- Email: [email protected]
Polymeric magnetic fibrous filters
J~lm~l of
Materials Processing Technology Journal of Materials Processing Technology 55 (1995) 345-350
ELSEVIER
i
Polymeric magnetic fibrous filters L.S. Pinchuk a'*, L.V. Markova a, Yu.V. Gromyko a, E.M. Markov a, U.S. Choi b Metal-Polymer Research Institute of Belarus Academy of Sciences, 32 A, Kirov Street, 246652 Gomel, Belarus Korea Institute of Science and Teehnology, Seoul, South Korea Received 12 July 1994
Industrial summary
The aim of this work is to investigate the process of cleaning working fluids and sewage water containing hard particles of impurities using polymeric fibrous filters, the latter being sources of magnetic fields. A mathematical model of a magnetic filter that has been explored experimentally is proposed, and the role of the main parameters of the filter material in filtration efficiency is analysed. Technological ways are determined to control the parameters of the filter material in the course of preparation, so that the required filtration characteristics can be ensured.
1. Introduction
The cleaning of machine working fluids of impurities is an important problem of modern technology. Of no less importance is the cleaning of industrial and municipal sewage waters. Such liquids contain great amounts of ferromagnetic particles as impurity; to separate them, filters encorporating electric and permanent magnets are usually employed. The complexity of the structure, its large dimensions, the considerable consumption of materials and the inadequate level of filtration prevent these filters from being used efficiently. To-day, polymeric fibrous filter materials [1] appear to offer the most effective means of cleaning fluids containing ferromagnetic particles. The filters fabricated from such materials are a package of adhesionally-bonded fibres formed from a ferrite-filled polymer material and subjected to magnetization. From a great number of technologies available for the fabrication of polymeric fibrous materials, the pneumatic extrusion process has become the most preferable in making ferrite-filled filter materials [2]. Materials produced by this technology are characterized by strong adhesional bond between the fibres, so that no additional treatment is required, e.g. to punch holes, to cross-link, to glue. The presence of a ferrite filler, even without additional magnetization, promotes the raising of the filtration efficiency of working fluids [3].
* Corresponding author. 0924-0136/96/$15.00 ~) 1996 Elsevier Science S.A. All rights reserved SSDI 0 9 2 4 - 0 T 3 6 ( 9 5 ) 0 2 0 2 4 - G
However, the lack of theoretical substantiation of the optimal ferrite-filler content and of experimentation with the technological process of obtaining magnetic fibrous materials, prevents the prediction of the filtration characteristics of the materials that are fabricated. The aim of this work was to understand how the structural, magnetic and technological parameters of polymeric fibrous materials, incorporating sources of magnetic fields, influence the filtration efficiency of fluids, and to determine technological ways of optimizing the filtration qualities of the materials under consideration.
2. Theory
Impurity particles become separated by tile filter material in the following manner. Larger particles ( > 20lain) are separated owing to inertia-trapping, gravitational-deposition and sieve-retention effect. Most problematic is the separation of smaller particles, these being trapped by the fibres, in the general case, due to touching (van der Waals interaction, if the particles approach the fibres sufficiently closely) and diffusional settling. Magnetic filler incorporated in the fibres enhances the degree of separation of smaller particles by magnetic interaction of the impurity particles and the fibre, and by particle coagulation under the action of the magnetic field of the filter materials. Markova et al. [4] have estimated the contributions of the different mechanisms in the total filtration process. The main mechanisms responsible for the separation of fine particles were
346
L.X Pinchuk et al. / J o u r n a l o f Materials Processing Technolog3' 55 (1995) 345 350
Table 1 Mathematical models of magnetic fibrous filter Filter model
Magnetic attraction force: designations
Type II
F(r) = 4m2r3/l 7, m is the magnetic m o m e n t of a single domain particle, / is the distance between an impurity particle and a ferrite particle
Type III
F(r) = mom
N~ N, 2~ r 2 + a2i + 2 r a i s i n ~ + 4a2j 2 2 E 2 j = - u j i = o , = o (rz + aziz + 2raisinct + a2jZ) 3'
mo is the magnetic m o m e n t of an impurity particle, a is the distance a between ferrite particles, Ni = (R - re)/a, re is the ferrite particle radius, Nj = Ida, If is the fibre half-length taken into account in the estimation of F(r), ct varies with step 1/i F(r)=nmom
Type IV
N, t~'. ~_. r 2 + aZ. i 2 4a2j2 ~ ~ Z, +2ra, isinct+ j= u~ i=o ~=0 (rz + a2i2 + 2raai sin ct + a2j2) 3'
aa is the distance b between agglomerates, Ni = (R - ro)/aa, ra is the agglomerate radius, r. = re 3 ~ , the ferrite particles in the agglomerate, N i = ldaa.
k is the compaction ratio of
a The a - values are found from the expression:
3 P.~b.Cm R 2 ;
(R-rO(R-rf+a) bThe aa
2a 3 -- 8n Pe values are found from the expression: 3 , P b C . , -R2 -'-' 1 8n pf r} n'
(R-ra)(R-ra+a.) 2a~
where Pb is the fibre density; Pe is the density of the ferrite particle.
