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Boycott effect with vertical cylinder for paramagnetic red blood cells under the inhomogeneous magnetic field
Boycott Effect with Vertical Cylinder for Paramagnetic Red Blood Cells under the Inhomogeneous Magnetic Field The sedimentation rate of paramagnetic erythrocytes in a vertical cylinder increased with the application of an inhomogeneous magnetic field in the horizontal direction. This phenomenon is similar to the socalled Boycott effect, which produces increased sedimentation in an inclined cylinder or channel. The detailed mechanism of this effect has not been obtained. Since the direction of force acting on the particles in a suspension can be changed continuously by changing the magnetic field strength, our method may be used to control the sedimentation rate of small paramagnetic particles in a liquid. © 1991Academic Press, Inc.
INTRODUCTION It is well known that small particles suspended in a fluid are sedimented much faster in an inclined cylinder (or channel) than in a vertical one. This phenomenon, known as "Boycott effect" (1), is used in industry to separate small particles from liquids. For example, it is used to separate yeast from fermentation products (2). The enhancement of sedimentation rate has been explained as follows (3-5): (i) In an inclined cylinder the particles can settle onto the upward-facing wall; (ii) These particles can slide down to the bottom of the cylinder; (iii) A transparent layer is formed near the downward-facing wall (3). (iv) This clear part (invisible) is buoyant, thus an up-current of the medium is easily generated. However, the details are not clarified unequivocally. In the present study, we demonstrate that paramagnetic erythrocytes in blood or in a buffer (or any paramagnetic particles in liquids) are sedimented much faster if an inhomogeneous magnetic field is applied (horizontal direction) to the upright cylinder containing the suspension. Since the force acting on the paramagnetic particles in the inhomogeneous magnetic field can be tilted from the vertical line, which corresponds to the long axis of the cylinder, this phenomenon can be regarded as a kind of Boycott effect. In the latter experiment, the cylinder itself (instead of the force) is tilted from the vertical line. Since the directions of the two forces, acting on the suspended particles and on the medium, are different from each other, this is another mode of the experiment which will be called "magnetic field-induced Boycott effect". This new experiment may contribute to the understanding of the Boycott effect and/or to the improved e~ciency of separation of small particles from liquids in industry. EXPERIMENTAL Freshly drawn venous blood was exposed to humidified N2 to deoxygenate hemoglobin in the erythrocytes. The erythrocytes were oxygenated by exposing the blood to atmospheric oxygen for 20 min. Erythrocytes with high
spin methemoglobin were prepared by treating washed erythrocytes with NaNO2 (20 m M) (6). Then the erythrocytes were washed five more times and suspended in an isotonic phosphate-buffered saline of pH 5.7. Erythrocyte sedimentation was observed at 25°C following the Westergren method (7, 8 ) unless otherwise specified; i.e., 4 ml of blood was mixed with 1 ml of 3.28% sodium citrate. Then the suspension was poured into a Pyrex cylinder with inner diameter of 2.5 mm at the depth of 20 cm. Growth of the clear layer was defined as erythroeyte sedimentation (E.S.) and measured along the long axis of the cylinder. Figure 1 shows a schematic view of the apparatus employed in the present study. An iron block ( 150 mm long) with a tapered edge (53 ° ) was attached on the pole piece of a Varian E-3 EPR spectrometer to generate an inhomogeneous magnetic field. One Westergren cylinder (Pyrex, 2.5 mm i.d.) was set along the edge of this iron block for the observation of "magnetic field-induced Boycott effect" and the other was set apart from the edge for the control experiment. The blood suspension was packed until the level reached the arrow shown in the right figure. The magnetic field distribution around this iron block was shown elsewhere (6). The product of the magnetic field and its gradient, B=. dBz/dz, averaged along the path (parallel with the long axis of the iron block), was about 28 TE/m (6). All the experiments were carried out at 25°C. RESULTS AND DISCUSSION Figure 2 shows the growth of the clear layer (E.S. in mm) due to sedimentation of erythrocytes with high spin methemoglobin as a function of time. The erythrocytes were suspended in isotonic buffered saline (0.9% NaCI) o f p H 5.7 at the hematocrit (i.e. vol%) of 17%. Curve 1 is E.S. in a homogeneous magnetic field of about 0.5 T, and curve 2 is E.S. in the inhomogeneous magnetic field described above. The sedimentation of erythroeytes is apparently accelerated in the inhomogeneous magnetic field, and the cause must be attributed to the interaction of paramagnetic erythrocytes with the inhomogeneous mag-
590 0021-9797/91 $3.00 Copyright © 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 146, No. 2, October 15, 1991
NOTES O~~
/ / /-
/ /
A@_~
5 91 Oxygenated
Deoxygenafed
~o
/ /, /.7.
