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Sediment structure of fine silica spheres in an electrolyte solution
Powder Technology 80 (1994) 159-163
ELSEVIER
Sediment
structure
mwDER TEcHnloloGY
of fine silica spheres in an electrolyte solution
M. Furuuchi”, S. Morib, K. Gotohb ‘Department of Civil Engineering, Faculty of Engineering, Kanazawa Universily, IGxzbtsuno 2-4@20, Kanazawa 920, Japan bDepartment of Emqy Engineering, Toyohashi University of TechnoIqy, Tempaku-cho, Toyohashi 441, Japan
Received 28 December 1993; in revised form 11 April 1994
Abstract Monodispersed fine silica spheres were sedimented in KC1 solution under an electrophoretic force applied in the gravitational or antigravitational direction. Effects of particle size, particle volume fraction, electrolyte concentration and applied field intensity were experimentally investigated. A Fast Fourier Transform analysis was conducted for the sediment surface and the degree of ordering of particles was evaluated. Two different conditions were found to affect the particle ordering, one related to the kinetic energy of the settling particle and the other related to the agglomeration. Keyworak
Silica; Sedimentation; Electrophoretic force
1. Introduction The characteristics of ceramic materials are affected to a large extent by the microstructure of green compacts of primary particles [1,2]. The presence of defects, such as large voids and fissures, leads to mechanical failure [3]. There are large numbers of contacts in closely packed green compacts, so that higher density can be achieved by sintering at relatively low temperatures [4]. An ordered structure is apt to involve defects such as domain boundaries and dislocations which promote the formation of heterogeneous flawed microstructures, while a disordered structure does not and has lower packing density [5-71. Hence, in order to improve the product quality and reduce production energy, it is important to control the packing structure of green bodies. The ordering of monodispersed particles in the sedimentation and filtration processes has been extensively investigated for this purpose [1,2,8-111, but the effects of the size and sedimentation velocity of particles have not been discussed in detail. In order to precisely control packing structures, one should elucidate the ordering condition. In the present study, monodispersed silica spheres of 0.5 to 3.0 pm in diameter were allowed to sediment in KC1 solution under an electrophoretic force applied
0032-5910/94/$07.00 0 1994 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02838-F
in the gravitational or antigravitational direction. Effects of particle size, particle volume fraction, electrolyte concentration and applied field intensity on packing structure were studied experimentally. The ordering condition was mapped in relation to electrolyte concentration and sedimentation velocity.
2. Experimental The test cell is schematically shown in Fig. 1. The transparent acrylic cylinder has an inner diameter of 40 mm and a height of 38 rinn. On the cell bottom, a square plate electrode of stainless steel, with sides of 20 mm and thickness 1 mm, is attached, above which its counterpart is placed at a separation of 10 mm. Commercial, monodispersed spherical SiO, particles of diameters 0.5, 1.0, 2.0 and 3.0 pm and density 1990 kg/m3 were used as the test particles. After uniformly dispersing the particles in the solution by ultrasonic vibration, the cell was filled with the suspension to a depth of 20 mm. The initial particle volume fraction and KC1 concentration were adjusted in the ranges 0.01 to 12 vol.% and 0 to 1 mol/l respectively. An electric field with intensity E from - 1 to +7 V/cm was applied between the electrodes in
160
h4. Furuuchi et al. 1 Powder
Technology 80 (1994) 159-163
Electrodes Fig. 1. Test cell.
order to increase or decrease the sedimentation velocity, where E is positive for an electrophoretic force applied in the gravitational direction. Thermal convection was not observed over the whole range of E. After all particles had settled on the bottom, the electrolyte solution was gently removed by means of a syringe and the sediment was dried in the room atmosphere. The surface of the sediment on the bottom electrode was observed by a scanning electron microscope and photographed.
