Liquid Saturation Profile in Capillary Suction Time Filter Paper

808

Ind. Eng. Chem. Res. 2001, 40, 808-813

Liquid Saturation Profile in Capillary Suction Time Filter Paper W. W. Lin and D. J. Lee* Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, 10617, Republic of China

This work reviews pertinent literature in modeling by considering the water movement in filter paper to measure capillary suction time (CST). Both the diffusion-like and piston-like approaches are described. In addition, liquid saturation profiles in the filter paper for pure water and some slurries are experimentally constructed. Experimental results indicate that the unsaturated flow in filter paper is unexceptionable in all tests. However, the CST correlations derived from either piston-like or diffusion-like approaches resemble each other in form, which is attributed to the s profile near the wet front resembling a power-law-type behavior. Introduction Developed by Gale and Baskerville1 to rapidly determine the filterability of filter cake, a capillary suction apparatus (CSA) consists of a sludge cylinder that rests on a filter (the Whatman No. 17 chromatography paper), which functions as the slurry reservoir. The capillary suction of the filter paper sucks out the filtrate from the slurry while cake forms inside the cylinder. The filtrate moves outward from the center of the filter. Figure 1 illustrates the propagation of the wet regime of a CSA test with kaolin slurry (1% w/w). The time for the wet front to travel between two concentric circular rings was referred to as the capillary suction time (CST). Baskerville and Gale2 suggested that a long CST indicates a difficult-to-filter slurry. CSA has been extensively applied since the pioneering works of Gale and Baskerville.3-19 Machine-made filter paper is not isotropic. That is, the flow across the grains encounters a greater resistance than that along the grain. The shape of the wet front is an ellipse rather than a circle.20 Nguyen21 used the geometric mean of the two principal radii as the average radius of the wet front. To overcome the anisotropic problem, Leu22 proposed the rectangular capillary suction apparatus (RCSA), which makes use of only one direction of the filter paper. In addition, Unno et al.23 and Tiller et al.24 further discussed the RCSA, while Herwijn et al.25 proposed a modified CST apparatus with an isotropic capillary suction medium. Nuygen21 developed the first mathematical model for the CSA test. Later, Leu22 refined the Nuygen’s model (for CSA) and proposed the first model for RCSA. With extension of the results of the above works, later investigations discussed the filtrate flow in both the filter cake and the filter paper.23,24,26-38 According to Meeten and Smeulders,36 all modeling works before Lee and Hsu30 assumed a saturated filter paper in the CSA test. These models treat the liquid invasion as a displacement process, while the porosity, capillary suction pressure, and hydraulic permeability of the filter paper are assumed to be constant (generally referred to as the piston-like approach). Lee and Hsu30 first noted that the filter paper is largely unsaturated rather than saturated. Later, Meeten and Smeulders36 as well as * Corresponding author. Fax: 886-2-2362-3040. E-mail: [email protected].

Smiles38 experimentally verified this finding: the water saturation profile is close to unity under the slurry reservoir and drops to zero at the wet front. The water permeability as well as the capillary suction pressure also varies according to the water saturation profile. By approximating the saturation profile as a power-lawtype function, Lee et al.31-34,39 arrived at the CST correlation by assuming that a nonlinear diffusion equation (generally referred to as the diffusion-like approach) controls the fluid flow. Although the diffusion-like description is more realistic than the piston-like approach, as Meeten and Smeulders36 stated, the latter could still accurately describe the flow process in the CSA test. Lee and Lin40 and Smiles38 conferred on a lasting uncertainty regarding the underlying mechanisms involved in the CST test. This work briefly reviews various theories in previous literature involving the transport processes in filter paper. Liquid saturation profiles of the filter paper for pure water and some slurries are then described, along with the validity of the piston-like approach discussed as well. Flow Equation Figure 2 schematically depicts the CSA and RCSA tests under investigation. The height of the slurry is generally not large, and the gravity term is neglected. In an unsaturated porous medium with two immiscible fluid phases (air and water), the transport equation for the liquid saturation that neglects the gravity term is stated as follows:41

