132
Ind. Eng. Chem. Fundam. 1982, 21 132-135 I
Eftect of Mixing on Flocculation K. Mlyanaml, K. ToJo,’ M. Yokota, Y. FuJlwara,and 1. Aratanl Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka, 59 1 Japan
The effects of mixing intensity and flocculation time on the suspended solids concentration in the effluent from a wastewater treatment system for heavy metals removal have been investigated by using a coagulant of lime sulfurated solution and aluminum sulfate or ferric sulfate solution. Two types of mechanical agitation, i.e., rotary agitation by an impeller and vibratory agitation by a vibrating dlsk, are employed. The behavior of the suspended solids is explained quite well by a model based on Smoluchowski’scojlision theory In a mild mixing region anj the liquid-liquid dispersion model in a rapid mixing region. The optimum Gt,the product of average shear rate 0 and the flocculation time t , can be determined from the intersection of the lines calculated based on the collision theory and the dispersion model. The treatment capacity is almost independent of the type of agitation if the power requirement per unit volume of content is of the same amount.
Introduction Flocculation is one of the most fundamental unit operations in water purification. Because the rate of flocculation in a mixing tank is usually low and is affected by various factors in diverse ways, estimating the optimum flocculation time and agitation intensity is the most important step in the rational design of wastewater treatment. If mixing in the flocculator is too mild, the flocs hardly grow in the tank and an extremely long flocculation time is required. On the contrary, too intensive mixing may cause breakup of coagulated flocs and this is detrimental to the efficiency of the wastewater treatment process. Therefore, an optimum mixing condition should exist depending on the problems at hand. In spite of the fact that not a few works have investigated the effect of mixing intensity on the rate of coagulation (Camp et al., 1943; Fair et al., 1964; Koga et al., 1979; Oldshue et al., 1978; Swift et al., 1964,Reich et al., 1959)both theoretically and experimentally, the rational design method for flocculation with mechanical agitation has not been established so far and further work is required to elucidate the effect of mixing on the rate of flocculation. In the present study, we develop a simple model for coagulation of floc particles, which is a combination of two processes: a coagulation process under mild mixing (Smoluchowski’s collision theory (1916, 1917) and a dispersion process at rapid mixing. The theoretical results are compared with the experimental results of a wastewater treatment system for heavy metal removal by using a coagulant of the mixture of lime sulfurated solution and aluminum sulfate or ferric sulfate solution. Two typea of mechanical agitation, rotary agitation by a turbine and vibratory agitation by a reciprocating disk, are utilized in the present study. Theory The rate of coagulation dN/dt can be determined by the number of contacts between floc particles in unit time (Saffman et al., 1956; Smoluchowski, 1917) W / d t = {(l/G)NlN2G(dl + d2)3 (1) where W / d t is the number of collisions per unit volume per unit time between particles type 1and 2, with number densities N 1 and N,, respectively; G is the local velocity gradient or shear rate to which the particles are exposed within the fluid; t is a collision efficiency. If the flow pattern does not vary with respect to mixing conditions, the average velocity gradient G related to the power dissipation per unit volume P, and the fluid viscosity, p, may be used in the place of G as
G
a
G = (PV/p)ll2
(2)
If dl '
i,
Cooqulant = AI,iSO,l,
10-31
IO
5
3
5
( 5 ) ; C*canst.
tisec) 5 4 0 E l 0 1803
I
lot
B Isec-0 Figure 3. Effect of average shear rate G on the concentration of suspended solids for rotary agitation.
Rotary
agitation
Figure 5. Effect of the product Gt on the concentration of suspended solids for rotary agitation. Key same as in Figure 3.
Vibratory
5
' ' 1 1 , I
1
agltation
,
, ,
, 1
, 1 1
G 0
239
C
954
4 7 7 001-
I
:
\
V i b r a t o r y agitation
K e y s same as In F i g 3 I
0
,,
I1
I
Figure 6. Effect of the product Gt on the concentration of suspended solids for vibratory agitation.
plotted in Figures 5 and 6, respectively. In these figures, the lines calculated by eq 5 and 11 are also plotted by solid lines for comparison. In both figures, the experimental results show a _closeagreement with the estimated lines except for low Gt operations. Generally, both the volume concentration of flocs and the collision efficiency in eq 5 may be influenced by the mixing intensity, while the dashed lines in Figures 5 and 6 are plotted assuming constant and C. This is a main reason for the discrepancy between the calculated and the experimental results in a low Gt operation. Assuming that the volume concentration C depends on the product of &, the experimental data have been reanalyzed and the following relationship has been obtained
r
C a (Gt)-0.67 for the coagulant of A12(S04)3,and
(13)
c 0: (Gt)-0.44 (14) for the coagulant of Fe2(S04)* The calculated lines by eq 13 and 14 are plotted as dashed line! in Figures 5 and 6. In the present study, the optimum G t value is lo4 to lo5 for both rotary and vibratory agitation. By combining eq 5,12, 13, and 14, the optimum operating condition can be obtained in terms of G and t.
135
Ind. Eng. Chem. Funciam. 1982, 21, 135-141
Conclusion
N, = number of flocs of diameter d,, m-3
The effects of mixing intensity and the flocculation time on the suspended solids concentration in the effluent from a wastewater treatment system for heavy metals removal have been investigated. The experimental resulta are well explained by a combined model of Smoluchowski’s collision theory and the liquid-liquid dispersion model on the basis of Kolmogoroff s theory of local isotropy. The optimum value of the product between the shear rate and the flocculation time, Gt,,, can be determined from the intersection of the lines calculated based on the collision theory and the dispersion model. It is also found that the treatment capacity is almost independent of the type of agitation if the power requirement per unit volume of wastewater is of the same amount.