(~)
'
• i00
y
Ill
(b)
,
EXperiment
g
0
¢
U
l
i
i
It
i
5
0
!
*
•5
20
40
,,,
9
Impurity particle diameter,/~ m
(c)~1oo
~
|
~
diameter,/~ m
Fibre
(d) ~100
-
m
l
o
,~'-
50
I
i
0
10
l
20
,
30
Fen'ite concentration, wt. %
,,,
..
,v
I
i
0
0.6
1.2
Material density, ~]crn3
Fig. I. Theoreticaland experimental efficienciesof water filtration through LDPE-basedfibrousmaterial, depending on impurityparticle diameter and materials' parameters.
shown to be contact and magnetic deposition; the diffusion settling mechanism can be neglected in the case of fluid filtration.
The mathematical model of a magnetic fibrous filter will be represented as a single fibre with spherical particles of magnetic filler (ferrite) distributed uniformly in it.
L.S. Pinchuk et al. /Journal of Materials Processing Technology 55 (1995) 345 350
347
(b)
(a) loo
'
Ili ~g
U
NXO Perin*nt III
ioo-
50 _, II
O
! ,
1
(~)
I
|
I
,
a
5 9 Impurity p a r t i c l e diarneter, t ~ m
Fibre
-100
(d)
• 50
/
0
Experiment
!
o
IO
40
ioo
_o
L..j
~ ~ " ° " -
!
20 diameter, ~ m
g
VT,
rv' !
!
20
30
0
0.6
Material
F'el'ri.te concentration, v~. %
1.2
density,
~P-,/cm3
Fig. 2. Theoretical and experimental efficiencies of petroleum oil filtration through PA-based fibrous material, depending on impurity particles diameters and materials' parameters.
This model is based on the theory [5-1 according to which filter efficiency is determined with regard for the capacity of a single fibre to catch impurity particles• Two methods were used to calculate the capacities of fibrous filters free of magnetic filler• One is based on the distribution of the Kuwabara flow field for gases and low-viscosity liquids [6], whilst the other uses the distribution of Lamb's field for high-viscosity liquids [5]. The results obtained by these two methods were analysed and compared with the experimental findings, whereupon Lamb's field method was seen to be most suitable for determining the capacities of fibrous filters• In this method the following expression determines the deposition efficiency (El) of a hard particle onto a fibre:
r[ (;)
Ef=21{La
2In
-1+
,
(1)
where r is the distance between a particle and a fibre, R is the fibre radius, La=2.0022-1nRe, and Re is Reynolds' number. If a ferrite filler is incorporated in the filter materials, Ef increases at the expense of the particles attracted magnetically. This rise can be taken into account by introducing the term F(r)fl/v into the above expression. This term characterizes the mobility acquired by the particle (by analogy with the filtration efficiency calculated for filters where the fibres carry electric charge
[5]}: Ef=~
21n
-1+
+
,
(2}
where F(r) is the magnetic attraction force between an impurity particle and a fibre,/3 = 1/6~ro ~1,ro is the impurity particle radius, ~ is the dynamic viscosity of liquid, and v is the mean flow velocity inside the filter. The following models of fibrous filters had been treated in view of the above: (I) unfilled fibres; (II) fibres containing a magnetic filler in the form of single-domain ferrite particles, the filter not being magnetized; (lid the same as in II but with a magnetized filter; and (IV) fibres filled with agglomerate of single-domain ferrite particles, the filter being magnetized. For models, II-IV, equations were derived to calculate the magnetic attraction forces acting between an impurity particle and a fibre, Table 1. The efficiency of such filters according to Davies [5] is E= 1-exp
-2
gR / '
(3)
where c is the filter material density, and h is the filter thickness. Figs. l(a) and 2(a) represent how the filtration efficiencies for water and petroleum oil depend on the particle size of the impurities. In the calculations, the following were assumed: R = 1 0 g m ; h = 2 m m ; c = 0 . 3 ; Cm= 20wt%; the liquid flow velocity was 0.5cm/s; the
348
L.S. Pinchuk et al. / Journal of Materials Processing Technology 55 (1995) 345 350
kinematic viscosity of water v = 0.01 cm2/s; that of oil 0.2 cm2/s; and the number of single-domain particles in the agglomerate n = I and n = 10. The filtration efficiency was but a little better with model IV than it was with model I, if no filler was used in the filter material. Ferrite filler added to the fibre (Model II) did not, in fact, change the filtration efficiency. However, if such a filter was magnetized (Model III) the magnetic attraction capacity of the impurity particles increased, essentially resulting in a higher filtration efficiency. For the case under consideration, a similar filter ensures complete separation of ferromagnetic impurity particles measuring 9/am or greater. In the case of filters free of magnetic fillers, such particles separation efficiency would be ca. 60%. In