Though often confused, agitation, mixing, dispersion are not synonymous. Agitation refers to the induced motion of a material in a specified way, usually in a circulatory pattern inside a vessel. Mixing is the random distribution, into and through one another, of two or more initially separate phases. Dispersion is when solid particles are merely suspended in a liquid.
The term mixing is applied to a variety of operations, differing widely in the degree of homogeneity of the "mixed" material. Consider, in one case, two gases that are brought together and thoroughly blended and, in a second case, sand, gravel, cement, and water tumbled in a rotating drum for a long time. In both cases the final product is said to be mixed. Yet the products are obviously not equally homogeneous. Samples of the mixed gases, even very small samples, all have the same composition. Small samples of the mixed concrete, on the other hand, differ widely in composition.
MIXING OF LIQUIDS
Liquids are agitated for a number of purposes, depending on the objectives of the processing step. These purposes include Suspending solid particles, Blending miscible liquids, Dispersing a gas through the liquid in the form of small bubbles, Dispersing a second liquid, immiscible with the first, to form an emulsion, Promoting heat transfer between the liquid and a coil or jacket, etc.
Liquids are most often agitated in some kind of tank or vessel, usually cylindrical in form and with a vertical axis. The top of the vessel may be open to the air; more usually it is closed. The proportions oft he tank vary widely, depending on the nature of the agitation problem. The tank bottom is rounded, not flat, to eliminate sharp corners or regions into which fluid currents would not penetrate. The liquid depth is approximately equal to the diameter of the tank. An impeller is mounted on an overhung shaft, that is, a shaft supported from above. The shaft is driven by a motor, sometimes directly connected to the shaft but more often connected to it through a speed-reducing gearbox. Accessories such as inlet and outlet lines, coils, jackets, and wells for thermometers or other temperature-measuring devices are usually included.
The impeller causes the liquid to circulate through the vessel and eventually return to the impeller. Baffles are often included to reduce tangential motion.
Impeller agitators are divided into two classes. Those that generate currents parallel with the axis of the impeller shaft are called axial-flow impellers; those that generate currents in a radial or tangential direction are called radial-flow impellers.
The three main types of impeller for low- to moderate-viscosity liquids are propellers, turbines, and high-efficiency impellers. Each type includes many variations and subtypes. For very viscous liquids, the most widely used impellers are helical impellers and anchor agitators.
Propellers. A propeller is an axial-flow, high-speed impeller for liquids of low viscosity. Small propellers turn at full motor speed, either 50—150 rpm; larger ones turn at 400 to 800 rpm. The direction of rotation is usually chosen to force the liquid downward, and the flow currents leaving the impeller continue until deflected by the floor oft he vessel. The highly turbulent swirling column of liquid leaving the impeller entrains stagnant liquid as it moves along, and the propeller blades vigorously cut or shear the liquid. Because of the persistence of the flow currents, propeller agitators are effective in very large vessels. A revolving propeller traces out a helix in the fluid, and if there were no slip between liquid and propeller, one full revolution would move the liquid longitudinally a fixed distance depending on the angle of inclination of the propeller blades. The ratio of this distance to the propeller diameter is known as the pitch of the propeller. A typical propeller is standard three-blade marine propellers with square pitch are most common; four-blade, toothed, and other designs are sometimes employed for special purposes. In a deep tank two or more propellers may be mounted on the same shaft, usually directing the liquid in the same direction.
Turbines. There in general several types of turbine impeller. The simple straight-blade turbine pushes the liquid radially and tangentially with almost no vertical motion at the impeller. The currents it generates travel outward to the vessel wall and then flow either upward or downward. Such impellers are sometimes called paddles.
The designer of an agitated vessel has an unusually large number of choices to make as to type and location of the impeller, the proportions of the vessel, the number and proportions of the baffles, and so forth. Each of these decisions affects the circulation rate of the liquid, the velocity patterns, and the power consumed. The number of baffles is usually 4; the number of impeller blades ranges from 4 to 16 but is generally 6 or 8. Special situations may, of course, dictate different proportions from those listed above; it may be advantageous, for example, to place the agitator higher or lower in the tank, or a much deeper tank may be needed to achieve the desired process result.
Impellers for highly viscous liquids. WelI-designed turbine impeller systems can be used with viscosities up to about 50 Pas. For viscosities above 20 Pas, however, the helical-ribbon impeller shown is often more effective. The diameter of the helix is very dose to the inside diameter of the tank, guaranteeing liquid motion all the way to the tank wall even with very viscous materials. Helical ribbons have been used successfully with viscosities up to 25,000 Pas.