3. Results and discussion Scanning electron micrographs of the sediment surface are shown in Figs. 2(a)-(c). The packing structure of the silica spheres changes with the size and volume fraction of the particles, the electrolyte concentration and the applied field intensity. For small particles settled at high particle volume fraction and low electrolyte concentration without an applied electric field, an ordered structure is obtained. However, as the particle size is increased and the particle volume fraction decreased, the packing structure becomes disordered as shown in Fig. 2(b). Higher sedimentation velocity caused by applying an electric field of higher intensity in the gravitational direction leads to a more disordered structure, as shown in Fig. 2(c). The ordered structure of the sediment surface was observed to prevail inside the sediment. In order to evaluate the degree of ordering of the particle arrangement, two-dimensional Fast Fourier Transform was applied to the micrograph images of the sediment surface using an image analyzer. The intensity distributions of the power spectrum were calculated for the radial distance r and the angle 8 about the spectrum center, where the maximum intensity = 100 and the e-directional distribution was calculated for sectors subtending an angle r/128 at the center point. p(r) and q(8) are respectively the radial
Fig. 2. SEM photographs of sediment surfaces: (a) D, = 1.0 pm, C. = 1 X 1O-5 moV1, f0=7.02 vol.%, E=O V/cm; (b) D,= 3.0 pm, C.=lxlO-“moI/1,f,=0.05 vol.%, E=+l.O V/cm; (c) D,=2.0 pm, c,=l~lO-~ mol/l,f0=0.05 vol.%, E= +4.0 V/cm.
and angular distributions of the intensity of the power spectrum. The results, shown in Fig. 3(a), correspond to the sediment shown in Fig. 2(a). Distinct peaks appear both in p(r) and q(8), indicating an ordered structure such as a cubic or close-packed hexagonal array. In the case of the disordered sediment [Fig.
M. Furuuchi et al. / Powder 100 69 75 L!_l
0
I, 256
128
1
I 384
, 512
r [dots] I
I
1
75 L!A A 50 m % 25
0
45
180
135 8
;!I
100 @) 75 L!A ‘;: 50 “a 25
Technology 80 (1994) 159-163
161
q(8) at every 60” (0); Group 2: distinct first peak in p(r), except Group 1 (A); Group 3: blunt first peak in p(r), except Group 1 (A); Group 4: no peaks in either p(r) or q(6) (a). The first two groups were categorized as ‘ordered’ and the latter two as ‘disordered’. Fig. 4 shows the packing structures of sediments in relation to the intensity E of the applied electric field and the particle diameter D,, where the electrolyte concentration C, and the initial particle volume fraction fO were fixed. When E =0 and D,$ 1 pm, that is, in the case of purely gravitational sedimentation, the sediments exhibit highly ordered structures. As the particle size and the electric field intensity are increased, the sedimentation velocity increases and the packing structure becomes disordered even for submicron particles. As denoted by the dotted line in Fig. 4, a clear boundary exists between ordered and disordered structures. Note that the boundary is broad rather than sharp, because various types of packing structures can exist between purely ordered and random ones. Similar results have been reported in previous papers [12,13]. The critical value of E decreases with increasing particle diameter. Hence, one can control the packing structure by adjusting the sedimentation velocity of particles. Since the sedimentation velocity was found to be a controlling factor for the ordering of packing structure, the experimental results will be related to the sedimentation velocity U, in the following. Fig. 5 shows the packing structure of sediments in relation to the initial particle volume fraction fO and the normalized sedimentation velocity UJU,, where U, is the average velocity of Brownian motion [14]. Denoting the terminal settling velocity in the Stokes region by U,,Usmay be written as
where
U,is the electrophoretic
u, = 2&Yf(%
velocity given by [14]:
(2)
Q/(377)
C, = 1 Xl Oe5 I mol/l 4. 0
45
90 8
r”
135
180
I
fo=0.051%1 0 A Order l A Disorder
1
Fig. 3. The intensity distributions of power spectrum, where p(r) and q(8) respectively are the radial and angular distributions: (a) ordered sediment; (b) disordered sediment.
