One of the oldest operations in the processing industries is separation of different types or sizes of solid particles, and such operations are still widely employed throughout the processing industries today.
Separation can be based on size, shape, color, density, aerodynamics, hydrodynamics, electromagnetic properties or visual appearance. Most of these techniques are employed in sequence or in combination in the screen room of a flour mill, to ensure raw material is presented to the milling operation as clean wheat, free from impurities that might damage the mill and would compromise the flour quality.
Within the mill itself, solids separation based on size is predominant as sifting operations — primarily plansifting, while aerodynamic differences in flour stocks are exploited within the purifiers to remove small bran particles from endosperm particles prior to entering the reduction system.
The techniques listed above are too numerous to consider in one article, so the following discussion concentrates on attempts to describe the principles underlying sifting operations mathematically, and identifies how modern computational techniques are showing opportunities for understanding this mechanically simple but physically complex operation.
PHYSICS AND ENGINEERING MYSTERY
"Sifting" is the term employed within flour milling, while the terms "sieving" and "screening" are more generally used elsewhere, with "sieving" generally referring to a batch operation and "screening" to continuous operations. Both are widely used — in industry as a unit operation for large-scale separation of particles according to size and in laboratories as a tool for the analysis of particle size distribution.
Industrial operations employing sieves or screens have spread into a variety of engineering categories, including minerals processing, food manufacture and pharmaceutical engineering. Billions of tonnes of particulate materials, including around 600 million tonnes of wheat, are subjected to industrial screening each year, and a quantitative understanding of the kinetics involved clearly has great economic significance.
Sieving is one of the oldest and most widely employed physical size separation methods, undoubtedly having its origins in ancient cereal processing dating back thousands of years. Despite this long history, an insightful understanding of the physics and engineering design principles of sieving has never been realized, due to the complicated size distribution and composition of industrial particulate solids and the influence on particle motion of various operational parameters and screen configurations. The lack of advanced analytical and experimental techniques for the study of particulate systems has also hindered the progress in this subject area. As a result, most published information on sieve and screen performance has been empirical in nature, such that industrial screening charts and formulae have proven very inaccurate and can produce results that vary by a factor of three.
SIEVING THEORIES
Most of the early studies in sieving aimed to establish factors that influence screening efficiency and to analyze sieving kinetics. These analyses are usually based on experimental data from conducting practical sieving operations and weighing the overflow and underflow streams.
The best known sieving theory is the "first-order rate law," which describes the change in the concentration of undersize particles remaining on the screen, W, in a batch sieving as a function of the screening time t:
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where K is the "intensity" of sieving or the sieving rate constant, which depends on the sieve mesh size and material characteristics and the mode and frequency of oscillation of the sieve, and is determined by experiments.
The similarity between batch sieving and continuous screening means that the time scale t of the former is related to the length scale and the feed rate of the latter. For a continuous screening operation, assuming a mean velocity v of the overflow stream, a similar form to Equation 1 can be written as:
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where k represents the intensity of screening and L is length along the screen.
The first-order rate law only applies to conditions of low probability of particle passage through the screen and low particle loading on the screen, in which particles can move independently and not in a "crowded" or interdependent way. This is the case when the particle bed is not very deep.
In continuous screening, when the feed rate onto the sieve is at a sufficiently high level and the material creates a crowded particle bed with a certain thickness, such as around the feed section, only particles in the layer in immediate contact with the screen have a chance to pass through the apertures; this is the situation in a flour milling sifter.
As long as the upper layers are capable of replenishing undersize particles to that contact layer, the traversal rate of the material will remain constant and Equation 2 is not applicable. As the material travels along the screen and more undersize particles pass through apertures, the overflow assembly becomes more dispersed and particles are more mobile and "separated." Then the transition from the "crowded" state to "separated" motion occurs and the first-order rate law may apply.
The above discussion highlights the inadequacy of the first-order rate law to describe industrially relevant sieving or screening conditions. Other mathematical models for sieving have been produced using probability theories. In general, these probabilistic models fail to account for the effect of the microscopic particle motion on sieves and the physical evolution of the mesoscopic structure of the particle assembly under various conditions.
