I N D U S T R I A L A N D ENGINEERING CHEMISTRY
144
surface attack, and it is therefore durable under long exposures to severe atmospheric conditions, as, for instance, around chemical plants. It is probable that glass insulators will not be as attractive to birds and spiders for nesting sites since they will not have the dark shadows that exist in a string of porcelain insulators.
Vol. 15, No. 2
The chief advantages of the Pyrex insulator are the facts that it does not absorb heat as does porcelain; has no cement in its construction to gradually absorb water and expand, ultimately fracturing the insulator; and has a mechanical strength that will average twice as high as any porcelain insulator yet on the market.
Tools of t h e Chemical Engineer.
I--Agitators’
By D.R.Killeffer 50
UNDAMENTALLY,
EAST4
1 s STRBET, ~ Nsw YORK, N. Y ,
stream of liquid caused by Agitation, as the term is applied to chemical engineering practice, agitation is accomthe rotating paddle. The may be defined as the operation causing mutual movement of particles plished by applying centrifugal component of of matter for the purpose of bringing about intimate contact between force toamore or less fluid the applied force builds u p them. Zn general practice the term is applied to the mixing of mass and then opposing the rapidly as the speed of rotadiyerent liquids, diyerent solids, and liquids and solids, although resulting movement in such tion increases, and is orin a strict sense its application to mixtures involving a gas phase a way as to alter its direcdinarily only opposed by is equally logical. The purpose of the present article is to rliscuss tion or otherwise emphasize the containing walls. The some of the fundamental principles of agitation and the means its selective action on varimovement in the mass available for putting them to work in the chemical plant. Experious parts of the mass. caused by this force is utilmental eoidence of the e$ectiaeness of any particular form of agitator Movement must be brought ized more or less incidenis sadly lacking, and nothing better than the old “cut and try” method about in parts of the mass tally in the ordinary paddle is available to the prospectioe user of such apparatus. There is no in such a way as to force mixer but becomes the prinmethod at present in use by which the effectiveness of any particular changes in the relative posicipal force in turbine mixers type of machine may be compared with any other, either as to speed tions of its various partiwhich will be considered of mixing or power consumed to dccomplish it. The result is that cles. The means by which later. Motion from the cenchemical engineers generally are inclined to instal tools which will this result is accomplished ter toward the walls of the give greater mixing than is actually necessary with consequent waste in practice may be roughcontaining vessel is changed of power. It is to be hoped that the generalizations put forth here ly classified into six groups: in directionat that obstrucmay lead to a closer study of the subject by those best equipped to tion into up or down motion (1) simple paddles and undertde it. modifications, (2) turbines following the wall, and is laraelv influenced by the and modifications, (3) propellers and modifications, (4)processes involving movement strong rotational movement which is-especially rapid at the of the containing vessel, (5) combinations of two or more periphery of the vessel. Few machines are now built which of the above, ( 6 ) miscellaneous unclassified types. are of the simple paddle type, as most builders incline the paddles in such a way as to add a force component in the PADDLES The simple paddle in the hands of a workman is seldom direction of the paddle’s axis. Combinations of paddles are frequently used. Two paddles found profitable in modern operations, but frequently its immediate successor, single or multiple vanes mounted on a mounted to revolve in the same direction at the focuses of rotating shaft, is found quite efficient where movement need an elliptical vessel, three paddles in a clover-leaf vessel, etc., not be violent, as in those cases where liquids of very nearly generate confficting currents in the liquid and bring about The mounting of the same specific gravity are to be mixed and where mixing is very efficient mixing in many processes. two sets of paddles on the same axis to revolve in opposite used as a means of aiding osmotic forces. Dissolvers and directions has been found to consume a disproportionate leachers of this class with slow-motion paddles are found to be efficient, as in these tools the problem is really the mixing amount of power. The use of single or multiple sets of of the strong solutio? in direct contact with the solute with the paddles mounted off-center in cylindrical tanks gives economical mixing in many cases where a centrally mounted paddle more dilute solvent. Paddle agitators involve the application of force with two would result in a simple rotation of the mass without r e d directional components, one in the direction of rotation and a mixing. Inclining the axis of a cylindrical vessel with a second centrifugally and a t right angles to the fist. The simple paddle revolving in its center produces a marked inrotating force is comparatively greatest and the centrifugal crease in mixing by utilizing gravitational force. TURBINES force least when the movement of the paddle is slow and tends The turbine type agitator is really a special case of the to bring the mass as a whole into rotation at a speed approximating that of the paddle. Actual mixing in this event is paddle type, but since the principal force used is centrifugal comparatively slight. The inertia of the mass, as well as the rather than rotational, it must be considered separately. resistance to rotation offered by the walls of the containing In this type of agitator the rotating unit is so designed as t o vessel, tends to start cross currents of various kinds and thus minimize the rotational component of force and increase the promotes some mixing. Increases in the resistance to this centrifugal Component to a maximum. Its operation is in all rotational motion are made by introducing stationary paddles respects similar to that of a centrifugal pump, with the exor simple vanes projecting from the sides of the containing ception that the motion of the liquid is permitted in every vessel in various ways which break up the otherwise solid radial direction instead of being forced in a single direction by a casing or pipe. The radial currents are directed toward 1 Received October 26, 1922.
