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January 2021 / 29 size of approximately 500 microns. The fine powder was found to be very cohesive, and its strength increased dramatically after only 8 hours when under consolida- tion. By increasing the fertilizer's median particle size from 10 microns to 500 microns, the fertil- izer's cohesive strength decreased, and the fertilizer became nonco- hesive and remained noncohesive when stored at rest. So, how much caking is accept- able? Consider the following example. The stress on impact when a bag of bulk material is dropped from a height of 1 meter is approx- imately 10 kilopascal (kPa). From a study on pinch strengths, 6 the stresses imparted between the thumb and index finger of an adult male and adult female are typically approximately 400 kilopascal and 250 kilopascal, respectively. (The study was obviously not performed in my household!) From personal experience, a hammer imparts approximately 2,500 kilopascal of stress onto a thumb. The test results reflected in Figure 2 suggest that the 500-micron-sized material is unlikely to cake and pose a problem because its cohesive strength is low, whereas the fine 10-micron-sized material will cake due to the materi- pactors. Sintering devices include auger extruders, screw extruders, and ram extruders. Why intentional agglomeration works But how do we know the effective- ness of agglomeration in reducing caking? One method to quantify caking is to measure the powder's cohesive strength with a shear cell. 3 Shear cell testing is described by ASTM-D-6128 4 and ASTM-D-6773. 5 Conducted properly, the tests allow a bulk material's cohesive strength to be determined as a function of consolidation stress and time. If the tests reveal that the material's cohesive strength increases when the material is consolidated at rest for a period of time, the material is likely to cake during storage. Knowing this information, we can then take the necessary steps to enlarge the particle size so that the particles' cohesive strength is reduced and unwanted agglomera- tion won't happen. As an example of the effect particle size has on the materi- al's cohesive strength, Figure 2 shows results from strength tests performed on fertilizer powder samples comprised of 10-micron (μm) fertilizer particles that have been agglomerated to a particle stress that a material can withstand before breaking apart) experiment in which a compact of powder has a platen area equal to A and is comprised of particles having a diameter of d. 1 The tensile strength σ T is the force required to cause the compact to fail and is divided by the platen area. