Agitation and Mixing of Fluids and Power Requirements

Agitation: forcing a fluid by mechanical means to flow in a circulatory or other pattern inside a vessel.
Mixing : the taking of two or more separate phases, such as a fluid and a powdered solid or two fluids, and causing them to be randomly distributed through one another.
Equipment for Agitation
Generally liquids are agitated in a cylindrical vessel which can be closed or open to the air. The height of liquid is approximately equal to the tank diameter. Three-blade propeller agitator Baffled tank and three-blade propeller agitator with axial-flow pattern:
(a) side view,
(b) bottom view.
Paddle agitators low speeds( 20 and 200 rpm.) At low speeds ( unbaffled ) At higher speeds baffles are used( without baffles, the liquid is simply swirled around with little actual mixing. ) ineffective for suspending solids( little vertical flow). It is used with viscous liquids often used to process starch pastes, paints, adhesives, and cosmetics. Turbine agitators Turbines are used at high speeds for liquids with a very wide range of viscosities ( four or six blades.) useful for good gas dispersion; the gas is introduced just below the impeller and chopped into fine bubbles. pitched-blade turbine, with the blades at 45°, and useful in suspending solids. Helical-ribbon agitatorsused in highly viscous solutions and operates at a low RPM in the laminar region.

Agitator selection and viscosity ranges The viscosity affects the selection of the type of agitator. Propellers : < 3 Pa · s (3000 cp) turbines : < 100 Pa · s (100 000 cp); modified paddles such as anchor agitators: can be used above 50 Pa · s to about 500 Pa · s (500 000 cp) helical and ribbon-type agitators: about 1000 Pa · s and have been used up to 25 000 Pa · s. For viscosities < about 2.5 to 5 Pa · s (5000 cp) and above, baffles are not needed Flow Patterns in Agitation=f( the fluid properties, the geometry of the tank, the types of baffles in the tank, and the agitator itself. ) If a propeller or other agitator is mounted vertically in the center of a tank with no baffles, a swirling flow pattern usually develops.( this is undesirable, because of excessive air entrainment, development of a large vortex, surging, and the like, especially at high speeds).
To prevent this,
-an angular off-center position can be used with small horsepower.
-For vigorous agitation with vertical agitators, baffles. Baffles installed vertically on the walls of the tank ( Usually four baffles are sufficient)
In an agitation system, the volume flow rate of fluid moved by the impeller is important. Turbulence is important for mixing( Some require high turbulence with low circulation rates, others low turbulence with high circulation rates) Power Used in Agitated Vessels important factor is the power required to drive the impeller. The presence or absence of turbulence can be correlated with the impeller Reynolds number , defined as where Da is the impeller (agitator) diameter in m, N is rotational speed in rev/s, ρ is fluid density in kg/m3, and μ is viscosity in kg/m · s.

laminar in the tank for N’Re< 10 turbulent for N’Re > 104 between 10 and 104, the flow is transitional, being turbulent at the impeller and laminar in remote parts of the vessel. Power consumption is related to fluid density ρ, fluid viscosity μ, rotational speed N, and impeller diameter Da by plots of power number Np versus N’Re. The power number is where P = power in J/s or W. Figure 3.4-4 is a correlation for frequently used impellers with Newtonian liquids contained in baffled, cylindrical vessels. These curves may also be used for the same impellers in unbaffled tanks when is NRe 300 or less .( When is above 300, the power consumption for an unbaffled vessel is considerably less than for a baffled vessel.) Variations of various geometric ratios from the “standard” design can have different effects on the power number NP in the turbulent region of the various turbine agitators as follows (B3):
-For the flat six-blade open turbine,