F
145
INDUSTRIAL A N D ENGINEERING CHEMISTRY
February, 1923
(b)
(Q)
{ a ) PROPELLER Tws WITH DRAFTTUBE( P A T E N T I 3D) WITH PROPELLER I N ( b ) NITRATOR OFF-CENTER PXOPELLER
INDEPENDENT
TUBB
(6)
SLOW-SPEED PROPELLER. VIRTUALLYA COMBINATION OF
MULTlPLE
TYPES I M P L E
PROPELLER A N D PADDLE
PADDLE
COMBINATION PROPELLER A N D PADDLE~SCRAPER
MODIFICATION
O F SIMPLE PADDLE PRINCIPLE C O W BINED WITH LIQUIDSTREAM
SIMPLEPADDLE SCRAPER COMBINATION PROPELLER A N D SCREW TYPB
T W O ~ ~ P R O P E L L E R SROTATING I N OPPOSITE TIONS ON THE SAME SHAFT
DIREC-
COMBINATION PROPELLBR
AND
TYPEMIXER
TURBINE
COMBINATION PADDLE A N D PROPELLER OB
STONEWARE
146
INDUSTRIAL A N D ENGINEERING CHEMISTRY
v PROPELLER IN SQUARE D R A P T TUBE
SIMPLE PADDLE I N Z V E S S E L WITH
VANES.
EFFECT OF
HELICAL
PADDLE AND P R O P ~ L L E R
Vol. 15, No. 2
MULTIPLEPROPELLERS S E T OFF-CENTEK IN
CYLINDRICAL VESSEL
peller, out along the bottom to the sides of the tank, up the sides and thence to the center a t the surface of the liquid. The impeller itself is provided with a partial casing so arranged that the supply of liquid to the vanes is taken in near the center and forced directly out toward the periphery through the guiding effect of vanes in the partial casing. In some cases, especially where the liquids to be mixed are of nearly the same specific gravity and where the volume to be mixed is large, it is advantageous to elevate the impeller unit from the bottom t o the center of the tank, as here two whorls are started, one above and one below the impeller.
PROPELLERS Ship-propeller agitators introduce a third force component in a vertical direction to SIMPLE PADDLB IN INCLINED V~SSEL those already considered, and it is thl'ough the emphasis of this component to the detriment of others that such agitators are made efficient. A simple propeller set in the center of the mass of liquid imparts motion to it in STIRRERS FOR MACHINES WITH each of three directions, horizontally, rotaVERTICALSHARTS tionally, and vertically with respect to the STMPLF: TURBINE: MIXER propeller. At slow speed these effects are negligible, but they increase rapidly with the velocitv of rotation. until a Doint is reached and up along the walls of the containing vessel by placing the a t which the resistanie t o motidn, and cence the power turbine itself close to the bottom. I n general, the speed of the consumed, becomes too great to permit efficient operation. rotating member is high and sufficient force can be com- The efficient speed of the propeller is ordinarily intermemunicated to the liquids t o bring about efficient mixing of diate between those of the turbine and the simple liquids of widely differing specific gravities. Its use is prac- paddle. tically limited to liquids of low viscosity and to those which The first step in limiting the effects of the rotational and do not contain solids except in very finely divided form. Its centrifugal components was to reduce the first by altering the efficiency depends upon the mobility of the liquid and upon shape of the containing vessel by vanes more or less vertically giving it a high velocity. placed on its sides, or by otherwise altering it to increase the Ordinarily, turbine mixers are most efficient when placed resistance to rotation. From this it was an easy step to place in the center of the bottom of cylindrical tanks in such a way these vanes in a vertical open tube closer to the propeller as to permit free movement of the radial streams to the walls than the walls of the vessel, in such a way as to limit both the of the vessel where they are turned in a vertical direction. rotational and centrifugal forces to action on a small part of The flow of liquid in this case is down in the center to the im- the mass while permitting the vertical component to act
February, 1923
I N D UXTRIAL A N D ENGINEERING CHEMISTRY
freely on the whole.2 These draft tubes, as they are called, force high-velocity streams of liquid in a vertical direction, and it has been generally found that this method gives the greatest mixing of two liquids of markedly different specific gravities, such as acids and hydrocarbons. Since such reactions as nitration are strongly exothermic, the mass of liquid
147
Other modifications of the application of the propeller principle involve setting one or more off-center in much the same way as described for paddle stirrers, inclination of the containing vessel, multiple blades, propeller mounted on the same shaft to rotate in the same direction but to produce vertical components in opposite directions, continuous screws set in less fluid masses, and so on through every conceivable variation as varied in type and design as the engineers who have studied the question. The universal appeal of the propeller type agitator to the imaginations of designers is well borne out by even the most cursory survey of the field.