To provide good agitation near the floor of the tank, an anchor impeller may be used. Because it creates no vertical motion, it is a less effective mixer than a helical ribbon, but it promotes good heat transfer to or from the vessel wall. For this purpose both anchors and helical ribbons may be equipped with scrapers that physically remove liquid from the tank wall.
The way a liquid moves in an agitated vessel depends on many things: the type of impeller; the characteristics of the liquid, especially its viscosity; and the size and proportions of the tank, baffles, and impeller. The liquid velocity at any point in the tank has three components, and the overall flow pattern in the tank depends on the variations in these three velocity components from point to point. The first velocity component is radial and acts in a direction perpendicular to the shaft of the impeller. The second component is longitudinal and acts in a direction parallel with the shaft. The third component is tangential, or rotational, and acts in a direction tangent to a circular path around the shaft. In the usual case of a vertical shaft, the radial and tangential components are in a horizontal plane, and the longitudinal component is vertical. The radial and longitudinal components are useful and provide the flow necessary for the mixing action. When the shaft is vertical and centrally located in the tank, the tangential component is generally disadvantageous. The tangential flow follows a circular path around the shaft and creates a vortex in the liquid, as shown in Fig. 9.6 for a f1at-blade turbine. Exactly the same flow pattern would be observed with a pitched-blade turbine or a propeller. The swirling perpetuates stratification at the various levels without providing longitudinal flow between levels. If solid particles are present, circulatory currents tend to throw the particles 10 the outside by centrifugal force; from there they move downward and to the center of the tank at the bottom. Instead of mixing, its reverse-concentration-occurs. Since, in circulatory f1ow, the liquid flows with the direction of motion of the impeller blades, the relative velocity between the blades and the liquid is reduced, and the power that can be absorbed by the liquid is limited. In an unbaffled vessel, circulatory flow is induced by all types of impellers, whether axial flow or radial f1ow. If the swirling is strong, the flow pattern in the tank is virtually the same regardless of the design of the impeller. At high impeller speeds the vortex may be so deep that it reaches the impeller, and gas from above the liquid is drawn down into the charge. Generally this is undesirable. Prevention oJ swirling, Circulatory flow and swirling can be prevented by any of three methods. In small tanks, the impeller can be mounted off center. The shaft is moved away from the center line of the tank, then tilted in a plane perpendicular to the direction of the move. In larger tanks, the agitator may be mounted in the side of the tank, with the shaft in a horizontal plane but at an angle with a radius.
In large tanks with vertical agitators, the preferable method of reducing swirling is to install baffles, which impede rotational flow without interfering with radial or longitudinal f1ow. A simple and effective baffling is attained by installing vertical strips perpendicular to the wall of the tank. Baffles of this type are shown. Except in very large tanks, four baffles are sufficient to prevent swirling and vortex formation. Even one or two baffles, if more cannot be used, have a strong effect on the circulation patterns. For turbines, the width of the baffle need be no more than one-twelfth of the vessel diameter; for propellers, no more than oneeighteenth the tank diameter is needed.' For viscous liquids even narrower baffles are generally used, and baffles are not needed at all when fJ- > lO Pa . S. Baffles are also not needed with side-entering, inclined, or off-centre propellers.
Once the swirling is stopped, the specific fLow pattern depends on the type of impeller. Propeller agitators usualIy drive the liquid down to the bottom of the tank, where the stream spreads radially in all directions toward the wall, flows upward along the wall, and returns to the suction of the propeller from the top. Propellers are used when strong vertical currents are desired, for example, when heavy solid particles are to be kept in suspension. They are not ordinarily used when the viscosity of the liquid is greater than about 5 Pa s. Pitched-blade turbines with 45° downthrusting blades are also used to provide strong axial flow for suspension of solids. Axial-fiow impellers, however, tend to change their discharge flow pattern from axial flow at low liquid viscosities to radiaI flow when the viscosity is very high.38
Flat-blade turbines give good radiaI flow in the pIane of the impeller, with the flow dividing at the wall, to form two separate circulation patterns. One portion flows downward along the walI and back to the center of the impeller from below, and the other flows upward toward the surface and back to the impeller from above. In an unbaffled tank, there are strong tangential fiows and vortex formation at moderate stirrer speeds. With baffles present, the vertical flows are increased, and there is more rapid mixing of the liquid.