2(c)], no distinct peaks appear, as shown in Fig. 3(b). According to the type of p(r) and q(0) curves, the packing structures were classified into four groups and are denoted in the following figures by the corresponding symbols in parentheses. Group 1: distinct first peak in
Fig. 4. The packing structure of sediment intensity E and the particle diameter D,
in relation
to the field
162
M. Furuuchi et al. I Powder
Fig. 5. The packing structure of sediment in relation to the initial particle volume fraction f0 and the reduced sedimentation velocity U./U,. Table 1 Parameters used e: 7.08~10~r” (CV-* q: 9.04X10-4 (Pa’s) C. (mot/l)
r” (mV)
m-‘)
k (m-l)
&a,
K) (-)
0,=0.5 1 x10-s 1 x10-5 1x10-* 1x10-’ 1
- 138 - 67.3 - 36.0 - 32.0 - 29.3
3.28 1.04 3.28 1.04 3.28
x x X x X
lo6 10’ 10” lo9 IOr’
1.05 1.16 1.47 1.49 1.50
pm
1.0 pm 2.0 pm 3.0 pm 1.11 1.24 1.48 1.50 1.50
1.19 1.33 1.50 1.50 1.50
1.24 1.38 1.50 1.50 1.50
“Measured at pH 7.
in which E is the dielectric constant of solution, l is the zeta potential, E is the intensity of the applied electric field and n is the viscosity of the solution. f( Ka, K) is the Henry function [14], in which a =DP/2, K is the reciprocal thickness of the electric double layer and K= 0 for non-conducting particles. f(Ka, IS) denotes a velocity retardation effect induced by ion motion and becomes 1.5 and 1, respectively, for KUz=-1 and ~a -=z1. In the present calculation, empirical values are used for 5. The parameters are summarized in Table 1. As the initial particle volume fraction f0 decreases, the overlaps of the electric double layers of particles decrease, so that particle ordering occurs less readily. Hence, as depicted by the dotted curve in Fig. 5, the critical value of U&Y,, for ordering decreases with decreasingf,. Because of fluid dynamic and electrostatic interactions between settling particles, the actual sedimentation velocity becomes less than U, and its deviation from Eq. (1) may increase in the case off,>0.1[15-171. Hence, the actual boundary for ordering may lie slightly below the dotted curve. Similarly, as the electrolyte concentration C, increases, the boundary curve may shift to the right because the thickness of the electric double layer decreases so that particle ordering becomes difficult.
Technology 80 (1994) 159-163
Fig. 6 depicts the relation between the normalized sedimentation velocity Us/U,, and the concentration of electrolyte C,, in which the initial particle volume fraction f. was fixed at 0.05 vol.%, so that the effect of interaction between particles may be small except when particles locate just above a sediment surface. Two different conditions affect the ordering of the sediment structure. The boundary denoted by the solid line may be related to the kinetic energy V, of the settling particles. When V, exceeds a value large enough to overcome the potential barrier due to the electric double layer around the particle, the sediment structure may become disordered because the particles are forced to contact each other randomly, irrespective of the potential barrier [see Fig. 7(b)]. One should note that all data around this boundary are obtained under the applied electric field. The other boundary denoted by the dotted line may be related to the particle agglomeration. On the right-hand side of the boundary, all sediment structures become disordered [see Fig. 7(a)]. For the conditions around the boundary denoted by the dotted line in Fig. 6, the total interparticle potential V, for equal spheres [14] is depicted in units of kT in Fig. 7, where V, = ED&$ In{1 + exp( - A)}/4 - [AD,l(24h)]
(3)
where #o was replaced by the empirical value of l, A is the Hamaker constant (= 1.7 X 10W20J) and h is the distance between the spheres. As one can see from Fig. 7, for higher electrolyte concentrations the particles agglomerate while sedimenting, so that the sediment structure becomes disordered. The agglomeration phenomenon was confirmed by the rapid increase observed in the settling velocity. The above two types of particle disordering might also be related to the applied electric field. The electric double layer around an electrophoretically accelerated settling particle is distorted to be asymmetrical because of the relaxation effect [18]. Hence, the total interparticle 100
10-g
1o-5 C, I mol/l
10 I
Fig. 6. The packing structure of sediment in relation to the electrolyte concentration C. and the reduced sedimentation velocity U,/lJb.