/
7"
/
/
.-/
"x'°~
1:o 2:,I
/
E E \
/ /
"4
/
/
/.7 /
,/ / / / /
/ /-
3;
netic field since the homogeneous magnetic field gave little effect on the sedimentation rate. Figure 3 shows time courses of erythrocyte sedimentation (E.S.) for deoxygenated blood (paramagnetic; right) and oxygenated blood (diamagnetic; left) without the magnetic field (curves l)
Oc
E
E 10 Ld 20
30 120 ~
6'0
f/mm
FIG. 1. Experimental setups for the observation of accelerated erythrocyte sedimentation rate due to an inhomogeneous magnetic field. The side view (right) and the top view (left). The blood suspension was packed in Westergren cylinders (Pyrex, 2.5 mm i.d.) until the level reached the arrow. Cylinder A was set apart from the iron block for the control experiment and cylinder B was set along the iron block with a sharp edge, which was attached to the magnet pole piece.
6~0
10
10
/
/
Ld
/
./"
180 ,
f / rain FIG. 2. Effect ofinhomogeneous magnetic field on sedimentation of erythrocytes containing high spin methemoglobin: O, in homogeneous magnetic field of 0.5 T; O, in inhomogeneous magnetic field (the averaged product of magnetic flux density (B) and its gradient (dB/dz) was 28 T2/m). The hematocrit was 17%. E.S. was measured along the long axis of the cylinder.
5
910
12.0
310 6'0
9'0
t / rain
FIG. 3. Effect ofinhomogeneous magnetic field on sedimentation of, left, oxygenated erythrocytes; right, deoxygenated erythrocytes. O, without the magnetic field; e, with the inhomogeneous magnetic field of (B. dB/dz= ) 28 T2/m. E.S. was measured along the long axis of the cylinder.
or with the inhomogeneous magnetic fidd ( curves 2). Since these experiments were made following the Westergren method, the fluid contained sodium citrate at the concentration of 0.76% and its hematocrit was about 33%. In the case of deoxygenated blood, sedimentation oferythrocytes was accelerated as is deafly shown in the right diagram. In the case of oxygenated blood, on the other hand, no rnagnetic-field effect was observed. The much smaller magnetic-field effect for deoxygenated blood (Fig. 3) compared to that for oxidized erythrocytes (Fig. 2) may be due to the following causes: (i) The hematocrit employed for the oxidized-erythrocyte suspension was 17% and much smaller than those employed in other experiments with intact bloods. The hematocrit value for oxidized erythrocyte suspension was so chosen because erythrocyte sedimentation is very slow without plasma at higher hematocrit of say 35%. (ii) Incomplete deoxygenation of erythrocytes in the former case. (iii) The total spin of ferrous ion in deoxygenated hemoglobin is two (S = 2 in Eq. [6] and is smaller than that of high spin ferric ion (S = ~) in oxidized hemoglobin. (iv) In the former case, the suspension medium is plasma which is much more viscous than the buffer used in the experiment with oxidized erythrocytes. Figure 4 shows a schematic representation for the simplified model of the usual Boycott effect (right) and that for the magnetic field-induced one shown in this study (left). From these models, we obtain simple equations for the accelerated erythrocyte sedimentation rate (i.e. rate of growth of particle free layer, abbreviated as E.S.R. (mm/ s)) under the assumption that the length of the cell is much longer than the radius. For the usual Boycott effect under gravitational force (2, 5), the initial (i.e. t = 0) E.S.R. is given as E.S.R.(0) = Vo{1/cos O + aL sin(O)/A},
[1]
Journal of ColloM and Interface Science, VoL I46, No. 2, October 15, 1991
592
NOTES netic permeability, and z is the direction of the magnetic field gradient. Xv is calculated with the equation (6, 9)
I
×v = N'g2132S(S + 1)go/3kT,
f mag
f6~f
:'-.i-.:..