(

∂s 1 KKrl ) ∇ ∇Pp ∂t  µ

)

(1)

where s is the liquid saturation, P is the capillary suction pressure in the filter paper,  is the porosity, µ is the viscosity, and K and Krl are the permeability and relative permeability, respectively. An effective diffusivity D is defined as follows:

D)

FKKrl dPp/F µ ds

(2)

Then, eq 1 can be reduced to the following diffusion equation:

10.1021/ie000422h CCC: $20.00 © 2001 American Chemical Society Published on Web 01/05/2001

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 809

Figure 1. Time evolution of the wet regime in the CSA test. Kaolin slurry, 1% (w/w).

∂s ) ∇(D∇s) ∂t

(3)

where eq 3 is identical with eq 1 of Smiles38 if only onedimensional formulation is considered and s ) θ/θsat is placed, where θ and θsat are the unsaturated and saturated water volumes per unit horizontal projected area of the filter paper, respectively. Equation 3 can be solved if the permeability, relative permeability, and capillary suction pressure are given and are unique functions of water saturation (s). Piston-Like Approach Piston-like approach assumes a constant s ()ssat); hence, Krl ) 1. Equation 1 thereby reduces to the following equation for an isotropic saturated porous medium:

∇

(Kµ ∇P ) ) 0 p

(4)

Further assume that the filter paper used is an isotropic medium (constant K). Then, the one-dimensional version of eq 4 in a cylindrical coordinate (CSA test)21 or in a rectangular Cartesian coordinate (for RCSA test)22 is

dPp µ )- q dr K

(5a)

mass flow rate through the filter cake equals the growth rate of the wet regime. The two superficial velocities q1 and q are related by

Aq1 ) Apqp

(7)

where A is the filtration area and Ap is the crosssectional area of the wet filter paper. For the CSA test, Ap ) 2πRδ, while for RCSA, Ap ) Wδ, where δ is the paper thickness and W is the width of the paper. The cumulative pressure drop is comprised of the pressure drop across the filter cake and that of the filter paper or, equivalently,

Pc ) ∆Pcake + ∆Pp

(8)

Because qp ) dR/dt or dZ/dt in CSA or RCSA tests, eq 5a or 5b implies that ∆Pp is proportional to dR2/dt or dZ2/dt. Notably, the solid mass ωc is replaced with the filtrate volume in eq 6 (ωc ) Cv, where C is the slurry concentration and v is the specific filtrate volume). This implies the same dependence on R and Z as those for ∆Pp. Take Pc as a property of the filter paper and the group CJsRav as a constant. Then, the substitution of eq 5a together with eq 6 into eq 8 yields the following form for the CSA test:22

( ( )

t ) aC(R4 - R04) + bC R2 ln

or

)

R2 - R2 + R02 (9) R02

where

dPp µ )- q dz K

(5b)

where r and z are the radial and axial positions, respectively, and q is the superficial velocity of the filtrate in the filter paper. The pressure drop across the filter paper, ∆Pcake, can be obtained by integrating eq 5 with respect to the spatial coordinate with two boundary conditions set at the wet front and the edge of the slurry reservoir. Meanwhile, the cake formed in the reservoir whose pressure drop can be expressed as follows:22

∆Pcake ) µJsRavq1ωc

(6)

where Rav is the average specific resistance of the filter cake, q1 is the superficial velocity of the filtrate, Js is the correcting factor for the superficial velocity variation in the filter cake, and ωc is the total solid mass deposited per unit filtration area. Because the liquid does not accumulate in the filter paper (saturated medium), the

aC )

µπ2δ22 CJsRav 2A2Pc

(10a)

µ 4KPc

(10b)

bC )

Notably, the two extreme conditions of eq 9, i.e., no cake forms on the filter paper and the cake resistance is much greater than the filter paper, correspond to the model results of refs 35 and 36. Restated, Meeten et al. repeated the works by Leu at Js ) 1.0 (incompressible cake). Substitution of eq 5b instead of eq 5a into eq 8 leads to the case for the RCSA test:

t ) aR(Z2 - Z02) + bR(Z - Z0)2 where

(11)

