408
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
Adsorption Kinetics and Diffusional Mass Transfer Processes during Color Removal from Effluent Using Silica Frank Alexander, Victor J. P. Poots, and Gordon McKay' Department of Industrial Chemistty, The Queen's University of Belfast, Belfast BT9 5DL. Northern Ireland
The ability of Sorbsil silica gel to remove dye from solution has been studied. The effects of contact time, initial dye concentration, and adsorption isotherms have been determined for different particle size ranges. The kinetics of the adsorption process have been studied and an overall diffusion coefficient has been evaluated. The diffusivity for the adsorption of Astrazone Blue on silica has been determined to be 1.2 (f0.2)X lo-' cm2 s-'.
Introduction Colored effluents, although not normally toxic, have possibly caused the loudest cries of indignation from the public purely because of their appearance. Apart from the visible effects of the streams, color interferes with the transmission of sunlight into the stream and therefore lessens photosynthetic action. Most colored effluents are composed of nonbiologically oxidizable organic componenta because of the molecular size and structure of the dyestuffs, so some form of treatment is necessary. Adsorption appears currently to offer the best prospects for overall treatment according to Weber and Morris (1962) and it can be expected to be useful for a broad range of substances. Activated carbon, the most popular adsorbent, has been used with great success (IC1America Inc., 1971). It has a high capacity, but it is expensive and fragile, making regeneration and consistency of particle size difficult to maintain. Consequently new materials are continuously being studied; for example, activated bauxite and Fuller's earth (Mutch, 1946; Parsons, 1913; Thornton and Moore, 1953), peat moss, and woodmeal (Dufort and Ruel, 1972, Poots et al., 1976), and some have met with considerable success. The aim of this paper is to study the mechanism of adsorption for a commonly used basic dye, namely, Astrazone Blue FRR69, on Sorbsil silica gel. There appears to be a limited amount of information on water treatment using silica (Middleton, 1971) although surface studies on silica, even using colored compounds, are well documented (Sing and Madeley, 1953; Giles and Nakhwa, 1962; Giles and D'Silva, 1969). Experimental Section The influence of contact time on the transport of dyes onto the surface of silica was studied using a cylindrical vessel, 0.10 m diameter, containing four baffles evenly spaced around the circumference. Agitation was achieved using a 50-mm diameter, six-bladed impeller rotating a t 100 rpm. In preparation for each run, a 500 mL volume of 200 ppm dye solution was placed in the vessel and 10 g of silica was added. Samples of 2 mL were withdrawn from the vessel, using a syringe, at known time intervals for analysis. Further experimental details have been described elsewher,e (Poots et al., 1976a). Results and Discussion (i) Effect of Contact Time. The results of the contact time investigations are shown in Figure 1 for seven different particle sizes of silica. The fraction of dye adsorbed i.e., (C, - C,)/Co,is plotted against time of contact. The plots show the same general form of an initial steep rise
in adsorption with time and then a rapid levelling off as equilibrium is established. In all cases 90% of the equilibrium value has been fully reached after 240 min contact. There is only a small effect on the contact time required to reach saturation due to a variation in particle size. Figure 2 shows the influence of initial dye concentration for silica of constant particle size range (355-500 pm). The time to reach equilibrium is almost concentration independent but increases slightly with increasing dye concentration. In addition, the fraction dye adsorbed at equilibrium decreases with initial dye concentration. Contact times were carried out first to determine the contact time to reach equilibrium so that this information may be used to predict experimental conditions necessary for adsorption isotherms. Contact times also provide valuable information on the mechanism of dye adsorption onto silica gel. (ii) Rate Processes. The contact time experiments can be used to establish the time dependence of the system. The