I
~'""/'"-:
FIG. 4. Schematic representation of the mechanism. Left, modified Boycott effect under inhomogeneous magnetic field; right, usual Boycott effect. In the usual Boycott effect, small particles sediment vertically from the level as well as from the downward-facing wall. The latter sedimentation is invisible because the particle-free fluid flows upward by the buoyant force and joins promptly with the upper transparent layer. In the magnetic-field induced Boycott effect, paramagnetic particles are pulled toward the stronger magnetic field (horizontal direction), thus an invisible particle-free layer may be formed along the wall on the opposite side of the iron block.
where v0 is the settling velocity of erythrocytes in the vertical direction, 0, A, and L are the tilting angle, the sectional area, and the area of downward facing wall, respectively, of the cylinder, and a is a correction factor (1.0 in the ideal case). On the other hand, in the case of "magnetic field-induced Boycott effect," formation rate of the clear fluid at t = 0 (V¢l~,r(0); volume/s) is obtained as the volume of the arrowed region in the left diagram of Fig. 4., Velar(O) = voA + Lvmag,
[21
where Vm~ is the drift velocity (horizontal direction) of erythrocytes to the stronger magnetic field. Since v~,,g is equal to Votan(0), E.S.R. (length/s) is given as E.S.R.(0) = v0{1 + a ' L . t a n ( O ) / A } ,
[3]
where a' is also a correction factor and is ideally 1.0 in the above model. 0 represents the angle between the vertical axis (i.e. tong axis of the cylinder) and the force acting on the erythrocyte. Thus, 0 = tan-l(fm.g]ft),
[41
where fG a n d f . ~ are the forces acting on the erythrocytes from the gravity and the inhomogeneous magnetic field, respectively, f~,~ is given b y t h e equation (9) fm~g = X v V ( B . dB/dz)/izo,
[5 ]
where Xv is the volume susceptibility of paramagnetic erythrocyte, B is the magnetic flux density, ~ is the mag-
JournalofColloidandInterfaceScience,Vol. 146, No. 2, October 15, 1991
[6]
where Nis the number density of paramagnetic hemoglobin ( 14 m M ; 8.4 X 1024/m3), g is Lande's g-factor (ZOO), is Bohr's magneton (9.27 X 10 -24 J / T ) , S is the spin of the paramagnetic center (S = 5 for high spin methemoglobin), k is the Boltzman factor, and T is the absolute temperature. Xv is thus calculated as 2.2 X 10 -6. The gravitational force which acts on the erythrocyte is the difference between the true gravitational force and the buoyant force from the medium, thus f ~ = V . A O.g,
[7]
where A0 represents the difference between the specific gravity of erythrocyte and that of the medium, and is calculated as 7.4 X 101 kg/m 3 for the experiment with oxidized erythrocytes (Fig. 2 ). Using Eqs. [ 3 ] - [ 61, the angle 0 for the present experiment for erythrocytes with high spin methemoglobin is calculated as 4.0 °. This is in a reasonable range judging from the relation between the observed E.S. and the inclination angle of the cylinder (3). This effect may easily be intensified more than tenfold by using a much stronger permanent magnet. Thus, this effect could be applied to the medical examination for a patient suspected of having a disease characterized with paramagnetic erythrocytes. In addition, this effect may be applied to the theoretical consideration of the mechanism of the Boycott effect. The qualitative understanding of the Boycott effect given above may be well accepted. However, quantitative prediction with theory is difficult, especially when the upward current of the medium along the downward facing wall is unstable. In the present experimental setups, the stability of upward current becomes different from that observed in the usual Boycott effect because the cylinder is set vertically so that the buoyant force acting in the medium is parallel to the long axis of the cylinder. REFERENCES 1. Boycott, A. E., Nature (London) 104, 532 (1920). 