810

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001

aR )

µW2δ22 CJsRav 2A2Pc

(12a)

µ 2KPc

(12b)

bR )

Unno et al.23 considered the gravity term and replaced the Pc term by Pc + Fgh in the above equations. (Note: Unno et al. erroneously mixed up the usage of symbols Z and Z - Z0 in their derivations.) In practice, the cake resistance is commonly found to be much greater than the paper resistance. Taking the time for the wet regime to travel from R1 to R2 as the CST, eq 9 reduces to the following equation:

CST ) a/C(R22 - R12)

(13a)

µπ2δ22 CJsRav(R22 + R12) 2 2A Pc

(13b)

where

a/C )

Equation 13a corresponds to eq 1 in Vesilind,28 with his filterability constant χ ) 4πδµC/Apa/C. The corresponding reduced form for RCSA is Figure 2. Schematics of the CSA and RCSA tests.

CST ) a/R(Z22 - Z12)

(14)

Upon derivation of the above equations, the liquid pressure over the filter paper under the slurry reservoir is assumed to be uniform. The liquid invasion length is considered from the edge of the reservoir. Most pistonlike approaches produced identical results with minor modifications. For example, Chuang27 refined Leu’s model for the CSA test by considering the nonuniformity of the flow field under the reservoir. For example, Tiller et al.24 considered the effects of flow fields of the filtrate under the reservoir to the CST. Huisman and Kesteren37 employed the consolidation theory to describe the cake formation in the CSA test. Because these works employed the same basic equations, their CST typically changes with the square of the size of the wet regime. Restated, the piston-like approach normally leads to an expression for CST in a form similar to eq 13a or eq 14 but with different definitions of a/C or a/R. Experimental CST results depend on R2 or Z2, thereby correlating with the piston-like approach.36 Although researchers may estimate the values of certain unknowns in their models, like P and K, by regression of the CST data, the regressed values reported in the literature differ markedly with each other. For example, Baskerville and Gale2 estimated P ) 10 000 Pa, Leu22 proposed P ) 14 853 Pa, Tiller et al.24 gave P ) 4900 Pa, and Meeten and Smeulders36 gave P ) 7470 Pa. Such a discrepancy might be attributed to the different model assumptions, while the capillary suction pressure is taken as a fitting parameter. Diffusion-Like Approach The diffusion-like approach uses eq 3 to interpret the CST data. Information regarding the functional form of diffusivity (D) to water saturation of the filter paper is required to complete the formulation. However, only our group attempts to deduce the CST correlation based on the diffusion-like approach.

As a preliminary trial, Lee and Hsu30 adopted a power-law-type D(s) as

D ) Dssn

(15)

and proposed the corresponding s(r) profile

s)

(

)

R(t) - r R(t) - R0

1/n

s0

for r > R0

(16a)

and

s ) s0

elsewhere

(16b)

where s0 in eq 16a,b denotes the saturation under the reservoir. A later investigation applied a similar form to the RCSA test.32 The n value, which was correlated with the CST data, was estimated as 3.6. With the assistance of eq 16a,b, Lee and Hsu30-32 arrived at a dependence similar to the piston-like approach: t ∝ R2 for the CSA test and t ∝ Z2 for the RCSA test. Restated, both the piston-like approach and the diffusion-like approach led to the same dependence between CST and the size of the wet regime. Meeten and Smeulders36 constructed the liquid saturation profile in the CSA test and, although the s(r) shape found markedly differs from that suggested by eq 16, also found that the filter paper is far from saturated. However, Meeten still employed a piston-like approach to interpret the CST data. In a pioneering work, Smiles38 provided the diffusivity (D) and the capillary suction (-Ψ ) P) data of Whatman No. 17 filter paper. Figure 3 redraws Smiles’ data with the saturation (s). Here θsat is taken as δ ) (0.131 cm)(0.72) ) 0.94 cm. Notably, D increases while (-Ψ) decreases with liquid saturation. At s > 0.8, the capillary suction pressure is less than 3 kPa. The corresponding diffusivity approaches a plateau value of approximately (1.4-3.7) × 10-5 m2/s. On the other hand,

