In the mixing of miscible liquids, any practical scale of scrutiny embraces a very large number of particles.
THE MIXING OF LIQUIDS
In
the mixing of miscible liquids, any practical scale of scrutiny embraces a very
large number of particles. If, therefore, a mixture of liquids is randomized by
agitation, for all practical purposes, it can be regarded as uniform. Miscible
liquids are classified as positive mixtures and would, given time, mix
com-pletely without external help. The time required for mixing is reduced by
agi-tation during which the scale of segregation is reduced, allowing a fast
decay in the intensity of segregation by natural diffusion. In general, no
great problems are encountered unless the scale of the operation is very large.
Miscible
liquids are most commonly mixed by impellers rotating in tanks. These are
classified as
1. paddles,
2. propellers, and
3. turbines.
In
conjunction with the design of the containing vessel, these provide
1. a. a region of intense shear in the vicinity of the
impeller with the induction of high-velocity gradients and turbulence within
the liquid and
2. the projection of the disturbance as a flow pattern
extending throughout the volume of the container. This is dictated by the type
and position of the impeller, the design of the tank, and the flow properties
of the material.
All the material
should pass through the impeller zone at frequent intervals of time, the design
of the mixer preventing the formation of “dead” zones. The turbulent,
high-velocity flow of liquid from the impeller causes mixing by projecting
eddies into and entraining liquid from the neighboring zones. The thin ribbons
of one component in another rapidly become diffuse and finally disappear through
molecular diffusion.
The flow pattern may
be analyzed in terms of its three components of motion; radial flow, in a
direction perpendicular to the impeller shaft; longitu-dinal or axial flow, in
a direction parallel to the shaft; and tangential flow, in which the liquid
follows a circular path around the shaft. A satisfactory flow pattern depends
on the correct balance of these components. In a cylindrical tank, radial flow
will give rise to axial flow by reaction at the wall of the tank. Tangential
flow receives no such modification. Its predominance as laminar flow
circulation supports stratification at various levels. Furthermore, a vortex is
created at the surface of the liquid, which may penetrate to the impeller,
causing air to be dispersed in the liquid. In general, tangential flow should
be minimized by moving the impeller to an off-center position, thus destroying
the symmetry of the mixer, or by modification of the flow pattern by means of
baffles. Tanks with vertical agitators may be baffled by one, two, or more
strips mounted vertically on or just away from the vessel wall. These reduce
but do not elimi-nate tangential flow, whereas little modification of radial
and axial flow occurs. Baffles produce additional turbulence.
Additional factors
must be applied to the mixing of two immiscible liq-uids. This operation, which
is encountered, for example, in liquid-liquid extraction, involves the
production and maintenance of a large interfacial con-tact area. In addition,
separation of phases because of differences in density must be opposed by an
adequate axial flow pattern. The high rates of shear induced by the rotation of
a propeller or turbine cause globules of the disperse phase to be drawn into an
unstable filament of liquid, which breaks and reforms into smaller globules.
Unless stabilized by surface-active agents, the reverse process, coalescence,
occurs in zones where velocity gradients are small.
Four types of paddle
mixer are illustrated in Figure 13.7. The mixing element is large in relation
to the vessel and rotates at low speeds (10–100 rpm). A simple paddle, with
upper and lower blades, suitable for mixing miscible liquids of low viscosity,
is shown in Figure 13.7A. A tangential flow pattern predominates with zones of turbulence
to the rear of the blades. The gate paddle (Fig. 13.7B) is suitable for mixing
liquids of higher viscosity, and the anchor paddle (Fig. 13.7D), with low
clearance between pan and blade, is useful for working across a heat transfer
surface. Stationary paddles intermeshing with the moving element sup-press
swirling in the mixer, illustrated in Figure 13.7C. In the other examples,
baffles are necessary. Unless paddle blades are pitched, poor axial turnover of
the liquid occurs. Paddles are not, therefore, suitable for mixtures that
separate.
Propellers
are commonly used for mixing miscible and immiscible liquids of low viscosity.
The marine propeller is typical of the group. High-speed rotation (400– 1500
rpm) of the relatively small element provides high shear rates in the vicinity
of the impeller and a flow pattern with mainly axial and tangential components.
They may be used in unbaffled tanks when mounted in an off-center position or
are inclined from the vertical. Horizontal mounting in the side of the vessel
is frequently used when the scale of the operation is large.
FIGURE 13.7 Paddle mixers.
Turbine
designs are intermediate between paddles and propellers. Turbines are effective
mixers over a wide viscosity range and provide a very versatile mixing tool.
The ratio of radial flow to tangential flow, which are the predominating
components with this impeller, increases as the operating speed increases.
Pitched-blade turbines are sometimes used to increase axial flow. Baffles must
be used to limit swirling unless a shrouded turbine is used. With this
impeller, a discharge with no tangential component is produced.
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