water cleaning, filters of type III would be even more effective: particles measuring ~> 3/am can be separated. The equations in Table 1 show the fibre diameter, the density of filter material, the concentration (Cm) and the size of the ferrite particles to be the main parameters of the filter material. The calculated dependence of the filtration efficiency on these parameters for an impurity particle diameter, of 5/am are depicted in Figs. I(a)-(d) and 2(b)-(d). If the fibre diameter in filters Type IIl is reduced from 40 to 6/am, the oil filtration efficiency increases from 10% to 100% (Figs. l(b) and 2(b). If the filters do not contain magnetic filler, this dependence shifts to the region of smaller fibre diameters, i.e. in order to separate all particles the fibre diameters should be reduced to <4/am, which makes the filter material production-process more difficult. Adding an agglomerated filler shifts the above dependence but little in the right-hand direction. When the ferrite concentration is increased from 5 to 30 wt%, the oil filtration capacity increase from 25% to 90%, if filters of Type III are used (Figs. l(c) and 2(c)). In the case of water (Fig. l(c)) the ferrite concentration of 20 wt% is quite sufficient to separate all of the impurity particles of diameter 5/am. A many-fold increase of the magnetic component of separation in filters Type IV 8 times would not improve the total efficiency: the latter does not, in fact, depend on the ferrite concentration. Filters of Type III, for which the material is less dense than that without magnetic filler, are capable of catching all particles (Figs. l(d) and 2(d)). The figures described show the magnetized filters containing single-domain ferrite particles (Type III) to be more effective compared with other models discussed. In real filter materials, however, the magnetic filler is a collection of single-domain particles and their agglomerates. In this case, mean value n should be used in the calculations.
supported by experimental findings (Figs. l(b)-(d) and 2(b)-(d)). The data were obtained for polyamideand polyethylene-based filter materials prepared following the pneumatic extrusion process. Samples of diameter 60 mm were cut from filter material of thickness 2 mm. The mean diameter of the fibres was 20/am; the average number of ferrite particles in an agglomerate was 4; and the ferrite concentration in the fibre was 20 wt%. The filtration characteristics were determined by passing contaminated liquids through specimens using a test bench. The liquid samples were analyzed before and after the trials by making use of an optical-magnetic detector [-7] capable of determining the magnetic-particle concentration in the fluid tested. The following fluids were used. To test polyethylene-based filter material, water was used as the fluid; whilst in the case of polyamide-based material, petroleum oil MC-20 was the fluid. The contaminants used were: carbonyl iron powder of dispersity 0.5-12/am (the mean diameter was 5 pro). The experimental relationships are seen to lie in the figures between the curves calculated for filters containing single-domain ferrite particles (Type III) and those for filters containing filler in the form of agglomerates of 10 single-domain particles (Type IV). Thus, the mathematical model of fibrous magnetic filter that has been proposed, after having been evaluated experimentally, is seen to be able to optimize the filter material's parameters (density, fibre thickness, size and concentration of filler particles) at the design stage, with due regard for the requirements set on filtration (the type of liquid, the speed of flow, the size of impurity particles, and the filtration efficiency). The next stage of a filter material's preparation is to determine the technological regimes ensuring obtaining the most favourable structures.
3. Comparison of theory with the experiment
4. Technology
The correctness of using the proposed mathematical model of a filter to analyze filtration efficiency has been
The pneumatic-extrusion technology, Fig. 3, was used to prepare filter materials, involves the extrusion of
Granulated ~.*"
polymeric rr~terial
EXtruder
Screw revolution f~quency
Mat
Air terrlpe r~.tur Air p r e s s u r e Fig. 3. Arrangement for fabrication of polymer magnetic fibrous materials.
L,S. Pinchuk et al. /Journal of Materials Processing Technolog>'55 (1995) 345-350 i
(a)
x LDPE o LDPl~+ferrite ( 2 0 w t % ) u
x
170
/
}
%
| 10
2~.: o
~crew
3.o
rotational
~o
velocity,
• P A pA.+ferrite ( 2 0 w t % )
L
"
o.~ ~c~e~-
rpm
rotational
velocity,
(d) ~8 g
a
of !
9.5
: 20
12o
,
,
-~p
/
. ..-.--...--..---0.
50
o.~
150
i
I
I
0.~ 0 a
?
i
pressure , k P a
40
!
!