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 811

Figure 3. Diffusivity (D) and capillary suction (P) versus saturation (s) plot. Whatman No. 17 filter paper. Data extracted from Smiles.38

at a lower s, the capillary suction pressure markedly increases, while the corresponding diffusivity significantly declines. At s ) 0.5, for example, D ) 1.1 × 10-6 m2/s and P ) 10 kPa. According to Smiles’ results, the P value at the s ) 0 limit should markedly exceed 10 kPa. Consequently, the piston-like approach generally underestimates the P values. Lee and Hsu30 reported a value of 62 200 Pa at s ) 0. However, no direct comparisons can be made with Smiles’ data. Although the diffusion-like approach adequately describes the flow field in the filter paper, even with the diffusivity data provided by Smiles,38 difficulties are encountered in deriving a simple correlation for CST as in the piston-like approach. Experimental Section In this section, the liquid saturation profiles of some slurries were constructed on a RCSA. CaCO3, kaolin, UK ball clay, and a waste-activated sludge were the testing materials. The particle size distribution for powders was determined by Sedigraph 5100C (Micromeritics, Norcross, GA) with an addition of 0.5% (w/w) dispersant (Darvan C, R. T. Vanderbuilt Co., Norwalk, CT). The particle size distributions were monodispersed, and the mean particle diameter for CaCO3, kaolin, and clay are approximately 21, 4.6, and 2.3 µm, respectively. The true solid density was measured by Accupyc pycnometer 1330 (Micromeritics, Norcross, GA). Results obtained from CaCO3, kaolin, and clay are 2746, 2727, and 2584 kg/m3, respectively. A waste-activated sludge sample was taken from the wastewater treatment plant in Neili Bread Plant, Presidental Enterprise Co. (Taoyuan, Taiwan), and was tested within 2 h after sampling. The chemical oxygen demand (COD), suspended solids (SS), and turbidity data were for the supernatant drawn from the sludge, determined using Taiwan Environmental Protection Administration standard methods. The experimental results read as follows: 5.6 mg/L (COD), 7.1 mg/L (SS), and 1.39 NTU (turbidity). The weight percentage of the sludge sample was 0.7% (w/w). True solid density data for sludges were measured as 1450 kg/m3. The mean particle size is 70 µm.

Figure 4. Liquid saturation profiles. RCSA.

Herein, RSCA tests were conducted to establish the saturation profiles. Details regarding the apparatus, data acquisition system, and experimental procedures can be found elsewhere.32 A rectangular cell with an inner thickness of 1.0 cm was used. The width of the filter paper and also that of the cell were fixed at 6.9 cm. Whatman No. 17 filter papers were used as the filter medium. A JVC video camera with a timer was used to record the wet front dynamic data. The measurement errors for time and position were less than 0.01 s and 0.5 mm, respectively. Slurry tests were conducted with fluid flowing along and across the grain. However, only the former is reported herein. The sampling errors were reduced by using liquid nitrogen to freeze the liquid saturation profile instantly during the test. The frozen filter paper was cut into pieces along the axial position at an interval of 3 mm. The water contents in the strips were measured by weighing and drying at 103 °C. Notably, estimating the liquid saturation under the reservoir requires removal of the cake from the paper surface. Doing so tears off paper along with the cake and induces substantial error in the saturation calculations. Finally, a mass balance was conducted to enhance the reliability of the measurement. Liquid Saturation Profiles Figure 4 displays typical liquid saturation profiles for the materials tested herein. The data from Smiles38 were also depicted for comparison. In all tests with and without cake formation, the filter paper under the wet regime is largely unsaturated rather than saturated. This observation closely corresponds to the literature.36,38 According to Smiles,38 the unsaturated flow in the filter paper is unexceptionable in all CST tests. The filter paper in tests with water, CaCO3 slurry, or activated sludge contains a liquid saturation profile that resembles that proposed by Lee and Hsu30 (with a somewhat different best-fitted n value, )2.5-2.8, however). In the kaolin sludge tests, a (small) reduction in s close to the reservoir as reported by Meeten and Smeulders was also observed. This drop becomes more obvious for clay slurries at the same solid content. Adding clay powers into the CaCO3 slurry causes a slight reduction in liquid saturation (data not shown).

