L L’
= length of resin column, ft.
h’
= normal force, Ib., = resin pressure, Ib. flsq. ft. = liquid pressure, Ib. f/sq. ft.
PR PL
= generalized distance above reference line, ft.
EL= total
pressure differential betbveen two elevations in column, lb. ,/cu. ft.
dL
=
mean density of resin bed. Ib.
cu. ft.
= coefficient of friction = subscript denoting force
p f
literature Cited
(1) Drake, G. M., “Experimental Study of the Performance Characteristics of a Continuous Countercurrent Ion Exchange Column,” M. S. thesis, LJniversityof Tennessee, 1957. ( 2 ) Hiester, N. K . , Phillips, R. C., Cohen, R. K., Chem. Eng. Progr. Symp. Set.. 50, No. 14, 51-72 (1954).
(3) Higgins, I. R., Roberts, T. J., Ibzd., p. 87. (4) Jury, S. H., “Theory and Some Applications of the Hydraulic Ram as Applied to Countercurrent Ion Exchange,” U. S. At. Energy Comm. ORNL CF-56-6-74 (1956). (5) McCormack, R. H., Howard, J. F., Chem. Eng. Progr. 49, 401 (19 53). (6) McIlhenny, \V. F., McConnel, V. O., U. S. Patent 2,617,714 (1954). (7) Mihara, S., Terasaki, Y . , Japan Patent 2223 (1951). (8) Selke, W. A., Muendel, C. H., “Continuous Ion Exchange with a Cotton Belt,” U. S. At. Energy Comm., Doc. NYO-962 (1953). (9) Spencer, R. S..Gilmore, G. B., Wiley, R. M., J . Appl. Phys. 21. 527 11950). (IOj’Stantbn, L. S., “Continuous Separation by Ion Exchange,” M. S. thesis, University of Washington, 1950. (11) Toor. H. L., Eagleton, S. D., Ind. Eng. Chem. 48, 1825 (1956). RECEIVED for rr\iew November 23, 1962 ACCEPTED July 31, 1963
COEFFICIENT OF KINETIC FRICTION FOR DOWEX 50 ION EXCHANGE RESIN MOVING DOWN A G LASS CO LU M N.
Noncompacted Bed
, PEEB LES,
DA N I EL H E RS H EY
FR ED N
.
University of Cincinnati, Cincinnati, Ohio Cniversity of
Tennesser, Knour~ilie, Tenti.
For Dowex 50 ion exchange resin, coefficient of kinetic friction values were obtained from measurements of the drag force on a thin-walled smooth metal cylinder supported from a spring scale. The noncompacted b e d of resin moved downward, past the cylinder, and was subjected to a countercurrent water feed stream. The coefficient values ranged from 0.0026 a t fluidization to 0.0068.
has been derived and experiments have been ( 7 ) whereby it is possible to obtain values for the coefficient of kinetic friction for the Dowex-glass interface. The resin was in a noncompacted, dense bed condition and moved do\vn past an up\\-ard-floiving water stream. I n the investigation reported here: coefficient of kinetic friction values \vere obtained from measurements of the drag force o n a thin-walled smooth metal cylinder supported from a spring scale. The noncompacted bed of resin moved doivnward, past the cylinder, and \vas subjected to a countercurrent Lvater feed stream.
u
EQUATION
A-conducted
hydrostatic head could be maintained. Spring scale readings were taken with (1) no resin flow (static conditions) and (2) resin flow \vith a “balanced” column. A balanced column was attained when the U-tube manometer across the isolation zone indicated the same differential pressure as in the no-flou static condition. When balanced. there was no flow through Air
spring
Chamber
Scole
i t
L i q u i d Outlet
10
I+’’ Glass
Description of Experiment
I
Pipe,
The system consisted of a 4-inch glass column 4 feet high ivith a 1-foot section of column added on top to house the spring scale. T h e section housing the spring scale was kept dry bv being filled lvith air during operation. Suspended from the spring scale into the resin bed was a thin-walled smooth metal tube. Water was available for flow through the jet lift a t the bottom of the column, conveying resin from the bottom of the column to the top. This water and the liquid feed rising through the bed left through the liquid outlet. The liquid outlet \vas located above the column so that a constant
-1
S t a i n l e s s Steel Tube
The equipment shown schematically in Figure 1 was used in determining the variation of the coefficient of kinetic friction from the unpacked, normal dense bed condition to the ‘.loose” condition of the bed near fluidization.
3” 2;”
0.0. 1.0.