,_-,~o
i
2~)
|
•
o
l
Air pressure , k P a
/ I
C" s
,
20
!
oX,,.~
o [5
2.5O
.....
Air temperature
A i r temperature , ° C
Air
rpm
°.....w. o/W / /
~S
-~
349
i
Distance, c m
3~
O
-
o "-
|
°
- . °
15
3O I
II
Distance,
I
I
cm
Fig. 4. Parameters of polymer fibrous materials versus technological parameters of their fabrication.
polymeric materials containing between 0 and ca. 20wt% of strontium or barium ferrite: the molten composition is sprayed by compressed air; the jet is directed onto the receiving drum of the manipulator;
and the material is magnetized by a magnetic field source. It was examined how the material's characteristics are affected by basic technological parameters: the rotational
350
L.S. Pinchuk et aL / Journal of Materials Processing Technolo~, 55 (1995) 345 350
velocity of the extruder screw; the temperature and pressure of the air; and the distance between the spray head and the receiving drum of the manipulator. The polymeric binders used for obtaining the fibrous materials were low-density polyethylene (LDPE) and polyamide (PA). The filter was strontium ferrite with a particle size of between 5 and 10 ~tm. The main relationships between the fibre diameter, the filter material density and the technological parameters are represented in Fig. 4. Variations in the rotational velocity of the screw can be seen to affect most strongly the fibre diameter in case of unfilled LDPE, whereas in the case of PA and filled LDPE the dependences almost coincide, Fig. 4(a). At the same time, increased rotational velocity of the screw used to process ferrite-filled PE results in a material with a higher density than that of the other materials, Fig. 4(b). Higher temperatures of the spray air (Figs. 4(c) and (d)) lead to greater fibre draw degrees. Nevertheless, the density of PE-based materials cannot be controlled by this means. It is much easier to vary a material's density by adjusting the air pressure (Fig. 4(f)) and the distance between the nozzle and manipulator (Fig. 4(h)). Pressure variations affect most of all the fibres of ferrite-filled material (Fig. 4(c)). Obviously greater spray gas pressure causes the fibre temperature to drop, thus leading to weaker bonding between the fibres. The greater density for PE-based materials can be explained by the fibres which hit the manipulator's drum's surface being in a viscous-flowable state. Under the action of the spray air jet they spread over the drum surface, to result in the compaction of the material. The graphs of fibre diameter versus distance between the nozzle and manipulator have a similar appearance for every pair of filled and unfilled binders (Fig. 4(g)). The curves for LDPE show a typical minimum corresponding to 10 cm distance in the case of filled materials and 20 cm distance for unfilled materials. The enlarged fibre diameters observed after the minimum can, probably, be caused by greater shrinkage values in those fibres which underwent simultaneous drawing and cooling in the course of moving within the air jet. The graphs obtained appeared helpful in establishing variation limits for the basic parameters related to the polymer molten composition pneumatic spraying, and in
optimizing the regimes for the fabrication of ferrite-filled fbrous filter materials.
5. Conclusions
Polymeric fibrous filter materials containing sources of magnetic field were designed. The filtration of liquids through them has specific features associated with the effect of the intrinsic magnetic field of the filter on hard impurity particles. A model of magnetic fibrous materials has been proposed to be used for calculating fluid filtration efficiency through materials having different structural and magnetization parameters. The comparison of theories and experimental findings has supported the validity of the model in question. This was then made the basis for optimizing the fibrous materials' structural and magnetic parameters by the filtration criteria. Experiments have been conducted to investigate the technological process intended to fabricate polymeric fibrous materials, containing sources of magnetic field, by spraying molten polymeric composition into a gas stream. The control limits within which the filter material's structural parameters can be adjusted by technological regimes of the pneumatic extrusion process were determined. Polymeric fibrous materials containing sources of magnetic field are a new type of engineering material permitting filtration problems to be solved successfully.
References [1] L.S. Pinchuk, V.A. Goldade and O.K. Kwon, Doklady Ran 332(2) (1993) 207 (in Russian). [2] L.S. Pinchuk and V.A. Goldade, Proc. lnternat. Advances in Materials and Processing Technologies Conf., Vol. 1, (1993) p. 347. [3] V.A. Goldade, Yu. V. Gromyko, Eu. M. Markov and L.S. Pinchuk, Proc. lnternat Automative Technology and Automation Conf., (1993) p. 391. [4] L.V. Markova, Eu.M. Markov, Yu.V. Gromyko and LS. Pinchuk, Doklady A N Belarusi, 38(1) (1994) 119 (in Belarus). [5] C.N. Davies, Air Filtration, Academic Press, London-New York, 1973, p. 1. [6] S. Kuvabara, J. Phys. Soc. Japan, 14(4) (1959) 527. [7] L.V. Markova, Friction Wear, 11(2)(1990) 338 (in Russian).