2. Davis, R. H., and Acrivos, A.,Annu. Rev. Fluid Mech. 17, 91 (1985). 3. Falvo, F., Ramsey, C., Zongrone, M., Stasiw, D., and Cerny, L. C., Biorheotogy 16, 465 (1979). 4. Leung, W-F., and Probstein, R. F., Ind. Eng. Chem. Process Des. Dev. 22, 58 (1983). 5. Abe, K., Takano, Y., and Oka, S., Biorheology 23, 17 (1986). 6. Okazaki, M., Maeda, N., and Shiga, T., Eur. Biophys. J. 14, 139 (1987). 7. Westergren, A., Acta Med. Scand. 54, 247 (1920). 8. International Committee, Br. 3. Haematol. 24, 671 (1973). 9. Kittel, C., "Introduction to Solid State Physics," 3rd ed., Chap. 14. Wiley, New York, 1966.
NOTES MASAHARU OKAZAKI * AKITOSHI SEIYAMA~ KAZUNORI KON~
NOBUJI MAEDA~ TAKESHI SHIGA§' 1
•Government Industrial Research Institute Nagoya, Hirate, Kita Nagoya, 462, Japan ?Department of Physiology School of Medicine Ehime University
l To wh om correspondence should be addressed.
593
Shigenobu, Onsen-gun Ehime, 791-02, Japan SDepartment of Physiology Ehime College of Health Science Tako-oda, Tobe, lyo-gun Ehime, 791-21, Japan §Department of Physiology School of Medicine Osaka University Yamadaoka 2-2 Suita Osaka, 565, Japan Received December 10, 1990; accepted March 19, 1991
JournalofColloidandlnterfaceScience.Vol. 146,No~2, October 15, 1991
INTRODUCTION It is well known that small particles suspended in a fluid are sedimented much faster in an inclined cylinder (or channel) than in a vertical one. This phenomenon, known as "Boycott effect" (1), is used in industry to separate small particles from liquids. For example, it is used to separate yeast from fermentation products (2). The enhancement of sedimentation rate has been explained as follows (3-5): (i) In an inclined cylinder the particles can settle onto the upward-facing wall; (ii) These particles can slide down to the bottom of the cylinder; (iii) A transparent layer is formed near the downward-facing wall (3). (iv) This clear part (invisible) is buoyant, thus an up-current of the medium is easily generated. However, the details are not clarified unequivocally. In the present study, we demonstrate that paramagnetic erythrocytes in blood or in a buffer (or any paramagnetic particles in liquids) are sedimented much faster if an inhomogeneous magnetic field is applied (horizontal direction) to the upright cylinder containing the suspension. Since the force acting on the paramagnetic particles in the inhomogeneous magnetic field can be tilted from the vertical line, which corresponds to the long axis of the cylinder, this phenomenon can be regarded as a kind of Boycott effect. In the latter experiment, the cylinder itself (instead of the force) is tilted from the vertical line. Since the directions of the two forces, acting on the suspended particles and on the medium, are different from each other, this is another mode of the experiment which will be called "magnetic field-induced Boycott effect". This new experiment may contribute to the understanding of the Boycott effect and/or to the improved e~ciency of separation of small particles from liquids in industry. EXPERIMENTAL Freshly drawn venous blood was exposed to humidified N2 to deoxygenate hemoglobin in the erythrocytes. The erythrocytes were oxygenated by exposing the blood to atmospheric oxygen for 20 min. Erythrocytes with high