M. Furuuchi et aL / Powder Technology 80 (1994) 159-163
ordering, one related to the kinetic energy of the settling particles and the other related to the agglomeration.
200
f, =0.05D[I
List of symbols
I--,,,.,
A
~
.~Ce--
I I
lx10 -~
.
c~ Dp E
I I 1!/'¢t ~'''°
fo
o-'
h p(r) q(O)
-100 10-5 2OO
-
163
O0
h/Dp - I
ihi' '1
'1
'l
'1
'1
Dp= I/tml I
us vt
C'= 1X10-51
Greek letters
3.0
//~ /_~
u~ u~
~0 C, = 1×t0 -2
? 10 -5
Hamaker constant (J) concentration of electrolyte (mol/1) particle diameter (m) intensity of electric field (V/em) initial particle volume fraction (-) distance between particles (m) radial distribution of intensity of power spectrum of surface image (-) angular distribution of intensity of power spectrum of surface image (-) average velocity of Brownian motion (m/s) electrophoretic velocity (m/s) Stokes velocity of particle (m/s) sedimentation velocity = Ug+ Ue (m/s) total interparticle potential (J)
1O0 h/Dp [ - l
Fig. 7. The total interparticle potential for equal spheres in units of kT. (a) corresponds to data for UJUb--0.7 in Fig. 6 and (b) for UJUb--11. Solid curves correspond to ordered structure.
potential may deviate from Eq. (3). In the present experiments, the influence of the applied electric field may be not so significant, because of its low intensity. However, further experiments, especially for the gravitational sedimentation of particles of D o > 3 /~m, are necessary for this study. 4. Conclusion
Ordering of monodispersed fine silica spheres in the sediment becomes significant as the sedimentation velocity and the electrolyte concentration decrease. The critical sedimentation velocity for ordering decreases with the initial particle volume fraction. A map for the ordering condition was obtained in relation to the electrolyte concentration and sedimentation velocity. Two different conditions were found to affect particle
dielectric constant of solution (CV-1 m-1) zeta potential of particle (V) surface potential of particle (V)
References [1] M.D. Sacks and T. Tseng, J. Am. Ceram. Soc., 67 (1984) 526. [2] E.A. Barringer and H.K. Bowen, Commun. Am. Ceram. Soc., C (1982) 199. [3] R.W. Davidge and A.G. Evans, Mater. Sci. Eng., 6 (1970) 281. [4] W.H. Rhodes, J. Am. Ceram. Soc., 64 (1981) 19. [5] F.F. Lange, B.I. Davis and I.A. Aksay, J. Am. Ceram. Soc., 66 (1983) 407. [6] E. Liniger and R. Raj, J. Am. Ceram. Soc., 70 (1987) 843. [7] E. Dickinson, S.J. Milne and M. Patel, Ind. Eng. Chem. Res., 27 (1988) 1941. [8] K. Higashitani, K. Hata, Y. Okanaka and K. Ueshima, J. Chem. Eng. Jpn., 24 (1991) 346. [9] K. Ueshima, Y. Kanda and K. Higashitani, J. Chem. Eng. Jpn., 24 (1991) 351. [10] G.Y. Onoda, Amer. Phys. Soc., 55 (1985) 226. [11] K. Ueshima, H. Iizuka and K. Higashitani, Z Chem. Eng. Jpn., 24 (1991) 647. [12] M. Bargiel and E.M. Tory, Adv. Powder Technol., 4 (1993) 79. [13] J. Moscinski, M. Bargiel, Z.A. Rycerz and P.W.M. Jacobs, MoL Sim., 3 (1989) 201. [14] K. Iinoya, K. Gotoh and K. Higashitani (eds.), Powder Technology Handbook, Marcel Dekker, New York, 1991. [15] D.R. Oliver, Chem. Eng. Sci., 15 (1961) 230. [16] J.F. Richardson and W.N. Zaki, Trans. Inst. Chem. Eng., 32 (1954) 35. [17] G.IC Batchelor, Z Fluid Mech., 52 (1972) 245. [18] P.H. Wiersema, A.L. Loeb and J.T.G. Overbeek, J. Colloid Interface Sci., 22 (1966) 78.