Materials Processing Technology Journal of Materials Processing Technology 55 (1995) 345-350
ELSEVIER
i
Polymeric magnetic fibrous filters L.S. Pinchuk a'*, L.V. Markova a, Yu.V. Gromyko a, E.M. Markov a, U.S. Choi b Metal-Polymer Research Institute of Belarus Academy of Sciences, 32 A, Kirov Street, 246652 Gomel, Belarus Korea Institute of Science and Teehnology, Seoul, South Korea Received 12 July 1994
Industrial summary
The aim of this work is to investigate the process of cleaning working fluids and sewage water containing hard particles of impurities using polymeric fibrous filters, the latter being sources of magnetic fields. A mathematical model of a magnetic filter that has been explored experimentally is proposed, and the role of the main parameters of the filter material in filtration efficiency is analysed. Technological ways are determined to control the parameters of the filter material in the course of preparation, so that the required filtration characteristics can be ensured.
1. Introduction
The cleaning of machine working fluids of impurities is an important problem of modern technology. Of no less importance is the cleaning of industrial and municipal sewage waters. Such liquids contain great amounts of ferromagnetic particles as impurity; to separate them, filters encorporating electric and permanent magnets are usually employed. The complexity of the structure, its large dimensions, the considerable consumption of materials and the inadequate level of filtration prevent these filters from being used efficiently. To-day, polymeric fibrous filter materials [1] appear to offer the most effective means of cleaning fluids containing ferromagnetic particles. The filters fabricated from such materials are a package of adhesionally-bonded fibres formed from a ferrite-filled polymer material and subjected to magnetization. From a great number of technologies available for the fabrication of polymeric fibrous materials, the pneumatic extrusion process has become the most preferable in making ferrite-filled filter materials [2]. Materials produced by this technology are characterized by strong adhesional bond between the fibres, so that no additional treatment is required, e.g. to punch holes, to cross-link, to glue. The presence of a ferrite filler, even without additional magnetization, promotes the raising of the filtration efficiency of working fluids [3].
* Corresponding author. 0924-0136/96/$15.00 ~) 1996 Elsevier Science S.A. All rights reserved SSDI 0 9 2 4 - 0 T 3 6 ( 9 5 ) 0 2 0 2 4 - G
However, the lack of theoretical substantiation of the optimal ferrite-filler content and of experimentation with the technological process of obtaining magnetic fibrous materials, prevents the prediction of the filtration characteristics of the materials that are fabricated. The aim of this work was to understand how the structural, magnetic and technological parameters of polymeric fibrous materials, incorporating sources of magnetic fields, influence the filtration efficiency of fluids, and to determine technological ways of optimizing the filtration qualities of the materials under consideration.
2. Theory
Impurity particles become separated by tile filter material in the following manner. Larger particles ( > 20lain) are separated owing to inertia-trapping, gravitational-deposition and sieve-retention effect. Most problematic is the separation of smaller particles, these being trapped by the fibres, in the general case, due to touching (van der Waals interaction, if the particles approach the fibres sufficiently closely) and diffusional settling. Magnetic filler incorporated in the fibres enhances the degree of separation of smaller particles by magnetic interaction of the impurity particles and the fibre, and by particle coagulation under the action of the magnetic field of the filter materials. Markova et al. [4] have estimated the contributions of the different mechanisms in the total filtration process. The main mechanisms responsible for the separation of fine particles were
346
L.X Pinchuk et al. / J o u r n a l o f Materials Processing Technolog3' 55 (1995) 345 350
Table 1 Mathematical models of magnetic fibrous filter Filter model
Magnetic attraction force: designations
Type II
F(r) = 4m2r3/l 7, m is the magnetic m o m e n t of a single domain particle, / is the distance between an impurity particle and a ferrite particle
Type III
F(r) = mom
N~ N, 2~ r 2 + a2i + 2 r a i s i n ~ + 4a2j 2 2 E 2 j = - u j i = o , = o (rz + aziz + 2raisinct + a2jZ) 3'
mo is the magnetic m o m e n t of an impurity particle, a is the distance a between ferrite particles, Ni = (R - re)/a, re is the ferrite particle radius, Nj = Ida, If is the fibre half-length taken into account in the estimation of F(r), ct varies with step 1/i F(r)=nmom
Type IV
N, t~'. ~_. r 2 + aZ. i 2 4a2j2 ~ ~ Z, +2ra, isinct+ j= u~ i=o ~=0 (rz + a2i2 + 2raai sin ct + a2j2) 3'
aa is the distance b between agglomerates, Ni = (R - ro)/aa, ra is the agglomerate radius, r. = re 3 ~ , the ferrite particles in the agglomerate, N i = ldaa.
k is the compaction ratio of
a The a - values are found from the expression:
3 P.~b.Cm R 2 ;
(R-rO(R-rf+a) bThe aa
2a 3 -- 8n Pe values are found from the expression: 3 , P b C . , -R2 -'-' 1 8n pf r} n'
(R-ra)(R-ra+a.) 2a~
where Pb is the fibre density; Pe is the density of the ferrite particle.