spin methemoglobin were prepared by treating washed erythrocytes with NaNO2 (20 m M) (6). Then the erythrocytes were washed five more times and suspended in an isotonic phosphate-buffered saline of pH 5.7. Erythrocyte sedimentation was observed at 25°C following the Westergren method (7, 8 ) unless otherwise specified; i.e., 4 ml of blood was mixed with 1 ml of 3.28% sodium citrate. Then the suspension was poured into a Pyrex cylinder with inner diameter of 2.5 mm at the depth of 20 cm. Growth of the clear layer was defined as erythroeyte sedimentation (E.S.) and measured along the long axis of the cylinder. Figure 1 shows a schematic view of the apparatus employed in the present study. An iron block ( 150 mm long) with a tapered edge (53 ° ) was attached on the pole piece of a Varian E-3 EPR spectrometer to generate an inhomogeneous magnetic field. One Westergren cylinder (Pyrex, 2.5 mm i.d.) was set along the edge of this iron block for the observation of "magnetic field-induced Boycott effect" and the other was set apart from the edge for the control experiment. The blood suspension was packed until the level reached the arrow shown in the right figure. The magnetic field distribution around this iron block was shown elsewhere (6). The product of the magnetic field and its gradient, B=. dBz/dz, averaged along the path (parallel with the long axis of the iron block), was about 28 TE/m (6). All the experiments were carried out at 25°C. RESULTS AND DISCUSSION Figure 2 shows the growth of the clear layer (E.S. in mm) due to sedimentation of erythrocytes with high spin methemoglobin as a function of time. The erythrocytes were suspended in isotonic buffered saline (0.9% NaCI) o f p H 5.7 at the hematocrit (i.e. vol%) of 17%. Curve 1 is E.S. in a homogeneous magnetic field of about 0.5 T, and curve 2 is E.S. in the inhomogeneous magnetic field described above. The sedimentation of erythroeytes is apparently accelerated in the inhomogeneous magnetic field, and the cause must be attributed to the interaction of paramagnetic erythrocytes with the inhomogeneous mag-
590 0021-9797/91 $3.00 Copyright © 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 146, No. 2, October 15, 1991
NOTES O~~
/ / /-
/ /
A@_~
5 91 Oxygenated
Deoxygenafed
~o
/ /, /.7.
/
7"
/
/
.-/
"x'°~
1:o 2:,I
/
E E \
/ /
"4
/
/
/.7 /
,/ / / / /
/ /-
3;
netic field since the homogeneous magnetic field gave little effect on the sedimentation rate. Figure 3 shows time courses of erythrocyte sedimentation (E.S.) for deoxygenated blood (paramagnetic; right) and oxygenated blood (diamagnetic; left) without the magnetic field (curves l)
Oc
E
E 10 Ld 20
30 120 ~
6'0
f/mm
FIG. 1. Experimental setups for the observation of accelerated erythrocyte sedimentation rate due to an inhomogeneous magnetic field. The side view (right) and the top view (left). The blood suspension was packed in Westergren cylinders (Pyrex, 2.5 mm i.d.) until the level reached the arrow. Cylinder A was set apart from the iron block for the control experiment and cylinder B was set along the iron block with a sharp edge, which was attached to the magnet pole piece.
6~0
10
10
/
/
Ld
/
./"
180 ,
f / rain FIG. 2. Effect ofinhomogeneous magnetic field on sedimentation of erythrocytes containing high spin methemoglobin: O, in homogeneous magnetic field of 0.5 T; O, in inhomogeneous magnetic field (the averaged product of magnetic flux density (B) and its gradient (dB/dz) was 28 T2/m). The hematocrit was 17%. E.S. was measured along the long axis of the cylinder.