ELSEVIER
Sediment
structure
mwDER TEcHnloloGY
of fine silica spheres in an electrolyte solution
M. Furuuchi”, S. Morib, K. Gotohb ‘Department of Civil Engineering, Faculty of Engineering, Kanazawa Universily, IGxzbtsuno 2-4@20, Kanazawa 920, Japan bDepartment of Emqy Engineering, Toyohashi University of TechnoIqy, Tempaku-cho, Toyohashi 441, Japan
Received 28 December 1993; in revised form 11 April 1994
Abstract Monodispersed fine silica spheres were sedimented in KC1 solution under an electrophoretic force applied in the gravitational or antigravitational direction. Effects of particle size, particle volume fraction, electrolyte concentration and applied field intensity were experimentally investigated. A Fast Fourier Transform analysis was conducted for the sediment surface and the degree of ordering of particles was evaluated. Two different conditions were found to affect the particle ordering, one related to the kinetic energy of the settling particle and the other related to the agglomeration. Keyworak
Silica; Sedimentation; Electrophoretic force
1. Introduction The characteristics of ceramic materials are affected to a large extent by the microstructure of green compacts of primary particles [1,2]. The presence of defects, such as large voids and fissures, leads to mechanical failure [3]. There are large numbers of contacts in closely packed green compacts, so that higher density can be achieved by sintering at relatively low temperatures [4]. An ordered structure is apt to involve defects such as domain boundaries and dislocations which promote the formation of heterogeneous flawed microstructures, while a disordered structure does not and has lower packing density [5-71. Hence, in order to improve the product quality and reduce production energy, it is important to control the packing structure of green bodies. The ordering of monodispersed particles in the sedimentation and filtration processes has been extensively investigated for this purpose [1,2,8-111, but the effects of the size and sedimentation velocity of particles have not been discussed in detail. In order to precisely control packing structures, one should elucidate the ordering condition. In the present study, monodispersed silica spheres of 0.5 to 3.0 pm in diameter were allowed to sediment in KC1 solution under an electrophoretic force applied
0032-5910/94/$07.00 0 1994 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02838-F
in the gravitational or antigravitational direction. Effects of particle size, particle volume fraction, electrolyte concentration and applied field intensity on packing structure were studied experimentally. The ordering condition was mapped in relation to electrolyte concentration and sedimentation velocity.
2. Experimental The test cell is schematically shown in Fig. 1. The transparent acrylic cylinder has an inner diameter of 40 mm and a height of 38 rinn. On the cell bottom, a square plate electrode of stainless steel, with sides of 20 mm and thickness 1 mm, is attached, above which its counterpart is placed at a separation of 10 mm. Commercial, monodispersed spherical SiO, particles of diameters 0.5, 1.0, 2.0 and 3.0 pm and density 1990 kg/m3 were used as the test particles. After uniformly dispersing the particles in the solution by ultrasonic vibration, the cell was filled with the suspension to a depth of 20 mm. The initial particle volume fraction and KC1 concentration were adjusted in the ranges 0.01 to 12 vol.% and 0 to 1 mol/l respectively. An electric field with intensity E from - 1 to +7 V/cm was applied between the electrodes in
160
h4. Furuuchi et al. 1 Powder
Technology 80 (1994) 159-163
Electrodes Fig. 1. Test cell.
order to increase or decrease the sedimentation velocity, where E is positive for an electrophoretic force applied in the gravitational direction. Thermal convection was not observed over the whole range of E. After all particles had settled on the bottom, the electrolyte solution was gently removed by means of a syringe and the sediment was dried in the room atmosphere. The surface of the sediment on the bottom electrode was observed by a scanning electron microscope and photographed.
