Liquid mixing mechanisms for fluids fall essentially into four categories: bulk transport, turbulent flow, laminar flow, and molecular diffusion. Usually, more than one of these mechanisms is operative in practical mixing situations.
Liquid Mixing Mechanisms
Bulk Transport
The movement of a relatively large portion of the material being mixed from one location in a system to another constitutes bulk transport. A simple circulation of material in a mixer, however, does not necessarily result in efficient mixing. For bulk transport to be effective, it must result in a rearrangement or permutation of the various portions of the materials to be mixed. This is usually accomplished by means of paddles, revolving blades, or other devices, within the mixer, arranged so as to move adjacent volumes of the fluid in different directions, thereby shuffling the system in three dimensions.
Turbulent Mixing
The phenomenon of turbulent mixing is the direct result of turbulent fluid flow, which is characterized by a random fluctuation of the fluid velocity at any given point within the system. The fluid velocity at any given instant may be expressed as the vector sum of its components in the x, y, and z directions. With turbulence, these directional components fluctuate randomly about their individual mean values, as does the velocity itself.
In general, with turbulence, the fluid has different instantaneous velocities at different locations and such velocity differences within the body of fluid produce a randomization of the fluid molecules. For this reason, turbulence is a highly effective mechanism of liquid mixing.
Turbulent flow can be conveniently visualized as a composite of eddies of various sizes. An eddy is defined as a portion of a fluid moving as a unit in a direction often contrary to that of the general flow. Large eddies tend to break up, forming eddies of smaller size until they are no longer distinguishable. The size distribution of eddies within a turbulent region is referred to as the scale of turbulence. Thus, when small eddies are predominant, the scale of turbulence is low.
An additional characteristic of turbulent flow is its intensity, which is related to the velocities with which the eddies move. A composite picture of eddy size versus the velocity distribution of each size eddy may be described as a complex spectrum. Such a spectrum is the characteristic of a turbulent flow and is used in its analysis.
Laminar Mixing
Streamline or laminar flow is frequently encountered when highly viscous fluids are being processed. It can also occur if stirring is relatively gentle and may exist adjacent to stationary surfaces in the vessels in which the flow is predominantly turbulent. When two dissimilar liquids are mixed through laminar flow, the shear that is generated stretches the interface between them. If the mixer employed folds the layers back upon themselves, the number of layers, and hence the interfacial area between them, increases exponentially with time. This relationship is observed because the rate of increase in interfacial area with time is proportional to the instantaneous interfacial area.
Mixers may also operate by simply stretching the fluid layers without any significant folding action. This mechanism does not have the stretch compounding effect produced by folding, but may be satisfactory for some purposes in which only a moderate reduction in mixing scale (defined in detail later) is required. It should be pointed out, however, that by this process alone, an exceedingly long time is required for the layers of the different fluids to reach molecular dimensions. Therefore, good mixing at the molecular level requires a significant contribution by molecular diffusion after the layers have been reduced to a reasonable thickness (several hundred molecules) by laminar flow.
Molecular Diffusion
The primary mechanism responsible for mixing at the molecular level is diffusion, resulting from the thermal motion of the molecules. When it occurs in conjunction with laminar flow, molecular diffusion tends to reduce the sharp discontinuities at the interface between the fluid layers, and if allowed to proceed for sufficient time, results in complete mixing.
The process is described quantitatively in terms of Fick’s first law of diffusion:
$$ \frac{dm}{dt}=-DA\frac{dc}{dx} $$
where the rate of transport of mass, dm/dt, across an interface of area, A, is proportional to the concentration gradient, dc/dx, across the interface. The rate of intermingling is governed also by the diffusion coefficient, D, which is a function of the variables, i.e. fluid viscosity and size of the diffusing molecules. The sharp interface between dissimilar fluids, which has been generated by laminar flow, may be rather quickly eliminated by the resulting diffusion. Considerable time may be required, however, for the entire system to become homogeneous.
Reference:
- Khar, R.,Vyas, S., Ahmad, F., & Jain, G. (2016). Lachman/Lieberman’s The Theory and Practice of Industrial Industrial Pharmacy. New Delhi, ND: CBS Publishers & Distributors Pvt Ltd.