(~)
'
• i00
y
Ill
(b)
,
EXperiment
g
0
¢
U
l
i
i
It
i
5
0
!
*
•5
20
40
,,,
9
Impurity particle diameter,/~ m
(c)~1oo
~
|
~
diameter,/~ m
Fibre
(d) ~100
-
m
l
o
,~'-
50
I
i
0
10
l
20
,
30
Fen'ite concentration, wt. %
,,,
..
,v
I
i
0
0.6
1.2
Material density, ~]crn3
Fig. I. Theoreticaland experimental efficienciesof water filtration through LDPE-basedfibrousmaterial, depending on impurityparticle diameter and materials' parameters.
shown to be contact and magnetic deposition; the diffusion settling mechanism can be neglected in the case of fluid filtration.
The mathematical model of a magnetic fibrous filter will be represented as a single fibre with spherical particles of magnetic filler (ferrite) distributed uniformly in it.
L.S. Pinchuk et al. /Journal of Materials Processing Technology 55 (1995) 345 350
347
(b)
(a) loo
'
Ili ~g
U
NXO Perin*nt III
ioo-
50 _, II
O
! ,
1
(~)
I
|
I
,
a
5 9 Impurity p a r t i c l e diarneter, t ~ m
Fibre
-100
(d)
• 50
/
0
Experiment
!
o
IO
40
ioo
_o
L..j
~ ~ " ° " -
!
20 diameter, ~ m
g
VT,
rv' !
!
20
30
0
0.6
Material
F'el'ri.te concentration, v~. %
1.2
density,
~P-,/cm3
Fig. 2. Theoretical and experimental efficiencies of petroleum oil filtration through PA-based fibrous material, depending on impurity particles diameters and materials' parameters.
This model is based on the theory [5-1 according to which filter efficiency is determined with regard for the capacity of a single fibre to catch impurity particles• Two methods were used to calculate the capacities of fibrous filters free of magnetic filler• One is based on the distribution of the Kuwabara flow field for gases and low-viscosity liquids [6], whilst the other uses the distribution of Lamb's field for high-viscosity liquids [5]. The results obtained by these two methods were analysed and compared with the experimental findings, whereupon Lamb's field method was seen to be most suitable for determining the capacities of fibrous filters• In this method the following expression determines the deposition efficiency (El) of a hard particle onto a fibre:
r[ (;)
Ef=21{La
2In
-1+
,
(1)
where r is the distance between a particle and a fibre, R is the fibre radius, La=2.0022-1nRe, and Re is Reynolds' number. If a ferrite filler is incorporated in the filter materials, Ef increases at the expense of the particles attracted magnetically. This rise can be taken into account by introducing the term F(r)fl/v into the above expression. This term characterizes the mobility acquired by the particle (by analogy with the filtration efficiency calculated for filters where the fibres carry electric charge
[5]}: Ef=~
21n
-1+
+
,
(2}
where F(r) is the magnetic attraction force between an impurity particle and a fibre,/3 = 1/6~ro ~1,ro is the impurity particle radius, ~ is the dynamic viscosity of liquid, and v is the mean flow velocity inside the filter. The following models of fibrous filters had been treated in view of the above: (I) unfilled fibres; (II) fibres containing a magnetic filler in the form of single-domain ferrite particles, the filter not being magnetized; (lid the same as in II but with a magnetized filter; and (IV) fibres filled with agglomerate of single-domain ferrite particles, the filter being magnetized. For models, II-IV, equations were derived to calculate the magnetic attraction forces acting between an impurity particle and a fibre, Table 1. The efficiency of such filters according to Davies [5] is E= 1-exp
-2
gR / '
(3)
where c is the filter material density, and h is the filter thickness. Figs. l(a) and 2(a) represent how the filtration efficiencies for water and petroleum oil depend on the particle size of the impurities. In the calculations, the following were assumed: R = 1 0 g m ; h = 2 m m ; c = 0 . 3 ; Cm= 20wt%; the liquid flow velocity was 0.5cm/s; the
348
L.S. Pinchuk et al. / Journal of Materials Processing Technology 55 (1995) 345 350
kinematic viscosity of water v = 0.01 cm2/s; that of oil 0.2 cm2/s; and the number of single-domain particles in the agglomerate n = I and n = 10. The filtration efficiency was but a little better with model IV than it was with model I, if no filler was used in the filter material. Ferrite filler added to the fibre (Model II) did not, in fact, change the filtration efficiency. However, if such a filter was magnetized (Model III) the magnetic attraction capacity of the impurity particles increased, essentially resulting in a higher filtration efficiency. For the case under consideration, a similar filter ensures complete separation of ferromagnetic impurity particles measuring 9/am or greater. In the case of filters free of magnetic fillers, such particles separation efficiency would be ca. 60%. In