5
910
12.0
310 6'0
9'0
t / rain
FIG. 3. Effect ofinhomogeneous magnetic field on sedimentation of, left, oxygenated erythrocytes; right, deoxygenated erythrocytes. O, without the magnetic field; e, with the inhomogeneous magnetic field of (B. dB/dz= ) 28 T2/m. E.S. was measured along the long axis of the cylinder.
or with the inhomogeneous magnetic fidd ( curves 2). Since these experiments were made following the Westergren method, the fluid contained sodium citrate at the concentration of 0.76% and its hematocrit was about 33%. In the case of deoxygenated blood, sedimentation oferythrocytes was accelerated as is deafly shown in the right diagram. In the case of oxygenated blood, on the other hand, no rnagnetic-field effect was observed. The much smaller magnetic-field effect for deoxygenated blood (Fig. 3) compared to that for oxidized erythrocytes (Fig. 2) may be due to the following causes: (i) The hematocrit employed for the oxidized-erythrocyte suspension was 17% and much smaller than those employed in other experiments with intact bloods. The hematocrit value for oxidized erythrocyte suspension was so chosen because erythrocyte sedimentation is very slow without plasma at higher hematocrit of say 35%. (ii) Incomplete deoxygenation of erythrocytes in the former case. (iii) The total spin of ferrous ion in deoxygenated hemoglobin is two (S = 2 in Eq. [6] and is smaller than that of high spin ferric ion (S = ~) in oxidized hemoglobin. (iv) In the former case, the suspension medium is plasma which is much more viscous than the buffer used in the experiment with oxidized erythrocytes. Figure 4 shows a schematic representation for the simplified model of the usual Boycott effect (right) and that for the magnetic field-induced one shown in this study (left). From these models, we obtain simple equations for the accelerated erythrocyte sedimentation rate (i.e. rate of growth of particle free layer, abbreviated as E.S.R. (mm/ s)) under the assumption that the length of the cell is much longer than the radius. For the usual Boycott effect under gravitational force (2, 5), the initial (i.e. t = 0) E.S.R. is given as E.S.R.(0) = Vo{1/cos O + aL sin(O)/A},
[1]
Journal of ColloM and Interface Science, VoL I46, No. 2, October 15, 1991
592
NOTES netic permeability, and z is the direction of the magnetic field gradient. Xv is calculated with the equation (6, 9)
I
×v = N'g2132S(S + 1)go/3kT,
f mag
f6~f
:'-.i-.:..
I
~'""/'"-:
FIG. 4. Schematic representation of the mechanism. Left, modified Boycott effect under inhomogeneous magnetic field; right, usual Boycott effect. In the usual Boycott effect, small particles sediment vertically from the level as well as from the downward-facing wall. The latter sedimentation is invisible because the particle-free fluid flows upward by the buoyant force and joins promptly with the upper transparent layer. In the magnetic-field induced Boycott effect, paramagnetic particles are pulled toward the stronger magnetic field (horizontal direction), thus an invisible particle-free layer may be formed along the wall on the opposite side of the iron block.