Greek Letters = average energy dissipation per unit mass of liquid, m2/s3 p = viscosity, Pa s 11 = Kolmogoroffs microscale, m v = kinematic viscosity, mz/s (,? = collision efficiency p = liquid density, kg/m3
Nomenclature
A = amplitude of disk vibration, m C = volume concentration of flocs defined by rdZ3N2/S C1= suspended solids concentration in the treated wastewater Co = suspended solids concentration in the initial wastewater d = floc diameter, m dl = floc diameter of size 1, m d2 = floc diameter of size 2, m do = floc diameter with aggregate number nN, m d p = floc diameter with aggregate number np, m dd = diameter of agitator, m f = frequency of disk vibration, s-l F, = coagulation force, N C = local velocity gradient, s-l G = average velocity gradient, s-l N = number of collision N l = number of particles of size 1, m-3 N 2 = number of particles of size 2, m-3 Nlo = initial number of particles of size 1, m-3
n = number of aggregate particles, m-3 nM = number of particles prior to disintegration, m-3 n, = average number of particles forming one floc, m-3 ni = impeller revolution speed, s-l t = flocculation time, s V = tank volume, m3 P, = power requirement per unit volume of wastewater, W/m3 (u2(dp))= mean square fluctuation velocity, m2/s2
L i t e r a t u r e Cited Akal, J. Master of Englneerlng Thesls, University of Osaka Prefecture, Sakai, Osaka, Japan, 1979. Aratani, T.; Yasuhara, S.; Matoba, H.; Yano. T. Bull. Chem. Soc. Jpn. 1979, 52, 218. Camp, T. R.; Stein, P. C. J. Boston SOC.Clvil Eng. 1943, 30, 219. Falr, Q. M.; Qemmeli, R. S. J . Colloid Sci. 1984, 79, 360. Hudson, H. E.,Jr. J . AWWA 1985, 57, 885. Koga, K. Ph.D. Thesis, Kyushu University, Kyushu, Japan, 1979. Koga, K.; Awatani, Y.; Kusuda, T. S u a Ky&ai Zasshi, 1979, No.535. 39. Nagata, S. “Mlxing, Principles and Applicatlons”; Kodansha: Tokyo, 1975. OMshue, J. Y.; Mady, 0. 6. Chem. Eng. Frog. Aug 1978, 103. Relch. I.; VoM, R. D. J . Phys. Chem. 1959, 63, 1497. Saffman, P. Q.; Turner, J. S. J . FluUMech. 1958, 7 , 16. Shinnar. R. J.; Church, J. M. I d . Eng. Chem. 1980, 52, 253. Smoluchowski, M. Phys. 2. 1918, 77, 557. Smoiuchowski, M. Phys. Chem. 1917, 92, 129, 155. Swift, D. L.; Friedlander, S. K. J . C d M Sci. 1984, 19, 621. ToJo, K.: Miyanami, K.; Mlnami, I.; Yeno, T. Chem. Eng. J . 1979, 77, 211.
Received for review March 9, 1981 Accepted November 30, 1981
Interaction Effects on Diffusion in Protein Solutions Chrlstle J. Geankoplls’ and Mlchael C. Hu Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
The blockage and binding effects of the protein bovine serum albumin on the diffusion of sodium caprylate were investigated. Teflon diaphragm cells were used to obtain the diffusivlties of 1 g/lOO mL of sodium caprylate and bovine serum albumin (BSA) wlth albumin concentrations in the range of 0 to 5 g/100 mL and pH values of 7, 8, and 9. In the presence of BSA, the dlffusivities of sodium caprylate decreased by about 25% because of blockage by the BSA and binding as albumin concentrations increased from 0 to 5 g/100 mL. The presence of sodium caprylate also retarded the diffusiviiies of BSA by 15 % Binding studies were carried out by the technique of ultrafiltratlon wlth the type CF-25 Amicon’s centriflo membrane cones. The increased pH value decreased the overal binding coelficlent of sodium captyiate on BSA. The experimentally measured interaction effects of blockage, binding, and retardation were modeled and the equations developed predicted the diffusion data of sodium caprylate in BSA within about f3 %
.
.
Introduction
It is well known that the protein serum albumin is capable of combining with a large variety of organic and inorganic ligands (Anderson et al., 1971; Makino, 1979; Steinhardt and Reynolds, 1969; Tanford, 1973). The majority of such studies have involved the binding of anionic amphiphiles to serum albumin since this protein functions biologically as a transport protein for fatty acid anion and other simple amphiphiles. The complete understanding of the transport phenomena of the amphiphilic ligands in albumin solutions is of importance in many 0196-43 13f82f 1021-0135$01.25/0
biological systems and processes. The presence of protein in solution reduces the effective area for the diffusing solute which must circumnavigate the relatively immobile protein molecules. Moreover, for a small solute the translational mobility will be reduced by an order of magnitude, when the solute becomes attached to a protein molecule. The presence of these socalled “blockage effects” and “binding effects” could frequently occur in bioengineering and biomedical systems. The purpose of this study was to observe the bovine serum albumin blockage and binding effects on the dif0 1982 American Chemical Society