3. Results and discussion Scanning electron micrographs of the sediment surface are shown in Figs. 2(a)-(c). The packing structure of the silica spheres changes with the size and volume fraction of the particles, the electrolyte concentration and the applied field intensity. For small particles settled at high particle volume fraction and low electrolyte concentration without an applied electric field, an ordered structure is obtained. However, as the particle size is increased and the particle volume fraction decreased, the packing structure becomes disordered as shown in Fig. 2(b). Higher sedimentation velocity caused by applying an electric field of higher intensity in the gravitational direction leads to a more disordered structure, as shown in Fig. 2(c). The ordered structure of the sediment surface was observed to prevail inside the sediment. In order to evaluate the degree of ordering of the particle arrangement, two-dimensional Fast Fourier Transform was applied to the micrograph images of the sediment surface using an image analyzer. The intensity distributions of the power spectrum were calculated for the radial distance r and the angle 8 about the spectrum center, where the maximum intensity = 100 and the e-directional distribution was calculated for sectors subtending an angle r/128 at the center point. p(r) and q(8) are respectively the radial
Fig. 2. SEM photographs of sediment surfaces: (a) D, = 1.0 pm, C. = 1 X 1O-5 moV1, f0=7.02 vol.%, E=O V/cm; (b) D,= 3.0 pm, C.=lxlO-“moI/1,f,=0.05 vol.%, E=+l.O V/cm; (c) D,=2.0 pm, c,=l~lO-~ mol/l,f0=0.05 vol.%, E= +4.0 V/cm.
and angular distributions of the intensity of the power spectrum. The results, shown in Fig. 3(a), correspond to the sediment shown in Fig. 2(a). Distinct peaks appear both in p(r) and q(8), indicating an ordered structure such as a cubic or close-packed hexagonal array. In the case of the disordered sediment [Fig.
M. Furuuchi et al. / Powder 100 69 75 L!_l
0
I, 256
128
1
I 384
, 512
r [dots] I
I
1
75 L!A A 50 m % 25
0
45
180
135 8
;!I
100 @) 75 L!A ‘;: 50 “a 25
Technology 80 (1994) 159-163
161
q(8) at every 60” (0); Group 2: distinct first peak in p(r), except Group 1 (A); Group 3: blunt first peak in p(r), except Group 1 (A); Group 4: no peaks in either p(r) or q(6) (a). The first two groups were categorized as ‘ordered’ and the latter two as ‘disordered’. Fig. 4 shows the packing structures of sediments in relation to the intensity E of the applied electric field and the particle diameter D,, where the electrolyte concentration C, and the initial particle volume fraction fO were fixed. When E =0 and D,$ 1 pm, that is, in the case of purely gravitational sedimentation, the sediments exhibit highly ordered structures. As the particle size and the electric field intensity are increased, the sedimentation velocity increases and the packing structure becomes disordered even for submicron particles. As denoted by the dotted line in Fig. 4, a clear boundary exists between ordered and disordered structures. Note that the boundary is broad rather than sharp, because various types of packing structures can exist between purely ordered and random ones. Similar results have been reported in previous papers [12,13]. The critical value of E decreases with increasing particle diameter. Hence, one can control the packing structure by adjusting the sedimentation velocity of particles. Since the sedimentation velocity was found to be a controlling factor for the ordering of packing structure, the experimental results will be related to the sedimentation velocity U, in the following. Fig. 5 shows the packing structure of sediments in relation to the initial particle volume fraction fO and the normalized sedimentation velocity UJU,, where U, is the average velocity of Brownian motion [14]. Denoting the terminal settling velocity in the Stokes region by U,,Usmay be written as
where
U,is the electrophoretic
u, = 2&Yf(%
velocity given by [14]:
(2)
Q/(377)
C, = 1 Xl Oe5 I mol/l 4. 0
45
90 8
r”
135
180
I
fo=0.051%1 0 A Order l A Disorder
1
Fig. 3. The intensity distributions of power spectrum, where p(r) and q(8) respectively are the radial and angular distributions: (a) ordered sediment; (b) disordered sediment.