-A baffled, vertical square tank or a horizontal cylindrical tank has the same power number as a vertical cylindrical tank.
The power number for a plain anchor-type agitators as follows for N’Re < 100 Agitator Scale-Up In the process industries, experimental data are often available for a laboratory-size or pilot-unit-size agitation system, and it is desired to scale up the results to design a full-scale unit.
-no single method can handle all types of scale-up problems Geometric similarity is, of course, important and simplest to achieve. Kinematic similarity can be defined in terms of ratios of velocities or of times Dynamic similarity requires fixed ratios of viscous, inertial, or gravitational forces. Even if geometric similarity is achieved, dynamic and kinematic similarity often cannot be obtained at the same time. the main objectives: equal liquid motion equal suspension of solids equal rates of mass transfer Scale-up procedure approximate guidelines :
– for mild agitation and blending, 0.1 to 0.2 kW/m3 of fluid (0.0005 to 0.001 hp/gal)
– for vigorous agitation, 0.4 to 0.6 kW/m3 (0.002 to 0.003 hp/gal)
– for intense agitation or where mass transfer is important, 0.8 to 2.0 kW/m3 (0.004 to 0.010 hp/gal).
This power in kW is the actual power delivered to the fluid (As an approximation, the power lost in the gear boxes and bearings and in inefficiency of the electric motor is about 30 to 40% of P.)
Mixing Times of Miscible Liquids an amount of HCl acid is added to an equivalent of NaOH and the time required for the indicator to change color is noted. Rapid mixing takes place near the impeller, with slower mixing, which depends on the pumping circulation rate, in the outer zones. In Fig. correlation of mixing time is given for a turbine agitator The dimensionless mixing factor ft is defined as Special Agitation Systems
1 Suspension of solids
Example: microorganisms are suspended in fermentation.
In the agitated system, circulation currents of the liquid keep the particles in suspension. The amount and type of agitation needed depend mainly on the terminal settling velocity of the particles.
2 Dispersion of gases and liquids in liquids
In gas-liquid dispersion processes, the gas is introduced below the impeller, which chops the gas into very fine bubbles. The type and degree of agitation affect the size of the bubbles and the total interfacial area. Typical of such processes are aeration in sewage treatment plants, hydrogenation of liquids by hydrogen gas in the presence of a catalyst, absorption of a solute from the gas by the liquid, and fermentation. Correlations are available for predicting the bubble size, holdup, and kW power needed.
3 Motionless mixers
Mixing of two fluids can be accomplished in motionless mixers in a pipe with no moving parts. stationary elements inside a pipe successively divide portions of the stream and then recombine these portions. One type of static mixer has a series of fixed helical elements (Note that most mixers have from six to 20 elements.) In the first element, the flow is split into two semicircular channels and the helical shape gives the streams a 180° twist. The next and successive elements are placed at 90° relative to each other and split the flows into two for each element.
Mixing of Powders, Viscous Materials, and Pastes
1 Powders
In mixing of solid particles or powders it is necessary to displace parts of the powder mixture with respect to other parts. The simplest class of devices suitable for gentle blending is the tumbler. ( A common type of tumbler is the double-cone blender, in which two cones are mounted with their open ends fastened together and rotated). Baffles can also be used internally. ( internal rotating device or charged with metal or porcelain steel balls or rods to break agglomerates. stepwise mixing for small concentrations Dough, pastes, and viscous materials In the mixing of dough, pastes, and viscous materials, large amounts of power are required as the material is divided, folded, or recombined, and as different parts of the material are displaced relative to each other so that fresh surfaces recombine as often as possible. Some machines may require jacketed cooling to remove the heat generated. The most commonly used mixer for heavy pastes and dough is the double-arm kneader mixer. The most widely used design employs two contrarotating arms of sigmoid shape which may rotate at different speeds. Power requirements in agitation and mixing of non-Newtonian fluids μa (apparent viscosity) is not constant but varies for non-Newtonian fluids N’Re,Gen (generalized NRe)=Da2Nρ/ μa average μa can be related to the average γ ( or average velocity gradient) as follows: Power Law fluid t=K(-dv/dy)nave K is consistency index, n is flow behaviour index Newtonian fluid t= μa (-dv/dy)ave so μa =K(-dv/dy)n-1ave Metzner experimentally found that For pseudoplastic fluid(n<1), (dv/dy)=11N So μa =(11N)n-1 K then N’Re,Gen=Da2N2ρ/11n-1.K Then use Fig3.5-6 to find Np Results differ for 10<N’Re,Gen<100 Pseudoplastic fluid uses less power than Newtonian fluid

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