water cleaning, filters of type III would be even more effective: particles measuring ~> 3/am can be separated. The equations in Table 1 show the fibre diameter, the density of filter material, the concentration (Cm) and the size of the ferrite particles to be the main parameters of the filter material. The calculated dependence of the filtration efficiency on these parameters for an impurity particle diameter, of 5/am are depicted in Figs. I(a)-(d) and 2(b)-(d). If the fibre diameter in filters Type IIl is reduced from 40 to 6/am, the oil filtration efficiency increases from 10% to 100% (Figs. l(b) and 2(b). If the filters do not contain magnetic filler, this dependence shifts to the region of smaller fibre diameters, i.e. in order to separate all particles the fibre diameters should be reduced to <4/am, which makes the filter material production-process more difficult. Adding an agglomerated filler shifts the above dependence but little in the right-hand direction. When the ferrite concentration is increased from 5 to 30 wt%, the oil filtration capacity increase from 25% to 90%, if filters of Type III are used (Figs. l(c) and 2(c)). In the case of water (Fig. l(c)) the ferrite concentration of 20 wt% is quite sufficient to separate all of the impurity particles of diameter 5/am. A many-fold increase of the magnetic component of separation in filters Type IV 8 times would not improve the total efficiency: the latter does not, in fact, depend on the ferrite concentration. Filters of Type III, for which the material is less dense than that without magnetic filler, are capable of catching all particles (Figs. l(d) and 2(d)). The figures described show the magnetized filters containing single-domain ferrite particles (Type III) to be more effective compared with other models discussed. In real filter materials, however, the magnetic filler is a collection of single-domain particles and their agglomerates. In this case, mean value n should be used in the calculations.
supported by experimental findings (Figs. l(b)-(d) and 2(b)-(d)). The data were obtained for polyamideand polyethylene-based filter materials prepared following the pneumatic extrusion process. Samples of diameter 60 mm were cut from filter material of thickness 2 mm. The mean diameter of the fibres was 20/am; the average number of ferrite particles in an agglomerate was 4; and the ferrite concentration in the fibre was 20 wt%. The filtration characteristics were determined by passing contaminated liquids through specimens using a test bench. The liquid samples were analyzed before and after the trials by making use of an optical-magnetic detector [-7] capable of determining the magnetic-particle concentration in the fluid tested. The following fluids were used. To test polyethylene-based filter material, water was used as the fluid; whilst in the case of polyamide-based material, petroleum oil MC-20 was the fluid. The contaminants used were: carbonyl iron powder of dispersity 0.5-12/am (the mean diameter was 5 pro). The experimental relationships are seen to lie in the figures between the curves calculated for filters containing single-domain ferrite particles (Type III) and those for filters containing filler in the form of agglomerates of 10 single-domain particles (Type IV). Thus, the mathematical model of fibrous magnetic filter that has been proposed, after having been evaluated experimentally, is seen to be able to optimize the filter material's parameters (density, fibre thickness, size and concentration of filler particles) at the design stage, with due regard for the requirements set on filtration (the type of liquid, the speed of flow, the size of impurity particles, and the filtration efficiency). The next stage of a filter material's preparation is to determine the technological regimes ensuring obtaining the most favourable structures.
3. Comparison of theory with the experiment
4. Technology
The correctness of using the proposed mathematical model of a filter to analyze filtration efficiency has been
The pneumatic-extrusion technology, Fig. 3, was used to prepare filter materials, involves the extrusion of
Granulated ~.*"
polymeric rr~terial
EXtruder
Screw revolution f~quency
Mat
Air terrlpe r~.tur Air p r e s s u r e Fig. 3. Arrangement for fabrication of polymer magnetic fibrous materials.
L,S. Pinchuk et al. /Journal of Materials Processing Technolog>'55 (1995) 345-350 i
(a)
x LDPE o LDPl~+ferrite ( 2 0 w t % ) u
x
170
/
}
%
| 10
2~.: o
~crew
3.o
rotational
~o
velocity,
• P A pA.+ferrite ( 2 0 w t % )
L
"
o.~ ~c~e~-
rpm
rotational
velocity,
(d) ~8 g
a
of !
9.5
: 20
12o
,
,
-~p
/
. ..-.--...--..---0.
50
o.~
150
i
I
I
0.~ 0 a
?
i
pressure , k P a
40
!
!