812

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001

time interval, U can be regarded as a constant and the transformation of the coordinate from z-Ut onto the z-t plane leads to

∂s ∂s ∂ ) as1/v ∂t ∂z ∂z

(

)

(18)

Equation 18 is a special case of eq 3 with a ) Ds and ν ) 1/n in eq 15. Consequently, because most of the pressure drop occurs near the wet front, while its s profile resembles a power-law-type function, the CST correlation provided in refs 30-32 remains valid. Namely, the CST changes with the square of the size of the wet regime. The piston-like approach, in which Darcy’s law with constant permeability is adopted, also yields the same form of the solution (as discussed in preceding sections). This coincidence makes the pistonlike approach a workable (although fundamentally wrong) model in interpreting the CST data. Figure 5. P versus z profiles. Pure water and clay slurry.

Conclusions Nevertheless, the s profile near the wet front still exhibits a power-law-type feature. Meeten and Smeluders36 observed s0 (saturation under the reservoir) of 0.92 ( 0.06. However, according to mass balance calculation, Chuang27 suggested that the s0 profile is far from uniform. Smiles38 contended that the filter paper under the reservoir should be saturated owing to the hysteresis in water invasion; in addition, the air cannot find a way to enter the filter paper. However, the capillary suction pressure at the interface between the kaolin cake and the filter paper was estimated as approximately 10 kPa. The corresponding s in Figure 3 is 0.5. A mismatch occurs in the fluid fields at the edge of the reservoir, thereby yielding a reduction in s noted in Figure 4. Furthermore, according to Figure 4, the liquid saturation under the reservoir (s0 in eq 16a,b) is close to unity in the water test but becomes less than unity in the slurry tests. Lee and Lin40 considered the potential role of fine invasion. The pore size of Whatman No. 17 filter paper is approximately 8 µm.36 As mentioned above, the particle size of slurries tested herein is as follows: clay < kaolin < pore size , CaCO3 < activated sludge. A drop in s near the reservoir strongly correlates with the particle size. Although Smiles38 criticized the particle invasion hypothesis, the possible role of paper blinding cannot be excluded in the present stage. Figure 5 presents some illustrative examples of the P profiles for water and clay slurry tests, as well as the data extracted from Smiles.38 Notably, for the water test and clay test, most of the pressure drop occurs near the wet front. This observation is attributed to the rather stiff decrease in the diffusivity as s < 0.8. Actually, Smiles38 could not provide the D values at s < 0.2. On the other hand, the tests with bentonite provided a substantially large fraction of pressure drop across the cake. Regardless of the s reduction near the reservoir, the s profile resembles a power-law-type function near the wet front. Equivalently, s ≈ |Z(t) - z|v, which is the solution of

-U

∂s d 1/v ds s )a ∂z dz dz

(

)

(17)