normal function of time ( t )is and Figure 3 shows the fraction of dye uptake against Similar plots are shown in Figure 4 and illustrate the influence of initial dye concentration. The seven plots at various particle size ranges and five plots for different initial dye concentrations are of the same general shape, i.e., an initial curved portion, a linear section, and a final curved portion. In this model, the particles are considered as being surrounded by a boundary layer film through which the dye molecules must diffuse prior to external adsorption on the silica surface, and this step is responsible for the initial curvature in Figures 3 and 4. The linear portion of the plots between 10-50% dye adsorption is due to intraparticle diffusion being predominant in the rate-controlling step. As the bulk dye concentration and the surface dye concentration start to decrease, the final portion of the figures begins to curve due to a decrease in the rate of diffusion. The adsorption of alkylbenzenesulfonatesonto activated carbon has been investigated (Weber and Morris, 1964) and the rate-controlling step was shown to be solely dependent on intraparticle diffusion. The same mechanism was postulated as a rate-controlling step in the uptake of other solutes by different types of granular adsorbents, including carbon (Edeskuty and Amundson, 1952). It seems likely that intraparticle diffusion is important in the adsorption of Astrazone Blue on silica. A rate parameter, k , is defined as the initial slope of a graph of the amount of dye adsorbed per gram of adsorbent against t0.5. Hence the k values are readily available from Figures 3 and 4 simply by multiplying the gradients by the initial dye concentrations. For example,
00l9-7882/78/l117-0406$01.00/00 1978 American Chemical Society
Ind. Eng. Chem. Process Des. Dev.. Vol. 17, NO. 4, 1978
08
p
0 6
0
04
c
0
E
02
0
o
PR
0
PR =
180-150 micron 355-250micron
0
PR =
7 1 0 - 5 0 0 micron
A
P R = 1000 -850 micron
:
c,
a
400ppm
C,=
500ppm
rnins
o
Co =
a
C,= 100 p p m C,= 2 0 0 p p m
0
2
4
50ppm
A
Co= 400ppm
o
c,=
6
0
1
~irn.8 mins” ~
0
’
Figure 3. Fraction dye adsorbed against time0,5for different initial dye concentrations using a constant particle size range (355-500 pm).
500ppm
0.9
o
180 - 1 5 0 p
a
250 -180 p 355 - 2 5 0 p
500 -355p
U 0
A
0.6
06
0 C
A
710 - 5 0 0 , ~ 850-710,~ 1000-850~
co- Ct
P .+
CO
0.3
0
04
100 200 3 Time of contact mins
0 2
Figure 2. Fraction dye adsorbed against contact time for various initial dye concentrationsusing a constant particle size range (355-500 rm). Table I. Rate Parameter, h , as a Function of Particle Size and Initial Dve Concentration
particle size, prn 150-180 180-250 250-355 355-500 500-710 710-850 850-1000
3 5 5-500 355-500 355-500 355-500 355-500
initial dye concn, C, , mg L-I
rate parameter, h , mg g - ’ min-0.5
200 200 200 200 200 200 200
0.93 0.87 0.70 0.62 0.54 0.45 0.32
50 100 200 400 500
0.36 0.58 0.64 0.83 0.87
using an initial dye concentration of 200 ppm, i.e., 10 mg of dye per 50 mL of solution, the amount of dye adsorbed per gram of silca, ( X I M ) , , is given by
(
$)t
and
= 200ppm
c,=
A 100 200 300 400 500 Time of contact
LL
c,
o
Figure 1. Fraction dye adsorbed against contact time for various particle size ranges of silica.
2f
= 50ppm
C, = 100 p p m
A
fF /--
407
=
(y )
x 10
0
2
4
6
8
1
0
~ i m e ” mlno5
Figure 4. Fraction dye adsorbed against time0.5for different particle size ranges of silica.
-
05
-10 - 1 2
-14
-16 -18 - 2 0 Log d c m s
Figure 5. Variation of log (rate parameter), k, against log reciprocal particle diameter.
From the linear portions of the plots the h values were determined and are listed in Table I. Although the k values do not have the normal dimensions for rates, their relative values for similar conditions should be significant as rate parameters. If the mechanism of uptake is one of adsorption on the external sites of a nonporous adsorbent, the rate of adsorption and hence the parameter, k , should vary reciprocally with the first power of the diameter of the silica particles (Weber and Morris 1964). This inverse
408
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
180
v p
= 500-355
v
710 - 5 0 0 p
= A
-
= 3 5 5 - 250
= 250 o
= 1000-050
v
0 03
--
15
LOP
0 02
2.5
20
X -
co
M
Figure 6. Variation of log (rate parameter), k, with log (initial dye concentration).
