimental distribution (Table 1) and calculation values of distribution function calculated on formula (17) depending on moisture of material are presented.

1 max

Hi

Fig. 5. Granules distribution on sizes depending on moisture: 1-0.14,2 -0.18, 3 - 0.22,4 - 0.26.

It has been noted that a value of \\i =<jd/^s , experimental measure of which is

impossible, exerts an essential influence on granule formation, deformation and consolidation. However, a problem of definition of value \|/ on measures and calculating values P(a.i) is the reverse incorrectly objective problem for the reason that very small mistakes in experimental and calculating values of granules distribution function lead to large mistakes in estimation v|/. In solving of reverse conditionally correct problem the main criteria of estimation \\f is the condition of minimum of quadratic relative mistake calculated on formula

о о

r P(aj)-P(a:t)

, PH .

dadt -^min/|.P(a,f)}.

The results of solving of this problem with the aim of estimation of approached values \i/ are presented in Figure 6.

££x10'

Fig.6. Estimation and change of value ctd/?ds

on granule formation time.

The granules distribution on sizes and equation (17) presented in works [5-7] can not always open a true pattern of character of change of sizes of granules, as these expressions do not consider multiple merge and coagulation of moist granules and their deformation. It is possible that taking into account secondary processes of coagulation the granules distribution on sizes can has a bimodal or multimodal character [4].

Symbols

a - diameter of granule; C - concentration of binding agent in granule; D - diffusion coefficient of binding agent in pores; J mass flow of liquid; Ks - plasticity coefficient of granule; P liquid pressure in pores; R - drum device radius; 5 -surface area of granule; t - granule formation time; w - granule moisture; Vg - granule motion rate; /' liquid flow rate; Fo - Fourier number; Pe - Peclet number; Sh - Sherwood number; St - Stokes deformation number. r\ - liquid viscosity; 9 - granule porosity; % - granule deformation factor; X - lamination thickness; t,s -shear viscosity; pg - granule density; pd - powder density; od ~ external deforming stress; co -rotation frequency of drum device.

References

1. Classen P.V., Grishaev I.G. Osnovy tekhniki granulirovaniia. M.: Nauka, 1982. 286 s.

2. Salman A., Hounslow N., Sevile J.P.R. Granulations. 11. Handbook of Powdered Technology, UK Elsevier, 2006. P. 1402-1409.

3. Badawy S.I., Hussain M.A., Effect of starting material particle size on its agglomeration behavior in high shear wet granulation // AAPS Pharm. Sci. Techn. 2004. 53. P. 1-7.

4. Bouwin A.M., Form, formation: the influence of material properties and process condition of the shape of granules by high shear granulation. Dissertations University of Groningen. 2005. P. 138-145.

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6. Kelbaliyev G.I., Samedli V.M., Samedov M.M. Modeling of granule formation process of powdered materials by the method of rolling // Powder Technology. 2009. 194. P. 87-94.

7. Ceylan K., Kelbaliyev G. Stochastically modeling of the granule size distribution in the agglomera-

tion processes of powder materials. Powder Technology. 2001. V. 119. P. 173-180.

8. Kelbaliev G.I. Mehanizm uplotneniia uprugo-sviazannykh chastitc v protcesse granulirovaniia poroshkoobraznykh materialov // Teor. Osn. Him. Tekhn. 1992. T. 26. 6. S. 749-754.Gluba T. The effect of wetting liquid droplet size on the growth of agglomerates during wet drum granulation // Powder Technology. 2003. V. 130. P. 219-224.

9. Tihonov A.N., Samarskii A.A. Uravneniia ma-tematicheskoi fiziki. M.: Nauka, 1966. 280 s.

10. Litster J.D. Liquid distribution in wet granulation: dimensionless spray flux // Powder Technology. 2001. V. 114. P. 32-39.

11. Ivenson S.M., Litster J.D. Growth regime map for liquid-bound granules: further development and experimental validation // Powder Technology. 2001. V. 117. P. 83-97.

12. Dries van den K., Granule breakage phenomena in a high shear mixer; influence of process and formulation variables and consequences on granule homogeneity // Powder Technology. 2003. V. 133. P. 228-236.

13. Ivenson S.M., Litster J.D. Growth regime map for liquid-bound granules // AIChE J. 1998. V. 44. 7. P. 1510-1518.

BARABAN TiPLi APARATLARDA TOZ§ObdLLi MATERlALLARIN DONavaRLa^DiRlLMOSiNDa

DONOLORlN formala§masi qanunauygunluqlari

Q.i.Kolbolivcv, V.M.Somodli, M.M.Somodov, A.B.askorov, G.M.Mommodova, A.A.Niyazova

Moqalodo to/sokilli materiallann baraban tipli aparatda donovorlosdirilmosinin no/ori vo eksperimental todqiqino dair mosololoro. voni donolori n mmliyinin onlann for ma las mas ma. deformasiyasina vo aparat daxilindo olciilori no gore paylanmasina baxilmisdir. Qeyd olunmusdur ki, eyni zamznda bas veren donovorlosmo vo sixlasma prosesi dalgavari xarakter da§iyir vo prosesin davam ctmosi noticosindo dalgavari xarakter todricon dii/xotli asililiq formasina gevrilir. Burada homcinin donolorin sixlasmasi prosesindo olaqolondirici maddonin mosamolor daxilindo konvektiv vcrdotismosinin tobioti avdinlasdirilib.

Agar si'n.br: с1эпзуэг1э§тэ, кийэоШгтэ, пэт1э§сИгтэ, mdhkamlik, deformasiya, masamalilik.

ЗАКОНОМЕРНОСТИ ФОРМИРОВАНИЯ ГРАНУЛ ПРИ ГРАНУЛИРОВАНИИ ПОРОШКООБРАЗНЫХ МАТЕРИАЛОВ В БАРАБАННЫХ АППАРАТАХ

Г.И.Келбалиев, В.М.Самедли, М.М.Самедов, А.Б.Аскеров, Г.М.Мамедова, А.А.Ниязова

Рассмотрены вопросы экспериментального и теоретического исследованию влияния влажности гранул на их формирование, деформацию и распределение по размерам при гранулировании порошкообразных материалов в барабанных аппаратах. Отмечено, что одновременное протекание процессов гранулообразования и уплотнения носит волновой характер. По мере протекании процесса волновой характер постепенно приобретает прямолинейную зависимость. Решена задача вынужденного конвективного переноса связующего вещества в порах гранулы при ее уплотнении.

Ключевые слова: грануляция, массообмен, увлажнение, прочность, деформация, пористость.