2(c)], no distinct peaks appear, as shown in Fig. 3(b). According to the type of p(r) and q(0) curves, the packing structures were classified into four groups and are denoted in the following figures by the corresponding symbols in parentheses. Group 1: distinct first peak in
Fig. 4. The packing structure of sediment intensity E and the particle diameter D,
in relation
to the field
162
M. Furuuchi et al. I Powder
Fig. 5. The packing structure of sediment in relation to the initial particle volume fraction f0 and the reduced sedimentation velocity U./U,. Table 1 Parameters used e: 7.08~10~r” (CV-* q: 9.04X10-4 (Pa’s) C. (mot/l)
r” (mV)
m-‘)
k (m-l)
&a,
K) (-)
0,=0.5 1 x10-s 1 x10-5 1x10-* 1x10-’ 1
- 138 - 67.3 - 36.0 - 32.0 - 29.3
3.28 1.04 3.28 1.04 3.28
x x X x X
lo6 10’ 10” lo9 IOr’
1.05 1.16 1.47 1.49 1.50
pm
1.0 pm 2.0 pm 3.0 pm 1.11 1.24 1.48 1.50 1.50
1.19 1.33 1.50 1.50 1.50
1.24 1.38 1.50 1.50 1.50
“Measured at pH 7.
in which E is the dielectric constant of solution, l is the zeta potential, E is the intensity of the applied electric field and n is the viscosity of the solution. f( Ka, K) is the Henry function [14], in which a =DP/2, K is the reciprocal thickness of the electric double layer and K= 0 for non-conducting particles. f(Ka, IS) denotes a velocity retardation effect induced by ion motion and becomes 1.5 and 1, respectively, for KUz=-1 and ~a -=z1. In the present calculation, empirical values are used for 5. The parameters are summarized in Table 1. As the initial particle volume fraction f0 decreases, the overlaps of the electric double layers of particles decrease, so that particle ordering occurs less readily. Hence, as depicted by the dotted curve in Fig. 5, the critical value of U&Y,, for ordering decreases with decreasingf,. Because of fluid dynamic and electrostatic interactions between settling particles, the actual sedimentation velocity becomes less than U, and its deviation from Eq. (1) may increase in the case off,>0.1[15-171. Hence, the actual boundary for ordering may lie slightly below the dotted curve. Similarly, as the electrolyte concentration C, increases, the boundary curve may shift to the right because the thickness of the electric double layer decreases so that particle ordering becomes difficult.
Technology 80 (1994) 159-163
Fig. 6 depicts the relation between the normalized sedimentation velocity Us/U,, and the concentration of electrolyte C,, in which the initial particle volume fraction f. was fixed at 0.05 vol.%, so that the effect of interaction between particles may be small except when particles locate just above a sediment surface. Two different conditions affect the ordering of the sediment structure. The boundary denoted by the solid line may be related to the kinetic energy V, of the settling particles. When V, exceeds a value large enough to overcome the potential barrier due to the electric double layer around the particle, the sediment structure may become disordered because the particles are forced to contact each other randomly, irrespective of the potential barrier [see Fig. 7(b)]. One should note that all data around this boundary are obtained under the applied electric field. The other boundary denoted by the dotted line may be related to the particle agglomeration. On the right-hand side of the boundary, all sediment structures become disordered [see Fig. 7(a)]. For the conditions around the boundary denoted by the dotted line in Fig. 6, the total interparticle potential V, for equal spheres [14] is depicted in units of kT in Fig. 7, where V, = ED&$ In{1 + exp( - A)}/4 - [AD,l(24h)]
(3)
where #o was replaced by the empirical value of l, A is the Hamaker constant (= 1.7 X 10W20J) and h is the distance between the spheres. As one can see from Fig. 7, for higher electrolyte concentrations the particles agglomerate while sedimenting, so that the sediment structure becomes disordered. The agglomeration phenomenon was confirmed by the rapid increase observed in the settling velocity. The above two types of particle disordering might also be related to the applied electric field. The electric double layer around an electrophoretically accelerated settling particle is distorted to be asymmetrical because of the relaxation effect [18]. Hence, the total interparticle 100
10-g
1o-5 C, I mol/l
10 I
Fig. 6. The packing structure of sediment in relation to the electrolyte concentration C. and the reduced sedimentation velocity U,/lJb.
M. Furuuchi et aL / Powder Technology 80 (1994) 159-163
ordering, one related to the kinetic energy of the settling particles and the other related to the agglomeration.
