Page 187 - Fluid mechanics, heat transfer, and mass transfer

MIXING 165

continuously discharge the finished product into the & Several dimensionless numbers, which are influ-
next piece of equipment in the process. A continuous enced by geometric factors, such as ratio of impeller
mixer is constantly fed with the correct amounts and to vessel diameter and ratio of clearance from vessel
proportions of ingredients at one end. As the materi- bottom to vessel diameter, are used in the design of a
als are being mixed, they are also conveyed to the mixer.
opposite end where the product is discharged. & Databases are available in the literature in order to
& In comparison to batch mixers, continuous mixers obtain impeller performance parameters forscale-up.
(also known as in-line or static mixers) have fairly From these databases, the dimensionless numbers are
low energy requirements. The energy of the flowing obtained for a variety of common impeller types.
fluid completes the mixing and that energy is derived Impeller N Re for a power law fluid is centric to
from a pump upstream of the mixer. different dimensionless numbers of significance.
& Continuous processing utilizes smaller vessels that . Define impeller Reynolds number.
2
reduce capital costs. Improved micromixing and N Re ¼ D Nr=m; ð6:1Þ
0
reaction selectivity reduce unwanted by-products.
where N is revolutions per second and D 0 is the impeller
. What are the effects of mixing on different types of
swept (maximum) diameter.
fluids (Newtonian and non-Newtonian)?
& N Re for power law fluids measures the ratio of inertial
& Newtonian: Unaffected by magnitude and kind of
to viscous forces within the mixer and is given by
fluid motion.
0
2 n 1
& Dilatant: Viscosity increases with increase in mixing N Re ¼ D Nr=ðk s nÞ ; ð6:2Þ
0
intensity.
where k s is the effective shear rate constant, n is the
& Bingham Plastics: Have definite yield values that 0
rotational shaft speed (rpm), and n is the flow
must be exceeded before flow starts. Once flow starts, behavior index of a power law fluid.
viscosity decreases with increase in mixing intensity. & For Newtonian fluids, laminar flow regime is for
& Pseudoplastics: Do not have a yield value, but vis-
N Re 10, transition flow is up to N Re of 300, and
cosity decreases with increase in mixing intensity. above 300 it will be turbulent flow. For N Re above
& Thixotropic: Viscosity normally decreases with in- 10,000, there will not be any effect of Reynolds
creased mixing, but this depends on duration of number on power consumption, since viscosity is
agitation, viscosity of fluid, and rate of motion before not a dominant factor.
agitation. & Some references state that turbulence is ensured
. How does non-Newtonian behavior affect agitation in a throughout the mixing vessel if N Re > 20,000 stating
mixer? that 10 < N Re < 20,000 is the transition region.
& The shear rate, g, in an agitated vessel is a function of . Define Froude number for an agitator.
position and time within the vessel. N Fr ¼ DN =g; ð6:3Þ
2
& The highest values of g occur near the impeller at
where D is the agitator diameter.
points of highest local velocity.
& Froude number is the ratio of applied forces to
& For open turbine impellers, velocity and shear rate
gravitational forces and is considered only if there
are highest at the tip of the impeller.
are significant gravitational effects present, such as in
& g decreases with increasing distance from the im-
vortexing systems. For systems with top-entering
peller and is lowest at the vessel wall. Therefore,
or bottom-entering agitators in baffled tanks or ap-
shear thinning liquids will have their lowest apparent
plications employing side-entering propellers and in
viscosity, m a , in the impeller region of an open
general for all types of systems where N Re < 300,
turbine.
there is no vortex formation, Froude number has no
& With close wall clearance impellers, such as helical effect.
ribbons, shear thinning liquids will have the lowest . Define power number for an impeller of a mixer?
m a near the vessel wall. 3 5
P o ¼ P=N D r: ð6:4Þ
& As the shear rate varies throughout the vessel, m a also
varies. Therefore, it is necessary to estimate effective & Impeller power number is a dimensionless number
impeller shear rate and effective m a in order to expressing the power drawn by an impeller and is a
quantify performance characteristics of an impeller. form of drag coefficient.
Experimental data are required for such & Power number expresses the ratio of energy causing
quantification. local turbulence to that providing bulk flow and is