In a vertical cylindrical tank, the depth of the liquid should be equal 10 or somewhat greater than the diameter of the tank. If greater depth is desired, two or more impelIers are mounted on the same shaft. The lowest impeller is commonly a radialflow unit such as a straight-blade turbine; the upper ones are usualIy axial-flow impellers. The lowest impeller is mounted about one impeller diameter above the bottom of the tank.
For a processing vessel to be effective, regardless of the nature of the agitation problem, the volume of fluid circulated by the impeller must be great enough to sweep out the entire volume in a reasonable time. Also, the velocity of the stream leaving the impeller must be sufficient to carry the currents to the remotest parts of the tank. In mixing and dispersion operations, the circulation rate is not the only factor, or even the most important one; turbulence in the moving stream often governs the effectiveness of the operation. Turbulence results from properly directed currents and large velocity gradients in the liquid. Circulation and turbulence generation both consume energy. Some agitation problems, call far large flows or high average velocities, while others require high local turbulence or power dissipation. Although both flow rate and power dissipation increase with stirrer speed, selection of the type and size of the impeller influences the relative values of flow rate and power dissipation. In general, large impellers moving at medium speed are used to promote flow, and smaller impellers operating at high speed are used where intense turbulence is required.
A turbine or propeller agitator is, in essence, a pump impeller operating without a casing and with undirected inlet and output flows. The governing impeller, the velocity gradient decreases, and the apparent viscosity of the liquid rises. The liquid velocity drops rapidly, decreasing the velocity gradients further and increasing the apparent viscosity still more. Even when there is high turbulence near the impeller, therefore, the bulk of the liquid may be moving in slow laminar flow and consuming relatively little power. The toroidal rings of slowly moving liquid are very strongly marked when the agitated liquid is a pseudoplastic.
Mixing is a much more difficult operation to study and describe than agitation. The patterns of fluid flow and velocity in an agitated vessel are complex but reasonably definite and reproducible. The power consumption is readily measured. The results of mixing studies, on the other hand, are seldom highly reproducible and depend in large measure on how mixing is defined by.the particular experimenter. Often the criterion for good mixing is visual, as in the use of interference phenomena to follow the blending of gases in a duct" or the color change of an acid-base indicator to determine liquid blending times. Other criteria that have been used include the rate of decay of concentration or temperature fluctuations, the variation in the analyses of small samples taken at random from various parts of the mix, the rate of transfer of a solute from one liquid phase to another, and in solid-liquid mixtures, the visually observed uniformity of the suspension.
Miscible liquids are blended in relatively small process vessels by propellers, turbines, or high-efficiency impellers, usually centrally mounted, and in large storage and waste treatment tanks by side-entering propellers or jet mixers. In a process vessel, all the liquid is usually well agitated and blending is fairly rapid in a large storage tank, the agitator may be idle much of the time and be turned on only.
When solids are merely suspended in a liquid, the size and surface area of the solid particles exposed to the liquid are fìxed, as is the total volume of suspended solids. At high shear rates, however, agglomerates may be broken up, and with fragile or sensitive materials the particles themselves may be degraded, their diameter reduced, and new surface area created. This is especially important in fermentations and similar operations, in which biological cells may be destroyed if the local shear rates in the vessel are too high.
In liquid-liquid and gas-liquid dispersion operations, also the size of the drops or bubbles and the total interfacial area between the dispersed and continuous phases vary with conditions and the degree of agitation. New area must constantly be created against the force of interfacial tension. Drops and bubbles are continually coalescing and being redispersed. In most gas-liquid operations, bubbles rise through the liquid pool and escape from the surface and must be replaced by new ones.
In this dynamic situation, the volume of the dispersed phase held up in the liquid pool depends on the rate of rise of the bubbles and the volumetric feed rate. In liquid-Iiquid dispersion, the holdup may depend on the rise or fall velocity of the dispersed drops, or it may be fixed by the ratio of the two phases in the feed. For both gas-liquid and liquid-liquid dispersions, statistical averages are used to characterize the system, since a distribution of drops or bubble sizes is expected, and the hold-up and interfacial area may vary with position in the vessel.
BLENDING IN PROCESS VESSELS
The impeller in a process vessel produces a highvelocity stream, and the liquid is well mixed in the region dose to the impeller because of the intense turbulence. As the stream slows down while entraining other liquid and flowing along the wall, there is some radial mixing, as large eddies break down to smaller ones, but there is probably little mixing in the direction of flow. The fluid completes a circulation loop and returns to the eye of the impeller, where vigorous mixing again occurs. Calculations based on this model show that essentially complete mixing (99 percent) should be achieved if the contents of the tank are circulated about 5 times. The mixing time can then be predicted from the correlations for total flow produced by various impellers.