,_-,~o
i
2~)
|
•
o
l
Air pressure , k P a
/ I
C" s
,
20
!
oX,,.~
o [5
2.5O
.....
Air temperature
A i r temperature , ° C
Air
rpm
°.....w. o/W / /
~S
-~
349
i
Distance, c m
3~
O
-
o "-
|
°
- . °
15
3O I
II
Distance,
I
I
cm
Fig. 4. Parameters of polymer fibrous materials versus technological parameters of their fabrication.
polymeric materials containing between 0 and ca. 20wt% of strontium or barium ferrite: the molten composition is sprayed by compressed air; the jet is directed onto the receiving drum of the manipulator;
and the material is magnetized by a magnetic field source. It was examined how the material's characteristics are affected by basic technological parameters: the rotational
350
L.S. Pinchuk et aL / Journal of Materials Processing Technolo~, 55 (1995) 345 350
velocity of the extruder screw; the temperature and pressure of the air; and the distance between the spray head and the receiving drum of the manipulator. The polymeric binders used for obtaining the fibrous materials were low-density polyethylene (LDPE) and polyamide (PA). The filter was strontium ferrite with a particle size of between 5 and 10 ~tm. The main relationships between the fibre diameter, the filter material density and the technological parameters are represented in Fig. 4. Variations in the rotational velocity of the screw can be seen to affect most strongly the fibre diameter in case of unfilled LDPE, whereas in the case of PA and filled LDPE the dependences almost coincide, Fig. 4(a). At the same time, increased rotational velocity of the screw used to process ferrite-filled PE results in a material with a higher density than that of the other materials, Fig. 4(b). Higher temperatures of the spray air (Figs. 4(c) and (d)) lead to greater fibre draw degrees. Nevertheless, the density of PE-based materials cannot be controlled by this means. It is much easier to vary a material's density by adjusting the air pressure (Fig. 4(f)) and the distance between the nozzle and manipulator (Fig. 4(h)). Pressure variations affect most of all the fibres of ferrite-filled material (Fig. 4(c)). Obviously greater spray gas pressure causes the fibre temperature to drop, thus leading to weaker bonding between the fibres. The greater density for PE-based materials can be explained by the fibres which hit the manipulator's drum's surface being in a viscous-flowable state. Under the action of the spray air jet they spread over the drum surface, to result in the compaction of the material. The graphs of fibre diameter versus distance between the nozzle and manipulator have a similar appearance for every pair of filled and unfilled binders (Fig. 4(g)). The curves for LDPE show a typical minimum corresponding to 10 cm distance in the case of filled materials and 20 cm distance for unfilled materials. The enlarged fibre diameters observed after the minimum can, probably, be caused by greater shrinkage values in those fibres which underwent simultaneous drawing and cooling in the course of moving within the air jet. The graphs obtained appeared helpful in establishing variation limits for the basic parameters related to the polymer molten composition pneumatic spraying, and in
optimizing the regimes for the fabrication of ferrite-filled fbrous filter materials.
5. Conclusions
Polymeric fibrous filter materials containing sources of magnetic field were designed. The filtration of liquids through them has specific features associated with the effect of the intrinsic magnetic field of the filter on hard impurity particles. A model of magnetic fibrous materials has been proposed to be used for calculating fluid filtration efficiency through materials having different structural and magnetization parameters. The comparison of theories and experimental findings has supported the validity of the model in question. This was then made the basis for optimizing the fibrous materials' structural and magnetic parameters by the filtration criteria. Experiments have been conducted to investigate the technological process intended to fabricate polymeric fibrous materials, containing sources of magnetic field, by spraying molten polymeric composition into a gas stream. The control limits within which the filter material's structural parameters can be adjusted by technological regimes of the pneumatic extrusion process were determined. Polymeric fibrous materials containing sources of magnetic field are a new type of engineering material permitting filtration problems to be solved successfully.
References [1] L.S. Pinchuk, V.A. Goldade and O.K. Kwon, Doklady Ran 332(2) (1993) 207 (in Russian). [2] L.S. Pinchuk and V.A. Goldade, Proc. lnternat. Advances in Materials and Processing Technologies Conf., Vol. 1, (1993) p. 347. [3] V.A. Goldade, Yu. V. Gromyko, Eu. M. Markov and L.S. Pinchuk, Proc. lnternat Automative Technology and Automation Conf., (1993) p. 391. [4] L.V. Markova, Eu.M. Markov, Yu.V. Gromyko and LS. Pinchuk, Doklady A N Belarusi, 38(1) (1994) 119 (in Belarus). [5] C.N. Davies, Air Filtration, Academic Press, London-New York, 1973, p. 1. [6] S. Kuvabara, J. Phys. Soc. Japan, 14(4) (1959) 527. [7] L.V. Markova, Friction Wear, 11(2)(1990) 338 (in Russian).