MOVING VESSELAGITATORS
S I M P L E PROPELLER
must be moved rapidly past large cooling surfaces. One type of agitator has been developed especially to accomplish this end. Here the propeller is placed in a tube outside the main container and a great mass of cooling coils is located in the main vessel. The inlet and outlet of this tube are so arranged that the stream of liquid through it causes a more or Iess pronounced swirl in the main volume around and through the mass of cooling coils. The effect of the marked difference in specific gravity of the liquids to be mixed is largely offset by introducing one of them, usually the hydrocarbon, a t a point in the draft tube just before the stream comes to its point of greatest agitation a t the propeller. Still other makers of agitators find a propeller provided with a narrow ring around its circumference highly efficient in producing a maximum vertical component, with little energy wasted in the other two directions. .%nother type has two propellers inounted on the same shaft in well a way :is to revolve in opposite directions, yet producing parallel veiticsl components. Here the rotational component is minimized by the action of the two oppo:ed propellers, and a pronounced vertical flow is achieved, while ROTATING BARRELTYPEMIXER the nent is neglected. The neglect of the latter feature is generally considered of little consequence, but it is conceivable that it might be more efficiently used than in present machines of this type. 2 The use of a cylindrical draft tube with vanes inside it has been patented. Other forms, such as a square tube, while possibly less efficient, are available without patent interference.
The types of agitating devices so far considered lend themselves most readily to fluid masses but are decidedly less efficient in handling viscous masses. Ordinarily such masses must be mixed slowly and it is frequently found best to accomplish this by making use of the force of gravity. The mixture to be agitated is placed in a more or less cylindrical vessel which can be rotated about a horizontal axis. I n this case the rotation of the 1, container raises the mass by degrees, and its fall from slight elevations brings about the desired mixing. The vessel may be cylindrical, in which case it is ordinarily provided with projections toward the center from its inside periphery, or it may assume a variety of shapes from spherical to cubical that will assist the operation of raising parts of the mass and allowing them to fall back into the original mass, their relative positions COMPl,ETE SCREWMIXER being thus altered. Cement VISCOUS MATERIALS kilns and barrel dissolvers used in shellac manufacture are the simplest practical tooIs of this type. The ball mills are modifications of the same principle since they include balls to assist the motion in the mass as well as to perform the grinding operation. The majority of agitators for mixing viscous massesaside from those above, the application of which is not limited t o this use-are modifications of the simple paddle mixer with some propeller action so altered as Ydpermit the application of the greater forces required. I n general, the principles involved are the same after allowance is made for the lack of fluidity of the mix and the consequently greater power requirement. As an engineering problem, however, viscous mixing presents many problems not involved in mobile mixing.