relationship holds also for porous adsorbents when the rate of transport to internal surface areas is controlled by an external resistance, i.e., film transport. Figure 5 indicates, that for Astrazone Blue adsorption on silica, the k values are found to vary reciprocally as some power, n, of the particle diameter. The variation observed is in accord with the equations for intraparticle diffusion given by Crank (1965) and the power constant n = 0.46. Theoretical equations for intraparticle diffusion indicate that the concentration dependence of a diffusion-adsorption process will vary depending on the characteristics of the adsorption isotherm and on the fraction of solute adsorbed at equilibrium. In the case of intraparticle diffusion only being the rate-determining step it was found that k varied with the square root of the initial concentrations used (Weber and Morris 1964). The results for silica are shown in Figure 6 and found to conform to the following equation
k = O.~~COO.~O
(3)
It is apparent that the mechanism of Astrazone Blue adsorption on silica is complex involving boundary layer diffusion and intraparticle diffusion in the rate-controlling step. (iii) Adsorption Isotherms. A series of experimental points for specific size ranges of silica particles are plotted from the adsorption to give the isotherm, Le., amount of dye adsorbed by a given weight of silica at equilibrium vs. the final concentration of the respective solution. The data are shown in Figure 7 and the plateau on each isotherm corresponds to monolayer coverage of the adsorbent surface by dye molecules. The adsorption curves were applied to Freundlich’s and Langmuir’s equations (Freundlich, 1906; Langmuir, 1916). The adsorption of Astrazone Blue on silica was found to conform to both equations and the Langmuir parameters, b and Qo, and the Freundlich parameters, K and n, are listed in Table 11. The Freundlich isotherm applies over the whole concentration range adopted in the experiment, whereas the Langmuir equation was only valid in the higher concentration range. In all cases the adsorption capacity per unit mass of adsorbent increases with a decrease in particle size. The final column in Table I1 shows the amount of dye adsorbed per square meter and the data indicates a mean specific surface coverage of 69 mg m-2 of silica surface. The influence of isotherm shape may be used to predict whether an adsorption system is “favorable” or not according to Weber and Chakravorti (1974) by using the Langmuir isotherm. All values of the constant b indicate a favorable adsorption process. (iv) Diffusion Coefficient. Theoretical treatments of intraparticle diffusion yield complex mathematical relationships which differ in form as functions of the geometry
0 01
0
500
loo0
Equilibrium conc
1500 ppm
Figure 7. Amount of dye adsorbed (8) per gram of silica against equilibrium dye concentration in solution. Table 11. Langmuir and Freundlich Constants for the Adsorption of Astrazone Blue on Silica ~
Freundlich constan ts .
Q,,
K,
particle size,pm
n,
L-
f;
150-180 180-250 250-355 355-500 500-710 710-850
2.90 3.33 4.81 4.50 4.17 6.80
2.5 2.9 2.5 2.7 2.1 2.0
f
Langmuir constants b, L mg-l
0.0038 0.0038 0.0063 0.0079 0.0085 0.0117
P; 34.5 30.3 16.1 13.5 11.8 6.3
dye adsorbed, m ,a!
67.6 75.0 60.0 67.5 81.0 67.0
Initial dye concentration C, = 200 mg L-’.
and nature of the adsorbent. The curves in Figure 3 indicate that the overall diffusivity must comprise a term for boundary layer diffusion and also for intraparticle diffusion. The following method involves an iterative procedure for comparing experimental and theoretical curves to determine a diffusion coefficient. An initial estimate of the diffusivity, D, was made from a solution available for the adsorption of dyes on fibres (Alexander and Hudson, 1950;Andrews and Medley, 1959) and values varying between 5 X cm2 and 5 X cm2 s-l were obtained depending on the particle size range. Using curve fitting techniques and a data plotter an overall diffusivity has been determined for the adsorption of Astrazone Blue on silica, namely
D
= 1.2 (*0.2) X lo-* cm2 s-l
(4) The mechanism of adsorption involves a study of the diffusional processes through the boundary layer surrounding the particle, adsorption onto the external surface of the particle followed by intraparticle diffusion into the bulk of the adsorbent particle. The mathematical theory of diffusion is based on the hypothesis that the rate of transfer of diffusing substance, through unit area of a section, is proportional to the concentration gradient measured normal, to the section, i.e., Fick’s first law F = -D-dC (5) dX where F is the rate of transfer per unit area of the section, C is the concentration of diffusing substance, X is the
