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Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 94-96
Physicochemical Aspects of the Filtration of Aqueous Suspensions of Fibers and Cement. 2. Influence of the Composition of the Suspension on Filtration Efficiency Jacques Schultz, Eugbne Paplrer, and Mlchel Nardln Centre de Recherches sur la Physico-Chime des Surfaces Solides, CNRS, 68200 Mulhouse, France, and Laboratolre de Recherches sur la Physico-Chimie des Interfaces de I'Ecole Nationale Supkieure de Chimie de Mulhouse, 68093 Mulhouse Cedex, France
I n a second part of the general study of the filtration of aqueous suspensions of fibers and cement, the filtration efficiency has been quantitatively related to the composition of the suspension and to the grid opening.
Introduction In the first part (Schultz et al., 1983) of this study of the filtration of aqueous suspensions of cement and fibers, the experimental conditions of filtration and the characteristics of the constituents of the suspension have been extensively described. A general relationship between efficiency and rate of filtration has been established. In this second part, the role on the filtration process of fiber content and total solid concentration, as well as the geometrical characteristics of the grid, will be investigated. The relevant parameter defining the geometry of the grid is the opening ( y ) , i.e., the ratio between the void and the total surface area of the grids. Influence of the Quantity of Fibers ( mor 7) The parameters defining the composition of the suspension are the weight (m)of fibers or the fraction of fibers in the total amount (M) of solid, 7 = m/M, and the concentration of solids in the volume (V) of suspension, C, = M / V. Figure 1 relates the filtration efficiency ( e ) to the amount of various fibers present in the suspension, the measurements being made under fixed experimental conditions ( M = 20 g; V = 100 mL; y = 64%). Experimental results can further be described by a linear relationship between l / e and l / m or 117. This relationship may be explained in the following way, knowing that mF =- 1 e = (1) mc + mF mF 1+mC where mF is the weight of filtrate and m, is the weight of cake. If the cement is not retained, neither by the grid nor by the fibers on the grid, then mF = md and m, = m where mc, is the weight of cement in the suspension. Therefore mF/mc = mcdm Let us suppose that in the general case, a similar form will hold mF - mct _ - awith a 5 1 mc m Thus the filtration efficiency may be written m e= m + amct or, since mc, = M - m m 7 e = (2) (1 - a)m + aM (1 - a)? + a 0196-4321/83/1222-0094$01.50/0
Table I. Values of Slope (F)and Intercept at the Origin I1- ( F / M ) l from ECI3 nature of fibers
r2
chrysotile cellulose glass fiber e glass fiber a ,
0.984 0.969 0.994 0,998
F (1-a)= (kg) X lo3 1 - ( F / M )
0.35 0.033 1.03 4.07
0.87 1.004 1.13 0.63
Table 11. Initial Filtration Coefficient (F)for Different Fibers
F (kg)x l o 3
nature of fibers glass fibers
a1
a,
a7 a8
4.07 5.42 3.45 2.65 1.19 3.63 2.97 1.80 2.40
i;:E i0.975 ;:E 0.65 0.345 3 0.20 0.066 0.014 1.16 0.071 0.169 0.159 0.53
carbon fibers rayon spun fibers polyvinyl alcohol fibers
which leads to a linear relationship between l l e and l l m or 117 e
m
(3)
with F = aM. Table I gives the experimental values of the slope (F) and the intercept at the origin [ l - ( F / M ) ] for the experiments presented in Figure 1,together with the correlation coefficient (r2). Equation 3 is verified only for 7 I 15% . For higher values of 7,deviations are observed due to the difficulty of obtaining a homogeneous suspension. 0 1983 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 1, 1983
95
m ( k g h lo3 3
2
1
0
t
a
a
"
;
"
'
'
1
v ( m3)x io4
'1
Figure 2. Filtration efficiency (e) vs. suspension volume (V) (for glass fibers a1 at M = 20 g and T = 10%). 100,
I
,
I
I
,
,
,
,
,
,
,
,
T(%)
Figure 1. Filtration efficiency (e) vs. fiber weight ( m ) or fiber content ( T ) .