COMBINATION AGITATORS Combinations involving two or more of the foregoing types of agitating devices may be found in most tools as commercially used. The combinations and their applications are as numerous as the uses to which they are put, as it is seldom that the operating engineer finds a tool ready built to suit his particular need, in spite of the variety offered by makers. Combinations of simple paddles with propellers and of turbines with propellers in greatest variety are to be found in most plants, yet the principles underlying them are much the same. One of the force components possible is emphasized a t the expense of others. This practice has become so common that it is indeed difficult a t present for one
INDUSTRIAL A N D ENGINEERING CHEMISTRY
148
Vol. 15, No. 2
to find tools made in which the agitation is accomplished by applied to operations not ordinarily considered agitation, a8 a device which does not involve a variety of principles. where it is desired to dissolve a solid in a liquid in the lixiviation of ores. Still another form which agitation takes is MISCELLANEOUS TYPES well illustrated in washing an immiscible liquid with water by Various types of devices are encountered in special fields pumping the heavier, in a stream more or less broken, into which do not involve any of the principles so far discussed. the lighter, as in washing nitrobenzene with water to free Blowing a gas through a liquid mass is often used for agitation it from acid. The circulation is accomplished by a pump where the interaction of the gas with the mass is either de- of any efficient type, although usually centrifugal, in a system sired or not objectionable, as in the cases of the aeration of virtually independent of the containing vessel which draws sewage and mixing of strong mixed acids, where it is desirable liquid from the bottom of the mass and pumps it in again at to blow out oxides of nitrogen. Many combinations of fluid the top through some kind of a spray head. streams, either liquid or gas, with paddles and propellers are met in practice. The stirring of a liquid being electrolyzed ACKNOWLEDGMENT in an electrolytic cell by surrounding it with a magnetic field has been found to be very highly efficient in many electrolytic The writer wishes to acknowledge the kindness of the operations where the presence of any foreign substance in the various manufacturers who have lent us the cuts and drawelectrolyte is objectionable. The cascade principle is often ings for this article.
Effect of Agitation on t h e Rate of Solution of Crystals' By E. V. Murphree MASSACHUSETTS INSTITUTE OP
TECHNOLOGY, CAMBRIDGE, MASS.
NE OF the problems in which agitation plays an important part is the solution of crystalline materials. It is possible to develop formulas for this case in which the only unknown quantity is the specific solution rate. This constant depends upon the effectiveness of agitation, and it is possible to test out experimentally an agitator suited for this work by determining this constant for the case of a given material dissolving in a given solvent. Comparison of the constant thus obtained with that found on other equipment used for the same purpose gives a measure of the relative agitation efficiencies of the two types of equipment. Assume a definite weight of crystals of size uniform or nearly so, added to a solvent and agitated a t a uniform rate. Assume also that the volume of the solution remains substantially constant. The rate of solution is proportional to the area of crystals exposed and to the degree of agitation. Furthermore, as has been shown by A. A. Noyes,2 the rate of solution a t any particular time is proportional to the difference in concentration of the saturated solution and that of the main body of the solution. This is because the solution in absolute contact with the crystal is saturated and the crystals dissolve only by diffusion of the solute through the stationary film of liquid around the crystals. This diffusion is of course proportional to the concentration difference. Since the diffusion rate will be inversely proportional to the thickness of this film, and since this film thickness is determined by the effectiveness of agitation, being approximately inversely proportional to the velocity of the liquid past the crystal, diffusion rate-i. e., the constant which represents the specific rate of solution for unit area of crystal surface-is a good measure of agitation efficiency.
0
GENERALFORMULA NOMENCLATURE
V = volume of solution. 8 = time. c, = concentration of saturated solution as weight per unit volume. 1 2
Received January 5 , 1923. Noyes and Whitney, Z. physik. Chem., 2s (1897), 689.
c
= concentration of solution at time 8 in same units.
linear dimension of crystal a t zero time.
x0
x
= linear dimension of crystal a t time
W,= total weight W = total weight n
e.
of crystals a t time zero, of crystals a t time e. W O
number of crystals = -, ax.2
-
p
weight of one crystal. bxo* = surface of one crystal. a and b are constants, the numerical value of which depends upon the form of the crystal grains. uxo8
It is assumed that when 8 = 0 the solvent contains no solute. 1 '
dC
-
de
=
K (ca- c ) 'n b n
w, - w
n
( m , 3
=
v,
- (1x3) = V,
- 3 anx2 dx
= V dc
On substituting for c and dc, rearranging, and integrating, Equation 1 takes the form
wherekS = A.
The value of Equation 2a.
3
in this formula can be found by means of
SPECIAL CASEI-When there are not enough crystals originally present to saturate the solution, the time for comp!ete solution is found from Equation 3 by making x = 0. This gives
