Page 280 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN006C-252 June 27, 2001 14:15

80 Fluid Mixing

in turbulent flow or to shear rate elements on the order If these three relations are combined it is seen that at
of that same size in viscous flow. Measurement of fluid constant power, one can vary the ratio of flow to impeller
mixing parameters at the microscale level involve the velocity head by a choice of D given by Eq. (2)
ability to resolve small elements of fluid parameters, as 8/3
well as understanding the dissipation of energy at the (Q /H) P ∝ D (2)
microscale level.
This equation indicates that large-diameter impellers run-
Physical uniformity criteria Criteria for fluid mixing
ning at low speed give high flow and low shear rates, but
which involves physical sampling of tank contents or
small-diameter impellers running at high speed give us
estimation of pumping of tank contents or estimation
high shear rates and low pumping capacities. This impor-
of pumping capacity and/or velocity values.
tant relationship also indicates that impeller velocity head
Radial flow impellers Impellers that pump fluid in es-
is related in principle to macroscale shear rates. Thus, one
sentially a radial direction when installed in a baffled
has the ability to change the flow to fluid shear ratio.
mixing tank.
In addition to the mathematical concepts brought out in
Eq. (2), axial flow impellers, often applied as the pitched
blade turbine (Fig. 1a), are inherently able to produce more
FLUID MIXING, as an engineering study, is the tech-
flow at a given horsepower and impeller speed than ra-
nology of blending fluid substances, including gases and
dial flow impellers, typified by the flat blade disc turbine,
solids, and is an integral process in most manufacturing
shown in Fig. 1b. Some processes, such as blending and
operations involving fluid products. An important aspect
solids suspension, are affected primarily by pumping ca-
of fluid mixing is the design and use of equipment. Fluids
pacity and are not greatly influenced by the fluid shear
can be mixed in containers with rotating impellers or by
rate. Therefore, it is typical in practice to use axial flow
means of jets, or in pipelines by internal baffles and pas-
impellers when dealing with solids suspension and blend-
sageways. Fluid mixing can involve primarily a physical
ing. Changes in D /T (where T is the tank diameter) can
suspension or dispersion that can be analyzed by the de-
affect the flow-to-fluid-shear rate ratio relative to the var-
gree of composition or uniformity. Other operations may
ious diameters:
involvemasstransferacrosstwo-phaseinterfacesorchem-
icalreactionsinoneormorephases.Informationaboutmi- (Q /H) P ∝ (D /T ) 8/3 (3)
croscale and macroscale mixing requirements are needed
for process analysis and scaleup. The introduction in recent years of the fluidfoil type of
impeller, shown in Fig. 1c, further improves the pumping
capacity of axial impellers and reduces the fluid shear rate
I. GENERAL PRINCIPLES by the actual design of the impeller blades themselves.
Figure 2 illustrates the phenomena of the fluidfoil. The il-
lustration indicates the desired flow pattern over the blade
The power put into a fluid mixer produces pumping Q
shape to minimize shear rate and maximize flow. For com-
and a velocity head H. In fact all the power P which is
parison,Fig.2bshowsfluidflowiftheangleoftheimpeller
proportional to QH appears as heat in the fluid and must
blade in the fluid is not set at this optimum flow position.
be dissipated through the mechanism of viscous shear.
As shown in Fig. 2b, the turbulence and drag behind the
The pumping capacity of the impeller has been measured
impeller blade will cause increased power and reduced
for a wide variety of impellers. Correlations are available
pumping efficiency. However, the turbulence and drag are
to predict, in a general way, the pumping capacity of the
not always a problem, because some processes require a
many impeller types in many types of configurations. The
certain level of turbulence and energy dissipation. In such
impeller pumping capacity is proportional to the impeller
processes, the use of the fluidfoil impeller type would not
speed N and the cube of the impeller diameter D,
be as effective as other types that develop higher internal
Q ∝ ND 3 impeller zone shear rates.
There are now several varieties of fluidfoil impellers in
The power drawn by an impeller in low- and medium-
use. The A310 is an effective impeller for the low vis-
viscosity fluids is proportional to the cube of impeller
cosity region and has a negative response to viscosity at
speed N and the impeller diameter D to the fifth power,
a Reynolds number of approximately 600. As shown in
3
P ∝ N D 5 (1) Fig. 3, the angle that the flow stream makes with the verti-
cal starts to become greater than with the A200 impeller,
At higher viscosities other exponents are involved (dis- so we can say effectively that the Reynolds number limi-
cussed later). tation on the A310 is approximately 200.