6” L e n g t h
~
L i q u i d Feed
&
Water Jet
Figure 1. friction
~
lift
U
Equipment for measuring coefficient of kinetic
VOL. 3
NO. 1
JANUARY 1 9 6 4
3
Spring
‘ i l t-
Liauid Outlet
.IFs
0.008
-
.-0 C 43
.x
Dowex-50
r
0
(840-1100
0.005
L
micron5)
c
.-
.o ”-
r
.=E
O L 432
OLL
I
o.ooel
I
0
I
Jet- lift
Liquid
7 d
Figure 2. Force acting on thin-walled smooth metal tube suspended in b e d of resin
the isolation zone and this balance could be maintained by adjusting the valve for inlet water to the jet lift. Thus the dynamic condition of the column was the same as the static condition except for the drag force of the resin past the tube and the pressure drop due to the liquid feed. Hence, with the resin circulating in a balanced column and water flowing u p through the resin, the change in scale reading (dynamic minus static) was a function only of the downward drag force of the resin and the upward force of the entering feed. Pressure drop data were also obtained. Calculating Coefficient of Kinetic Friction
Consider the resin circulating system as illustrated in Figure 2. With the thin-walled smooth metal tube suspended from the spring scale into the nonmoving resin bed, the spring scale will indicate a force, F,, which includes the weight of the tube, buoyancy effects, and the differential hydraulic pressures due to the finite thickness of the tube wall. The summation of all these forces is indicated in Figure 2 by a single force, TI’. If now the resin is circulated, the effect of the isolation zone (a zone of no liquid flow) is to enable the resin to “fall” through the isolation zone and be carried to the top of the column, where it again “falls” onto the resin bed. The liquid take-off a t the top enables the jet-lift liquid to leave the equipment without flowing through the resin bed and maintains a constant hydrostatic head above the column. Thus the initial static conditions are maintained during the resin flow condition and any increase in the spring scale reading when the resin is being circulated is equal to F’ - F,. ( F L is equal to the product of pressure drop across the tube and the annular area of the tube.) Therefore. F’ = AFscslere&ng f FL. Since the coefficient of friction is defined as p = F’,’A\T, it will be necessary to determine 11‘. iV is a function of the hydrostatic head, the height of the resin bed. and the surface area of the tube. An average value was calculated by measuring the height of the liquid and resin above the horizontal plane through the midpoint of the tube. Multiplying each height by the appropriate density value yielded the average pressures exerted by the liquid and the resin on the tube. If each average pressure is multiplied by the surface area, average normal forces exerted by the liquid and the resin are obtained. The addition of these two forces yields the average normal force, S.
4
100
l&EC P R O C E S S DESIGN A N D DEVELOPMENT
Figure 3.
I 200
I
300
F l o w Rate,
400
500
cc/min
Coefficient of kinetic friction vs. flow rate
Discussion of Results
Because of the fluidization of the bed a t about 380 ml. per minute, experimental runs were confined to liquid feed rates from 340 ml. per minute down to zero flo\c. For this flow range the corresponding values for the change in spring scale readings varied from 0.440 to 1.125 pounds. Figure 3 sho\rs the decrease in the coefficient of kinetic friction for a noncompacted dense bed as the flow rate approaches the fluidization velocity. The coefficient of kinetic friction ranged from 0.0068 with no liquid feed counterflow to 0.0026 for a liquid flow of 300 ml. per minute u p the column. Several interesting points \rere observed from the analysis of the values of the coefficient of friction. It \cas determined (7) that the minimum countercurrent flow which would keep the resin in its slug form was 900 ml. per minute. The resin slug at 900 ml. per minute was in its lowest density condition, and the coefficient of friction was 0.0100. This value could. therefore, be expected to approximate closely the value for the coefficient of friction for an unpressurized resin circulation system, described here. In fair agreement ivith this expectation, the coefficient of friction by the method ivith no liquid counterflow was 0.0068. Another point was the continuous decrease in the coefficient of friction as the countercurrent liquid feed rate increased. Thus it was apparent that the resin bed decreased in density as the feed was increased and a t 380 ml. per minute some fluidization of the bed occurred, corresponding to a coefficient of friction value of 0.0017.
Nomenclature
F’ = frictional drag force of resin past tube wall. 1b.J F L = force exerted by liquid feed on cylinder because of pressure drop of liquid flowing through resin, 1b.f
F, = force exerted by spring scale. 1b.f ;1‘ = IJ =
normal force acting on surface. 1b.f coefficient of friction
literature Cited (1) Hershey, Daniel, Peebles, F. N., IND. Esc. CHEW,PROCESS DESIGN DEVELOP. 3, 1 (1964).
RECEIVED for review November 23, 1962 ACCEPTEDJuly 31, 1963
