110
Ind. Eng. Chem. Fundam. 1981, 20, 110-111
effect of suction on the velocity profiles as given by Yuan and Finkelstein (1956). The velocity components in Lee's eq 11 are
u = uo
[ 1 - 7 - - ( -36 x
-4.(.,) A 83X2 Re R 1+-+18 5400 1
-&?- (166 - 7607 + 825$
-
+
u=uox2
10800
2x
[
7 - $2
-
6
1
3 0 0 ~ ~75q4 - 6q5)
10800 (- 417
(1)
+ 9q2 - 6q3 + q4) +
(1667 - 380 q2 + 2 7 5 -~ 75v4 ~ + 15v5-
(2) 00
where (3) In eq 3, v is the kinematic viscosity, uo is the maximum velocity at x = 0, and V , is the constant withdrawal velocity. The boundary conditions (B.C.) for the concentration field equation for a very thin central electrode and a leaky outer filter wall have been generalized to B.C.1: C(0,r) = C, (4)
B.C.2:
C(x,O) = finite
B.C.3: D ( g ) r=R
(5)
04
06
08
10
Figure 1. Computer outlet slurry concentrations in a tubular cross-flow electrofilter.
where &J is the applied potential between the radii R and ro. An analytical solution had been obtained by Liu (1980) using the method of separation of variables. Figure 1 shows the calculated exit slurry concentrations as a function of radial position for various dimensionless filter lengths, x , for one set of dimensionless parameters, where D EM*A4 (y = -* V,R ' P = RV, In W / r J
A more general solution for the annulus with deposition at the wire is in progress (Liu, 1980).
= [(l-mv, -
where K in eq 6 is a ratio of particle to fluid velocities leaving the porous filter. The filtration velocity, V,, in the absence of osmotic effects, can be related to the pressure drop across the thin porous tube (again neglecting curvature), AI', and to its thickness, 1, through Darcy's equation (7) where k is the permeability of the porous tubes. The electric field strength in Lee's eq 11 was evaluated using
E=
02
3
Literature Cited Gidaspow, D.; Wasan, D. T. "Separation of Particles from Coal Derived Liquids Based on Surface Charge Properties", Department of Energy Private Communication, Apr 4, 1979. Knudsen, J. G.; Katz, D. L. "Fluid Dynamics and Heat Transfer", McGraw-Hill: New York, 1958; pp 363-367. Lee, C.H.; Gidaspow, D.;Wasan, D. T. Ind. Eng. Chem. Fundam. 1980, 19, 166-175. Liu, Y. Ph.D. Thesis, Illinois Instiiute of Technology, 1980 (in progress). Wakeman, R. J . Ind. Eng. Chem. Fundam. 1980, preceding correspondence in this issue. Yuan, S. W.; Finkelstein, A. B. Trans. Am. SOC. Mech. Eng. 1956, 78, 719.
Department of Chemical Engineering Illinois Institute of Technology Chicago, Illinois 60616
Y. Liu D. Gidaspow* D. T.Wasan
Comments on "Cross-Flow Electrofilter for Nonaqueous Slurries"
Sir: Lee et al. (1980) are to be commended for their fresh approach to the problem of solid-liquid separation in the crude products of coal conversion processes. I should like to make two observations on this paper. Firstly, the phenomenon of dielectrophoresis is not mentioned, despite the fact that the electrofilter has the nonuniform (radial) electric field configuration commonly used in such studies. Dielectrophoresis and its application to solid-liquid separation in both aqueous and nonaqueous systems have been studied extensively over the past 30 years by Pohl (1978). The phenomenon is based on a 0196-4313/81/1020-0110$01.00/0
difference in polarizability between the particles and the fluid, and this difference is expressed theoretically in terms of the permittivities and conductivities of the particles and the fluid. Since permittivity and conductivity are bulk properties, dielectrophoresishas not generally been classed as an electrokinetic phenomenon, which involves surface processes. However, it was proposed by Lockhart (1980a), on the basis of dielectric studies of the surface and colloid characteristics of crude solvent-refined coal (without surfactant), that surface polarization of the particles would give rise to dielectrophoresis as well as electrophoresis. 0 1981 American Chemical Society
Ind. Eng. Chem. Fundam. 1981, 20, 1 1 1
voltage and decreasing frequency of the field, but were significantly reduced by insulating one electrode. The design and optimization of apparatus for electrical separation in coal liquefaction products may need to take account of all these factors.
This has been confirmed (Lockhart, 1980b) by microscopic observation, using direct and alternating electric fields applied to crude solvent-refined coal contained in cells having both parallel and coaxial electrode geometries. For the particular solvent-refined coal and experimental conditions used (Lockhart, 1980b),dielectrophoresis was much stronger than electrophoresis. Secondly, Lee et al. (1980) and Lee (1978) refer only to electrophoresis, which relates to the intrinsic surface charge on the particles. However, at the electric field strengths used by these authors charge injection from the electrodes might be expected, similar to the coronacharging step observed in electrostatic precipitation. Such an extrinsic charge injection and the accompanying attraction and repulsion effects at the electrodes have in fact been observed (Lockhart, 1980b) along with the intrinsic electrophoretic and dielectrophoretic phenomena. These extrinsic processes became more prominent with increasing
Literature Cited Lee, C. H. Ph.D. Thesis, Illinois Institute of Technology, 1978. Lee, C. H.; Gldaspow, D.; Wasan, D. T. Ind. E-. Chem. Fundam. 1980, 19, 166. Lockhart, N. C. J . Appl. Phys. 198Oa, 57, 2085. Lockhart, N. C. fuel 198Ob, 59, 389. Pohl, H. A. "Dielectrophoresis", Cambridge University Press: Cambridge, 1978.
CSIRO Institute of Earth Resources Physical Technology Unit Ryde, N.S.W. 2112 Australia
Sir: We agree with Lockhart that dielectrophoresis might be developed into a practical separation technique. However, in our application the electrophoretic separation depends upon the surface charge produced by the addition of the surfactant. As shown by Lee et al. (1979), the { potential and therefore the electrophoretic mobility measured with our Zeta meter is a strong function of the concentration of the surfactant added to the slurry. The original small charges present in the coal-derived slurries are overwhelmed by the surfactant. This gives us a means of controlling the separation independent of the original
Neville C. Lockhart
properties of the slurries that depend upon the type of coal used, the process conditions employed, possible oxidation of the liquids, etc.
Literature Cited Lee, C.; Gidaspow, D.; Wasan, D. T. Proceedings of the Technlcal Program. International Powder and Bulk Solids Handling and Processing, May 15-17, 1979, pp 529-534; Figure 1.
Department of Chemical Engineering Illinois Institute of Technology Chicago, Illinois 60616
CORRECTION The Viscosity and Thermal Conductivity of Simple Dense Gases, Y. Cohen and S. I. Sandler, I n d . E n g . Chem. F u n d a m . 1980,19,186.
Page 187. A factor of All2 is missing from both the ordinate and abscissa of Figure 3. These should be yX/A'12 and byplA1I2,respectively. Also, the denominator in eq 14 should be b e rather than p*.
0196-4313/81/1020-0111$01.00/0
111
0
1981 American Chemical Society
D. Gidaspow* D. T.Wasan
