I would like to begin this discussion by first congratulating Dr. John Carson of Jenike & Johanson on his lifetime achievement award recently received at the AICHE meeting in Salt Lake City, UT. I worked with John for 23 years at J&J and regard him as a mentor. John encouraged me to obtain my mechanical engineering degree and supported me throughout the process and my career at J&J. One of the toughest decisions I ever had to make was to leave J&J in order to eventually found Solids Handling Technologies. Thank you, John, for your inspiration and encouragement.
    
In previous articles, we discussed cohesive arching that can occur in a bin or hopper. In others, we discussed wall friction and its effects on hopper wall slopes required to ensure mass flow (flow along the walls). An important factor in determining the above bin design parameters is the compressibility of the material to be handled.
    
The bulk solids handling industry describes compressibility as a measure of the relative volume change of a solid as a response to a pressure (or mean stress) change. In other words, a material’s compressibility is its bulk density/pressure relationship. The bulk density of your product is determined as it undergoes the range of pressures or solids loading experienced due to flow in a bin. Sometimes, bulk density is expressed as loose density or packed density. However, there are more than two values of bulk density. Solids are compressible and experience bulk density changes over a range of solids pressure.
    
Photo 1 shows a compressibility tester that is composed of a 2.5-in.-diam cell that is 0.75 in. deep, that is loosely filled with product. A cover, dial gauge (used to measure the distance the material deflects or compacts), and weight hanger are applied. Weights are then individually stacked on the weight hanger and the deflection height recorded. Because the cell’s cross-sectional area and material height at each weight level are determined. Measuring the weight of the product in the cup allows us to calculate the bulk density, lb/cu ft, as a function of pressure applied. A materials bulk density can be expressed on a plot such as that shown in Photo 2.
    
Compressibility is affected by your material’s moisture content, particle size, elasticity, and temperature. While the compressibility test is a rather simple test, the information gathered during testing is used in many ways to identify your material's flow properties, as discussed here:

1. Cohesive properties. Bulk density values are used in the calculation of opening sizes required to prevent arching and ratholing. Cohesive properties are measured using a bench scale laboratory testing device like a Jenike Shear Tester. This device is used to determine a material’s “Flow Function” (cohesive strength/pressure relationship).

2. Wall friction angle. Your material's bulk density is used in the calculation of hopper wall pressures (the pressure exerted by the material normal to the hopper wall). These pressures are subsequently used to predict the wall friction angle that develops between the material and a sample of wall surface, which subsequently yields the recommended hopper slope for mass flow. Wall friction values are expressed as a wall friction angle or coefficient of sliding friction. The lower the coefficient of sliding friction, the less steep the hopper walls need to be to ensure mass flow.

3. Loads on walls. Bulk density directly affects the pressures acting on the walls of a hopper. Forces acting within the hopper are more accurately determined by determining the bulk density/pressure relationship. Solids flowing in mass flow exhibit a pressure distribution similar to the one shown in Photo 3. Here, the solids pressure increases in the constant cross-sectional area, cylindrical section. At the transition between the cylinder and the hopper, as the material now has to converge into a decreasing cross-sectional area (hopper), it densifies. Here a high peak pressure occurs that quickly diminishes as it travels to the hopper apex.

4. Loads on feeders. Knowing a material’s range of density allows you to predict the solids loads that will be applied to any feeding device or gate attached to the outlet of the hopper (see Photo 4). Keep in mind that the pressures at the outlet of a mass flow hopper are typically low, as head pressure is reduced due to shear along the walls.

An accurate determination of your product's compressibility provides important information that can affect your hopper and feeder design criteria significantly.

    Joseph Marinelli is a consulting engineer and president of Solids Handling Technologies. He has been providing testing and consulting services since 1972. As a former consultant with Jenike & Johanson Inc., he has years of experience testing powders and designing bins and feeders for reliable flow. He lectures frequently on the topic of powder handling and has published several papers, including an article in a chemical encyclopedia and two in a food powder book. For more information, call 803-802-5527 or email [email protected].

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