where v0 is the settling velocity of erythrocytes in the vertical direction, 0, A, and L are the tilting angle, the sectional area, and the area of downward facing wall, respectively, of the cylinder, and a is a correction factor (1.0 in the ideal case). On the other hand, in the case of "magnetic field-induced Boycott effect," formation rate of the clear fluid at t = 0 (V¢l~,r(0); volume/s) is obtained as the volume of the arrowed region in the left diagram of Fig. 4., Velar(O) = voA + Lvmag,
[21
where Vm~ is the drift velocity (horizontal direction) of erythrocytes to the stronger magnetic field. Since v~,,g is equal to Votan(0), E.S.R. (length/s) is given as E.S.R.(0) = v0{1 + a ' L . t a n ( O ) / A } ,
[3]
where a' is also a correction factor and is ideally 1.0 in the above model. 0 represents the angle between the vertical axis (i.e. tong axis of the cylinder) and the force acting on the erythrocyte. Thus, 0 = tan-l(fm.g]ft),
[41
where fG a n d f . ~ are the forces acting on the erythrocytes from the gravity and the inhomogeneous magnetic field, respectively, f~,~ is given b y t h e equation (9) fm~g = X v V ( B . dB/dz)/izo,
[5 ]
where Xv is the volume susceptibility of paramagnetic erythrocyte, B is the magnetic flux density, ~ is the mag-
JournalofColloidandInterfaceScience,Vol. 146, No. 2, October 15, 1991
[6]
where Nis the number density of paramagnetic hemoglobin ( 14 m M ; 8.4 X 1024/m3), g is Lande's g-factor (ZOO), is Bohr's magneton (9.27 X 10 -24 J / T ) , S is the spin of the paramagnetic center (S = 5 for high spin methemoglobin), k is the Boltzman factor, and T is the absolute temperature. Xv is thus calculated as 2.2 X 10 -6. The gravitational force which acts on the erythrocyte is the difference between the true gravitational force and the buoyant force from the medium, thus f ~ = V . A O.g,
[7]
where A0 represents the difference between the specific gravity of erythrocyte and that of the medium, and is calculated as 7.4 X 101 kg/m 3 for the experiment with oxidized erythrocytes (Fig. 2 ). Using Eqs. [ 3 ] - [ 61, the angle 0 for the present experiment for erythrocytes with high spin methemoglobin is calculated as 4.0 °. This is in a reasonable range judging from the relation between the observed E.S. and the inclination angle of the cylinder (3). This effect may easily be intensified more than tenfold by using a much stronger permanent magnet. Thus, this effect could be applied to the medical examination for a patient suspected of having a disease characterized with paramagnetic erythrocytes. In addition, this effect may be applied to the theoretical consideration of the mechanism of the Boycott effect. The qualitative understanding of the Boycott effect given above may be well accepted. However, quantitative prediction with theory is difficult, especially when the upward current of the medium along the downward facing wall is unstable. In the present experimental setups, the stability of upward current becomes different from that observed in the usual Boycott effect because the cylinder is set vertically so that the buoyant force acting in the medium is parallel to the long axis of the cylinder. REFERENCES 1. Boycott, A. E., Nature (London) 104, 532 (1920). 2. Davis, R. H., and Acrivos, A.,Annu. Rev. Fluid Mech. 17, 91 (1985). 3. Falvo, F., Ramsey, C., Zongrone, M., Stasiw, D., and Cerny, L. C., Biorheotogy 16, 465 (1979). 4. Leung, W-F., and Probstein, R. F., Ind. Eng. Chem. Process Des. Dev. 22, 58 (1983). 5. Abe, K., Takano, Y., and Oka, S., Biorheology 23, 17 (1986). 6. Okazaki, M., Maeda, N., and Shiga, T., Eur. Biophys. J. 14, 139 (1987). 7. Westergren, A., Acta Med. Scand. 54, 247 (1920). 8. International Committee, Br. 3. Haematol. 24, 671 (1973). 9. Kittel, C., "Introduction to Solid State Physics," 3rd ed., Chap. 14. Wiley, New York, 1966.
NOTES MASAHARU OKAZAKI * AKITOSHI SEIYAMA~ KAZUNORI KON~
NOBUJI MAEDA~ TAKESHI SHIGA§' 1
•Government Industrial Research Institute Nagoya, Hirate, Kita Nagoya, 462, Japan ?Department of Physiology School of Medicine Ehime University
l To wh om correspondence should be addressed.
593
Shigenobu, Onsen-gun Ehime, 791-02, Japan SDepartment of Physiology Ehime College of Health Science Tako-oda, Tobe, lyo-gun Ehime, 791-21, Japan §Department of Physiology School of Medicine Osaka University Yamadaoka 2-2 Suita Osaka, 565, Japan Received December 10, 1990; accepted March 19, 1991
JournalofColloidandlnterfaceScience.Vol. 146,No~2, October 15, 1991