Note that, according to eq 2, l / a or 1/F are the initial slopes of the curve e = f ( r )or e = f ( m )and are therefore important parameters related to the evolution of e for low fiber contents 0
The values of the initial filtration coefficient (F)for all the other fibers studied (glass, silica, carbon, cellulosic, and polymeric fibers) are given in Table 11. For all these fibers, the proposed filtration model defined by eq 2 is satisfactorily verified. Influence of the Concentration of Solids (C,) Figures 2 a 3 give for glass fibers a1 the variation of the filtration efficiency with respectively V ( r and M being constant) and M ( r and V being constant). These two variations can be represented on a single curve taking C, as the variable ( r being constant). The shape of the experimental curve, for the lower values of C,, may be represented by a hyperbolic form
1
3
2
4
5
6
M(kg) x 10' Figure 3. Filtration efficiency (e) vs. total weight (M) of the solids in the suspension (for glass fibers a1 at V = 100 mL and T = 10%). 100
e
(%I
e = - C, C, H
+
By combining eq 2 and 5 a=
0
rH
H=b(?) where b is a constant. Hence a = b/C, = b V / M , or F = bV. Therefore
(1 - %)r
+
m( 1 -
1000
CS(kg. 171.~1
(1 - T)C, Knowing that a is not a function of r , H takes the form
e=
500
%, +
(6)
bV
As seen in Figure 4, eq 6 describes in a satisfactory manner the experimental relationship between e and C, for values of C, I500 g L-l. An additional verification of
Figure 4. Filtration efficiency (e) vs. concentration of the solids (Cd in the suspension (for glass fibers al at T = 10%).
the validity of eq 6 is given in Figure 5 showing that e is constant when C, and T are kept constant. This observation indicates moreover that the amount of fibers per unit area of the grid is not a parameter affecting the filtration efficiency at least in the range studied, i.e., 1 5 r 5 15% and 10 5 C, I500 g L-l. Influence of the Grid Opening (y) This study was made with grids having various openings (12.5, 30, 64, and 82%) and using glass fibers al, a8 and bs. Figure 6 presents an example of the variation of e with 7 for different fiber contents (7). As pointed out previously, cement alone is not able to form a cake. This assumption has been verified with the three grids of y L
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 1, 1983
/
T=10%
T =5 % 0 5
0
v
lo'
2
15
mct(kg)JO2
Figure 5. Filtration efficiency (e) vs. suspension volume (V) (for glass fibers a1 at constant 7 and constant C, = 200 kg m-?. I$
1
0.5
0
1
( d x
Figure 7. Quantity of cement (m,l) retained on the grid of opening y = 12.5% vs. quantity of cement (ma)present in the suspension.
I
i
i
F(kg)x103
4t 0
50
,'(%)
WO
Figure 6. Filtration efficiency (e) vs. grid opening (y) Cfor glass fibers a1 at different fiber contents (T)>.
30%. However, this does not hold for the grid of y = 12.5% and therefore a correction was made in order to take into account the amount of cement retained by the grid. This correction is made as follows. As shown in Figure 7, the quantity of cement (mc;) retained on the grid of y = 12.5%, in the absence of fibers, varies linearly with the amount of cement present in the suspension (mCJ mc; = 6mct
To a first approximation, it can be considered that the actual weight of cake (n,") formed in the presence of fibers
0
12.5
30
64
82
v("4 Figure 8. Initial filtration coefficient (F)vs. grid opening (7).
must also depend on the initial volume (V) of the suspension, since F = bV = F l y = b o V ~ Introducing the variable y, the general eq 6 can be rewritten 7 m e = (7)
is equal to
mca= mcm- 6mct where mcmis the measured weight of the cake. In Figure 6, it appears that the filtration efficiency decreases rapidly when y increases up to 10%. In this range of openings the true phenomenon of filtration is obscured by the low permeability of the grid. For the higher values of y (y 2 80%), the efficiency again decreases since the majority of the fibers pass directly through the grid. In the intermediate range (30% C y C 80%), a quasi-plateau of e is observed. On a more quantitative basis, Figure 8 shows the variation of the initial coefficient of filtration F with y for the three types of glass fibers studied. For y S 64%, F is a linear function of y F = Fir Fl depends on the morphology of the fibers. For example, it increases with increasing fiber diameters. Besides, F
Conclusion In the second part of this general study of the filtration of aqueous suspensions of cement and fibers, the filtration efficiency has been quantitatively related to the composition of the suspension (fiber content, total solid concentration) and to the opening of the grids. Acknowledgment We acknowledge with thanks the support of this project by both Saint-Gobain Recherche and Everitube and the cooperation and advice of Drs. J. J. Massol, F. Naudin, and A. Sabouraud. Registry No. Cellulose, 9004-34-6. Literature Cited Schultz, J.; Papirer, E.; Nardin, M. Ind. Eng. Ch8m. Prod. Res. Dev. 1983. Part 1 in this issue. Received for review February 19, 1982 Accepted August 23, 1982