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
409
space coordinate, and D is the diffusion coefficient. The fundamental differential equation of diffusion in an isentropic medium where there is a concentration gradient along the X axis is given by Fick’s second law
Other forms of the diffusion equation follow by transformation of coordinates, or by considering elements of volume of different shape, for example, cylinders or spheres. Many molecular adsorption processes involve diffusive mass transport and the rigorous interpretation of overall behavior in terms of “true” diffusivity and intrinsic equilibrium sorption properties is difficult. A meaningful diffusion coefficient cannot often be derived: the standard procedure of fitting the overall rate behavior to the classical solution of Fick’s equation results in the derivation of apparent diffusion coefficients that often vary with concentration. Fick’s equation should be modified in a manner depending on the functional relationship between the concentration of free and immobilized species. For the adsorption of basic dye on silica, the silica particles have been considered as spheres, and Fick’s second equation in terms of spherical polar coordinates r, 8, and 4 is given by = - -Dr2-
dt
r2
ar
+ __ -D sin 8 dr sin 4 a8 a8
+sin2 8 a@ (7)
The mathematical solution of the differential equations for unsteady diffusion has been performed for spheres, subject to particular sets of boundary conditions. In this model the following assumptions are made in the mathematical analysis: (i) The concentration of dyestuff is uniform a t Co throughout the solution and is zero in the adsorbent particle at the start of diffusion (t = 0). (ii) Diffusion is radial, there being no variation in concentration with angular position. (iii) The resistance to transfer in the medium surrounding the particle is significant in the early stages of diffusion. The diffusion equation can be solved by applying the various boundary conditions to the mass transfer equation. In the presence of a barrier layer, a boundary conditions must be imposed as a consequence of the continuity of flow across the inside surface of the barrier. Assuming Db is the diffusion coefficient in the boundary layer, Cb is the equilibrium concentration in the boundary layer, and S is the partition coefficient of the diffusing substance between the boundary layer and the bulk of the silica particle, then Cb
s=c,
(8)
The flow of dye across the boundary layer is
where y is a constant given by DbCb
Y=-
6CS
and Co is the initial concentration of dye at the surface of the boundary layer, C, is the actual concentration just within the silica particle, and 6 is the thickness of the boundary layer.
355 250 0 180 o 150 I
0
0.25
-5OOp
-35511 -250~ -18Op I
I
05
0.75
10
Figure 8. Fraction of equilibrium dye uptake against Crank parameter ( D ~ / U ~theoretical )~? curves, -; experimental results, - - -.
The flow of dye into the interior is -D(aC/aX), so that when t > 0, the boundary condition is
If the sphere is at a concentration C1 at time t , the required solution of Fick’s second equation takes the form (Crank, 1965; Carslaw and Jaeger, 1947) C - Co 2~~ e-(D8m2tlo2) sin P,r/a
--
C1 - Co
-
--
r
c
+ L(L
m = l (pm2
-
I)) sin P,
(12)
The roots for 0, and L have been evaluated by Newman (1931) as follows p, cot p, + L - 1 = 0 (13)
and the expression for the total amount of diffusing substance entering the silica sphere is given as 6L2e-(Bm2Dt/a2) Mt _ -1(15) Mm m = l p,2jpm2 + L ( L - 1))
-
c
Equation 15 may be solved by the use of Laplace transform and the results are in terms of series or error functions. A numerical solution of eq 15 has been plotted graphically by the solid lines depicted in Figure 8. The curves are plotted for the fraction dye adsorbed a t time t, namely (C, - C,)/(Co - C), as functions of for various L values. McGregor and Peters (1965) have obtained analogous models for dye adsorption on cylindrical yarn filaments and plane sheets of cellulose by applying similar boundary conditions. The authors show that eq 9 applies only for the condition that k,6 >> Db (16) From eq 14 the relationship between L and 6 is obtained for a sphere
-
-
Consequently, in the limit, 6 0 and L m, and the rate of adsorption is controlled purely by the rate of diffusion within the solid. In Figure 8 the particle size
410
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