where U is the moving front velocity. During a short

This work reviewed pertinent literature in modeling the water movement in filter paper. Starting from the transport equation for an unsaturated porous medium with two immiscible fluid phases (i.e., air and water), the diffusion-like and piston-like approaches are deduced. Leu22 provided the first comprehensive solution that forms the basis of a piston-like approach. Liquid saturation profiles in the filter paper for pure water and some slurries are then experimentally elucidated. Experimental results indicate that the unsaturated flow in the filter paper is unexceptionable in all CST tests. Mismatch in liquid saturation at the edge of the reservoir or paper blinding is used to interpret the saturation drop close to the reservoir for clay slurry tests. Most of the pressure drop in the filter paper occurs at the wet front, while the s profile resembles a powerlaw-type function. Both piston-like and diffusion-like approaches yield the same dependence: CST changes with the square of the size of the wet regime. Acknowledgment The National Science Council, Republic of China, supports this work. Literature Cited (1) Gale, R. S.; Baskerville, R. C. Capillary Suction Method for Determination of the Filteration Properties of a Solid-Liquid Suspension. Chem. Ind. (London) 1967, 9, 355. (2) Baskerville, R. C.; Gale, R. S. A Simple Automatic instrument for Determining the Filterability of the Sewage Sludge. Water Pollut. Control 1968, 67, 233. (3) Gale, R. S. Some Aspects of the Mechanical Dewatering of Sewage Sludges. Sep. Filtr. 1968, 5, 133. (4) Gale, R. S.; Baskerville, R. C. Polyelectrolytes in the Filtration of Sewage Sludges. Sep. Filtr. 1970, 7, 37. (5) Karr, P. R.; Keinath, T. M. Influence of Particle Size on Sludge Dewaterability. Res. J. Water Pollut. Control Fed. 1978, 49, 1911. (6) Karr, P. R.; Keinath, T. M. Limitations of the Specific Resistance and CST Tests for Sludge Dewaterability. Sep. Filtr. 1978, 15, 543. (7) Kasakura, T.; Nomura, T.; Imaizumi, Y.; Itoh, H. CST (Capillary Suction Time) as an Index for Sludge Filterability. Gesuido Kyokaishi 1978, 15, 41. (8) Kavanagh, B. V. The Dewatering of Activated Sludge: Measurement of Specific Resistance to Filtration and Capillary Suction Time. Water Pollut. Control 1980, 79, 388.

Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 813 (9) Konechnik, T. J.; Hause, W.; Hem, S. L.; Jhawar, R. J.; Luber, J. R.; Pendharkar, C. M.; Drug, J. L. The Use of Capillary Suction Time to Characterize the Surface-Area of Aluminum Hydroxide Suspensions. Dev. Ind. Pharm. 1987, 13, 517. (10) Wilcox, R. D.; Fisk, J. V., Jr.; Corbett, G. E. Filtration Method Characterized Dispersive Properties of Shales. SPE Drilling Eng. 1987, 2, 149. (11) Dohanyos, M.; Grau, P.; Sedlacek, M. Interpretation of Dewaterability Measurements by Capillary Suction Time (CST). Water Sci. Technol. 1988, 20, 265. (12) Stephenson, R. J. The Use of a Simple Filtration Apparatus in Showing That High-Speed Blunging Affects Filter Pressing. Br. Ceramic Trans. J. 1988, 87, 149. (13) Vesilind, P. A.; Davis, H. A. Using the Capillary Suction Time Device for Characterizing Sludge Dewaterability. Water Sci. Technol. 1988, 20, 203. (14) Agerkvist, I.; Enfors, S. O. Characterization of EscherichiaColi Cell Disintegrates from a Bead Mill and High-Pressure Homogenizers. Biotechnol. Bioeng. 1990, 36, 1083. (15) King, R. O.; Forster, C. F. Effects of Sonication on Activated Sludge. Enzyme Microb. Technol. 1990, 12, 109. (16) Hayashi, N.; Iwata, M.; Kato, I.; Takemura, K.; Murase, T.; Shirato, M. Effect of Residual Polymer Flocculant on the CST Test for Determining the Optimum Dosage. Int. Chem. Eng. 1990, 30, 691. (17) Chen, G. W.; Lin, W. W.; Lee, D. J. Use of Capillary Suction Time for Estimating Sluge Dewaterability. Water Sci. Technol. 1996, 34, 443. (18) Chu, C. P.; Feng, W. H.; Tsai, Y. H.; Lee, D. J. Unidirectional Freezing of Waste Activated Sludge: The Presence of Sodium Chloride. Environ. Sci. Technol. 1997, 31, 1512. (19) Jean, D. S.; Lee, D. J.; Wu, J. C. S. Separating Oil from Oily Sludge by Freezing and Thawing. Water Res. 1999, 33, 1756. (20) Lee, D. J.; Chen, G. W.; Hsu, Y. H. On Some Aspects of Capillary Suction Apparatus Tests. J. Chin. Inst. Chem. Eng. 1994, 25, 35. (21) Nguyen, C. T. A Model for the Capillary Suction Apparatus. M.S. Thesis, University of Houston, Houston, TX, 1980. (22) Leu, W. F. Cake Filtration. Ph.D. Dissertation, University of Houston, Houston, TX, 1981. (23) Unno, H.; Muraiso, H.; Akehata, T. Theoretical and Experimental Study of Factors affecting Capillary Suction Time (CST). Water Res. 1983, 17, 149. (24) Tiller, F. M.; Shen, Y. L.; Adin, A. Capillary Suction Theory for Rectangular Cells. Res. J. Water Pollut. Control Fed. 1990, 62, 130. (25) Herwijn, A. J. M.; La Heij, E. J.; IJzermans, J.; Coumans, W. J.; Kerkhof, P. J. A. M. Ind. Eng. Chem. Res. 1995, 34, 1310.