COMPROMISED MILLING OPERATIONS
Although sieving, sifting and screening operations are mechanically relatively simple, they entail vastly complex physical interactions between particles and with the apertured surface. Thus detailed physical and mathematical descriptions of these systems are lacking, such that the design and operation of sifting in flour milling (and its counterparts in other industries) are compromised, as are the design, operation and control of the whole mill. This is not to overlook the fact that milling engineers have the benefit of vast empirical experience; nevertheless, incomplete understanding necessarily constrains engineers to be conservative, hampering innovative design and sound optimization of flour mills.
The crucial effects of discrete particle motion (i.e. the behavior of individual particles within the mixture) on the screening efficiency have been identified by a number of researchers. These include how segregation occurs in the material layer and contributes to separation (this is a particularly relevant phenomenon in sifting of flour stocks and in the operation of gravity tables) and how the undersize particles approach sieves and ultimately pass through apertures.
The change of particle size distribution during the transient process of screening alters the material composition at different layers and eventually affects the overall screening efficiency. To date there has been little report in the literature concerning the study of these phenomena either by advanced measuring techniques or by modern computational tools.
Early mathematical simulations of particulate systems usually adopted ideas from Computational Fluid Dynamics (CFD) and considered the solids as a continuum. This is not true when the particle size is large or the flow becomes dense.
DISCRETE ELEMENT METHOD
A developing category of multiphase flow models uses the Discrete Element Method (DEM), in which the motion of each individual particle is calculated as a consequence of all the forces acting on it. This method is able to take into account the simultaneous occurrence of various kinds of movements and the complex range of interactions that can occur between the particles and each other, between the particles and the walls and between the particles and the interstitial fluid. The advantages of this method over continuum techniques are that it simulates effects at particle level, there is less need for global assumptions, and the assembly response is a direct output from the simulation.
DEM simulations have reported positive results on a number of granular systems, including fluidized beds, hopper and pipe flows and particle mixing. DEM is an ideal technique for the simulation of discrete particle motion on sieves, but special attention needs to be given to the implementation of a boundary consisting of moving apertures.
Figure 1 illustrates the result of a DEM simulation of the separation of a binary mixture of particles passing over a stationary inclined mesh screen. The particles consist of spheres of 2 and 8 mm, in the ratio of 9:1 small:large particles by number, passing through an apertured screen consisting of 1 mm wires 4 mm apart, 1 m in length and inclined at an angle of 30°. This situation is relevant to the separation of, say, white peas from rapeseeds, but the details could easily be modified very slightly to describe the separation of wheat kernels from smaller or larger seeds in the screen room.
The simulation illustrates the crowding in the feed section, such that few undersized particles can approach the screen and pass through, as evidenced by few particles collecting underneath the screen.
From about 0.2 m along there is a clear build-up of particles collecting underneath the screen, indicating rapid traversal of undersized particles and efficient separation. Towards the end of the screen, the number of undersized particles naturally becomes depleted, and therefore their rate of passage through the screen inevitably drops.
Careful analysis of such simulations can also indicate evidence of segregation within the material layer on the screen and help in understanding and exploiting that phenomenon, and can allow the performance of the screen at different points to be quantified.
MODEL POTENTIAL
The above illustration is for a stationary inclined screen, but it is easy to see how this approach can be extended to describe particle motion on a gravity table or on a horizontal moving screen such as a plansifter.
Plansifter configurations are exceptionally complex, and for that reason are almost certainly not optimal; such simulations would give an enormously valuable tool to flour milling engineers to experiment with design configurations and operational parameters on the computer screen which offer much more freedom and less risk than in an operating mill.
Thinking more broadly, these simulations are also contributing to developing practical mathematical models of sifting operations which, in combination with models of roller milling, would allow the simulation of entire flour milling processes, for use in mill design, operation, control and troubleshooting, and be an invaluable teaching tool.