ranges lie between 150 and 1000 pm and the experimental curves have L values >1.5. Boundary layer diffusion is particularly important for L > 2, but only very limited data (McGregor and Peters 1965) are available for Db, c b , C,, and 6 , which are necessary to calculate L. By substituting the available data into eq 17, i.e., 6 = 3.0 X cm, Db = 1X cm2 s-l, Cb/Cs = 400, and D = 1.2 X cm2 s-', calculated values 5 < L < 35 were obtained for the same particle size ranges. Since experimental conditions and the chemical nature of the dyestuffs differed widely, the experimental and calculated L values are significantly close to justify the use of this model for basic dye adsorption onto silica. The major discrepancies will occur in the values of Db and 6. The diffusion coefficient of the dye in the particle, Db, is a function of the chemical structure of the dye and the nature of the adsorbent, whereas boundary layer thickness depends mainly on the extent of agitation in the system. Figure 8 shows the plots of Co - C,/C, - C , against ( D ~ / U ~for ) Othe . ~ different size ranges of Sorbsil silica. The major lines indicate the theoretical curves and the dashed lines are the experimental plots; comparison of the two sets of data indicates excellent agreement. The application of this model involves four conditions: (i) the particles are essentially spherical, (ii) diffusion is radial and occurs from a solution of finite volume, (iii) boundary layer diffusion and intraparticle diffusion are involved, and (iv) the C , values measured after 24 h contact time have reached equilibrium. Conclusion Analysis of the contact time data gives an indication of the mechanism and rate processes involved in an adsorption system. After establishing the mechanism, the technique of curve fitting the experimental results to theoretical curves provides an accurate means of determining the diffusion coefficient for the adsorption of Astrazone Blue dye on Sorbsil silica. Nomenclature A = component A a = radial distance (cm), 0 < a < r b = Langmuir constant, L mg-' C = dye concentration, mg L-' C = average concentration, mg L-l D = diffusivity, cm2 s-' k = rate parameter, mg of dye g-' of adsorbent k , = rate constant for adsorption K = Freundlich constant, mg of dye g-' of adsorbent
L = root of eq 20 equals a c: /D M = mass of adsorbent, g Mt = mass of dye adsorbed at time t , mg m = an integer n = Freundlich constant, g L-' Qo = monolayer coverage, mg of dye g-' of adsorbent R = equilibrium parameter r = radius of sphere, cm S = partition coefficient t = time, min X = dye adsorbed, mg Subscripts A = component A b = boundary layer 0,l = points 0,l etc. s = surface property t = time m = equilibrium @reek Symbols /3 = constant in eq 20 y = constant and equals DbCb/GC, 6 = boundary layer thickness 0 and 4 = polar coordinates Literature Cited Alexander, P., Hudson, R. F., Text. Res. J . , 20, 481-491 (1950). Andrews, N., Medley, J. A., Text. Res. J . , 28, 398-403 (1959). Carslaw, H. S.,Jaeger, J. C., "Conduction of Heat in Solids", Oxford University Press, Oxford, 1947. Crank, J., "The M a t t y a t i c s of Diffusion", Clarendon Press, London, 1965. Dufort, J., Ruel, M., Peat Moss as an Adsorbing Agent for the Removal of Colouring Matter", pp 212-221, Proc. Symp. Sherbrooke University, 1972. Edeskuty, F. J., Amundson, N. R., Ind. Eng. Chem., 44, 1698-1703 (1952). Freundlich, H., 2.Phys. Chem., 57, 385-470 (1906). Giles, C. H., D'Silva, A. P., Trans. faraday Soc., 65, 1943-1951 (1969). Giles, C. H., Nakhwa, S . N., J . Appl. Chem., 12; 266-273 (1962). IC1 America Inc., Evaluation of Granular Carbon for Chemical Process Applications", D116, 1971. J . Am. Chem. Soc., 38, 2221-2295 (1916). Langmuir, I., McGregor, R., Peters, R. H., J . S . D . C . , 81, 393 (1965). Middleton, A. B., Am. Dyest. Rep., 26-31 (Aug 1971). Mutch, N., 0.J . Pharm. Pharmacal., 19, 490-519 (1946). Newman, A. P., Trans. A.I.Ch.E., 27, 203 (1931). Parsons, C. L. U . S . Bur. Mines Bull. 77, 5-38 (1913). Poots, V. J. P.,McKay, G., Healy, J. J., WaterRes., I O , 1061 (1976a). Poots, V. J. P., McKay, G., Healy, J. J., Water Res., 10, 1067 (1976b). Sing, K. S. W., Madeley, J. D., J . Appl. Chem., 3, 549-556 (1953). Thornton, H. A., Moore, J. R., Sewage Ind. Wastes, 23, 497-504 (1953). Weber, T. W., Chakravorti, R . K., AIChE J . , 20, 228-238 (1974). Weber, W. J., Morris, J. C., "Removal of Biologically-Resistant Pollutants from Waste Waters by Adsorption", Vol. 2, .pp . 231-266, Pergamon Press, New York, N.Y.. 1962. Weber, W. J.. Morris, J. C., J. Sanii. Eng. Div. Am. Soc.Civ. Engr., 80, 79-107 (1964).
Received for review June 10, 1977 Accepted June 1, 1978