(26) Ju, S. C. A Study on the Batch Gravitational Filtration. M.S. Thesis, National Taiwan University, Taipei, Taiwan, 1982. (27) Chuang, C. J. M.S. Thesis, National Taiwan University, Taipei, Taiwan, 1983. (28) Vesilind, P. A. Capillary Suction Time as a Fundamental Measure of Sludge Dewaterability. Res. J. Water Pollut. Control Fed. 1988, 60, 215. (29) Lu, W. M.; Ju, S. C.; Chang, U. J. Using CST to Measure Particle Characteristic Diameter and the Specific Resistance. Proceedings of the Symposium on Transport Phenomena and Applications, Taipei, Taiwan, 1989. (30) Lee, D. J.; Hsu, Y. H. Fluid Flow in Capillary Suction Apparatus. Ind. Eng. Chem. Res. 1992, 31, 2379. (31) Lee, D. J.; Hsu, Y. H. Cake Formation in Capillary Suction Apparatus. Ind. Eng. Chem. Res. 1993, 32, 1180. (32) Lee, D. J.; Hsu, Y. H. A Study on Rectangular Capillary Suction Apparatus. Ind. Eng. Chem. Res. 1994, 33, 1593-1599. (33) Lee, D. J. A Dynamic Model of Capillary Suction Appratus. J. Chem. Eng. Jpn. 1994, 27, 216. (34) Lee, D. J. On The Slow Manifold Characteristics of Capillary Suction Apparatus Dynamics. Chem. Eng. Commun. 1995, 136, 13. (35) Meeten, G. H.; Lebreton, C. A Filtration Model of the Capillary Suction Time Method. J. Pet. Eng. 1993, 9, 155. (36) Meeten, G. H.; Smeulders, J. B. A. F. Interpetation of Filterability Measured by the Capillary Suction Time Method. Chem. Eng. Sci. 1995, 50, 1273. (37) Huisman, M.; van Kesteren, W. G. M. Consolidation Theory Applied to the Capillary Suction Time (CST) Apparatus. Water Sci. Technol. 1998, 37, 117. (38) Smiles, D. E. Water Flow in Filter Paper and Capillary Suction Time. Chem. Eng. Sci. 1998, 53, 2211. (39) Lee, D. J.; Hsu, Y. H. Use of Capillary Suction Apparatus for Estimating the Average Specific Resistance of Filtraction Cake. J. Chem. Technol. Biotechnol. 1994, 59, 45. (40) Lee, D. J.; Lin, W. W. Interpretation of Filterability Measured by the Capillary Suction Time Method. Chem. Eng. Sci. 1996, 51, 1353. (41) Dracos, Th. In Modelling and Applications of Transport Phenomena in Porous Media; Bear, J., Buchlin, J. M., Eds.; Kluwer Academic Publishers: Boston, MA, 1991; p 203.

Received for review April 18, 2000 Revised manuscript received September 26, 2000 Accepted October 4, 2000 IE000422H