Gases or low-viscosity liquids can often be satisfactorily blended by passing them together through a length of open pipe or a pipe containing orifice plates or segmented bafftes. Under appropriate conditions the pipe length may be as short as 5 to lO pipe diameters, but 50 to 100 pipe diameters is recomrnended.i"
More difficult mixing tasks are accomplished by static mixers, commercial devices which consist of a series of metal inserts placed in the pipe. One of the main types is the helical-element mixer (Fig. 9.19a) which is mainly used with viscous liquids and pastes. Each element, 1 to 1.5 pipe diameters in length, divides the stream in two, gives it a 180° twist, and delivers it to the next element, which is set at 90° to the trailing edge of the first element. The second element divides the already divided stream and twists it 180° in the opposite direction. Successive elements further subdivide the stream until the striations are so thin that the blending process can be finished by molecular diffusion.
The recommended number of helical elements is 6 for Re = 100 to 1,000, 12 for Re = l0 to 100, and 18 for Re < l0. More elements are needed for very viscous liquids because of the lower molecular diffusivity. The pressure drop per unit length is about 6 times that in the empty pipe when Re < l0, but increases to about 50 to 100 times that in the empty pipe when Re = 2,000.
For effective blending in a large tank, a side-entering propeller must be oriented precisely with regard to both its angle with the horizontal (for top-to-bottom circulation), and, in the horizontal pIane, the angle it makes with the tank diameter. For optimum results " the propeller should be exactly horizontal and make an angle with the diameter between 7 and 10°. The time required for stratified blending depends on the circulation rate but more importantly on the rate of erosion of the interface between the stratified liquid layers. No general correlations are available for stratified blending.
Circulation in large vessels may also be induced by one or more jets of liquid. Sometimes jets are set in clusters at several locations in the tank. The stream from a single jet maintains its identity for a considerable distance. The velocity in the jet issuing from the nozzle is uniform and constant. It remains so in a core, the area of which decreases with distance from the nozzle. The core is surrounded by an expanding turbulent jet, in which the radial velocity decreases with distance from the centerline of the jet. The shrinking core disappears at a distance from the nozzle of 4.3Dj, where Dj is the diameter of the nozzle. The turbulent jet maintains its
Particles of solids are suspended in liquids for many purposes, perhaps to produce a homogeneous mixture for feeding to a processing unit, to dissolve the solids, to catalyze a chemical reaction, or to promote growth of a crystalline product from a supersaturated solution. Suspension of solids in an agitated vessel is somewhat like fluidization of solids with Iiquids, as discussed, in that the particles are separated and kept in motion by the fluid flowing past them. However, the fluid flow pattem created by the agitator has regions of horizontal flow as well as upward and downward flow, and to keep the solids in suspension in a tank generally requires much higher average fluid velocities than would be needed to fluidize the solids in a vertical column. When solids are suspended in an agitated tank, there are several ways to define the condition of suspension. Different processes require different degrees of suspension, and it is important to use the appropriate definition and correlation in a design or scale up problem. The degrees of suspension are given below in the order of increasing uniformity of suspension and increasing power input.
Nearly complete suspension with filleting. Most of the solid is suspended in the liquid, with a few percent in stationary fillets of solid at the outside periphery of the bottom or at other places in the tank. Having a small amount of solids not in motion may be permissible in a feed tank to a processing unit, as long as the fillets do not grow and the solids do not cake. For crystallization or a chemical reaction, the presence of fillets would be undesirable.
Complete particle motion. AlI the particles either are suspended or are moving along the tank bottom. Particles moving on the bottom have a much lower masstransfer coefficient than suspended particles, which might affect the performance of the process.
Complete suspension or complete off-bottom suspension. AlI the particles are suspended off the tank bottom or do not stay on the bottom more than l or 2 s. When this condition is just reached, there will generalIy be concentration gradients in the suspension and there may be a region of clear liquid near the top of the tank. The gradient in solid concentration wilI have little effect on the performance of the unit as a dissolver or a chemical reactor, and the mass-transfer coefficient will not increase very much with further increases in stirrer speed.
Uniform suspension. At stirrer speeds considerably above those needed for complete suspension, there is no longer any clear liquid near the top of the tank, and the suspension appears uniform. However, there may still be vertical concentration gradients, particularly if the solids have a wide size distribution, and care is needed in getting a representative sample from the tank.