200
f, =0.05D[I
List of symbols
I--,,,.,
A
~
.~Ce--
I I
lx10 -~
.
c~ Dp E
I I 1!/'¢t ~'''°
fo
o-'
h p(r) q(O)
-100 10-5 2OO
-
163
O0
h/Dp - I
ihi' '1
'1
'l
'1
'1
Dp= I/tml I
us vt
C'= 1X10-51
Greek letters
3.0
//~ /_~
u~ u~
~0 C, = 1×t0 -2
? 10 -5
Hamaker constant (J) concentration of electrolyte (mol/1) particle diameter (m) intensity of electric field (V/em) initial particle volume fraction (-) distance between particles (m) radial distribution of intensity of power spectrum of surface image (-) angular distribution of intensity of power spectrum of surface image (-) average velocity of Brownian motion (m/s) electrophoretic velocity (m/s) Stokes velocity of particle (m/s) sedimentation velocity = Ug+ Ue (m/s) total interparticle potential (J)
1O0 h/Dp [ - l
Fig. 7. The total interparticle potential for equal spheres in units of kT. (a) corresponds to data for UJUb--0.7 in Fig. 6 and (b) for UJUb--11. Solid curves correspond to ordered structure.
potential may deviate from Eq. (3). In the present experiments, the influence of the applied electric field may be not so significant, because of its low intensity. However, further experiments, especially for the gravitational sedimentation of particles of D o > 3 /~m, are necessary for this study. 4. Conclusion
Ordering of monodispersed fine silica spheres in the sediment becomes significant as the sedimentation velocity and the electrolyte concentration decrease. The critical sedimentation velocity for ordering decreases with the initial particle volume fraction. A map for the ordering condition was obtained in relation to the electrolyte concentration and sedimentation velocity. Two different conditions were found to affect particle
dielectric constant of solution (CV-1 m-1) zeta potential of particle (V) surface potential of particle (V)
References [1] M.D. Sacks and T. Tseng, J. Am. Ceram. Soc., 67 (1984) 526. [2] E.A. Barringer and H.K. Bowen, Commun. Am. Ceram. Soc., C (1982) 199. [3] R.W. Davidge and A.G. Evans, Mater. Sci. Eng., 6 (1970) 281. [4] W.H. Rhodes, J. Am. Ceram. Soc., 64 (1981) 19. [5] F.F. Lange, B.I. Davis and I.A. Aksay, J. Am. Ceram. Soc., 66 (1983) 407. [6] E. Liniger and R. Raj, J. Am. Ceram. Soc., 70 (1987) 843. [7] E. Dickinson, S.J. Milne and M. Patel, Ind. Eng. Chem. Res., 27 (1988) 1941. [8] K. Higashitani, K. Hata, Y. Okanaka and K. Ueshima, J. Chem. Eng. Jpn., 24 (1991) 346. [9] K. Ueshima, Y. Kanda and K. Higashitani, J. Chem. Eng. Jpn., 24 (1991) 351. [10] G.Y. Onoda, Amer. Phys. Soc., 55 (1985) 226. [11] K. Ueshima, H. Iizuka and K. Higashitani, Z Chem. Eng. Jpn., 24 (1991) 647. [12] M. Bargiel and E.M. Tory, Adv. Powder Technol., 4 (1993) 79. [13] J. Moscinski, M. Bargiel, Z.A. Rycerz and P.W.M. Jacobs, MoL Sim., 3 (1989) 201. [14] K. Iinoya, K. Gotoh and K. Higashitani (eds.), Powder Technology Handbook, Marcel Dekker, New York, 1991. [15] D.R. Oliver, Chem. Eng. Sci., 15 (1961) 230. [16] J.F. Richardson and W.N. Zaki, Trans. Inst. Chem. Eng., 32 (1954) 35. [17] G.IC Batchelor, Z Fluid Mech., 52 (1972) 245. [18] P.H. Wiersema, A.L. Loeb and J.T.G. Overbeek, J. Colloid Interface Sci., 22 (1966) 78.