## Theory Of Operation

The prevailing theory of the action in a colloid mill is shear. Fluid shear occurs in a layer of liquid between two planes, one stationary and the other mobile. There exists a gradient of velocity between these two planes. At the mobile plane the velocity is at its maximum, and at the stationary plane it is at its minimum (zero velocity). This means there are parallel layers of liquid moving past each other at different velocities subjecting dispersed particles to a disrupting force. The rate of change in velocity over the distance between these two planes is the shear rate. A common method of estimating the shear rate in a colloid mill is given as (8)

y = nnDr!h where n is the number of revolutions per second, Dr is the rotor diameter, and h is the gap width. By this equation, a colloid mill with a rotor diameter of 2 inches (50.8 mm), a speed of 20,000 rpm, and a gap of 0.010 inches (0.254 mm) produces a shear rate of 2.09 x 10® sec-1. At a gap of 0.002 inches (0.0508 mm) the shear rate is 1.05 x 106 sec"1. A rotor diameter of 5 inches (127 mm) at 3,600 rpm with a gap of 0.005 inches (0.127 mm) has a shear rate of 1.88 x 105 sec. ~ \ These examples illustrate the high shear rate generated in a colloid mill, and how this shear rate varies with operating conditions.

Some authors have suggested that other mechanisms besides shear are important in a colloid mill. Turbulence and cavitation may occur in mills with corrugated rotors and stators (6). Some researchers believe that the dispersion is caused by the collision of particles against each other at the surface of the rotor. Particles are set into rotation by the high shear field in the gap between the rotor and stator. A lift force pushes the rotating particles against the rotor. The comminution or emulsification occurs by "autogenous grinding empowered by the rotational kinetic energy of particles in suspension" (7). The rotational energy spectrum varies with "particle size, fluid viscosity, gap size, mill speed, and other parameters in the system" (7).

A recent paper describing the mechanism of emulsification in a colloid mill emphasizes the importance of residence time in the working area (8). Two models for droplet breakup are presented. One model is capillary breakup, where a droplet is stretched into an elongated form that is then broken into many droplets. The other model is a binary breakup where a cascade of events is needed to complete the reduction of the droplet. There was good agreement between experimental observation and the capillary model. One significant parameter in these models is residence time in the gap. Because these models require a certain time for breakup of the droplets, the residence time is an important factor in understanding scale-up and variations in colloid mill designs.

Residence time in a colloid mill is important because the flow rate in a mill is dependent on several factors. The flow rate depends on the rheological properties of the product, the clearance between the rotor and stator, the in-feed pressure to the mill, the shape of the rotor and stator, the amount of restriction to flow at the discharge from the mill, and the speed of the rotor. Some factors that reduce the flow rate of the mill are high viscosity, reduced clearance between the rotor and stator, restriction to flow at the discharge, and a flow path that is axial or tends radially inward. Factors that increase flow through the mill are increased in-feed pressure, large clearance between the rotor and stator, increased speed of the rotor, low viscosity fluid, no restriction to flow at the discharge, and a flow path that tends radially outward.

The temperature rise in a product flowing through a mill depends on the residence time in the working area. The longer the fluid is in the working area, the greater the temperature rise. Therefore, all the factors that increase residence time most likely increase temperature of the product.

Figure 2 shows the consequences of varying these factors for mayonnaise. Mayonnaise was processed in a laboratory-sized colloid mill. The flow rate, the product viscosity, and the in-feed pressure were measured during the test. When the in-feed pressure is increased, the flow rate through the mill is also increased. However, as the in-feed pressure is increased, the product viscosity is decreased because the residence time for the product is reduced and less work is done on the product.

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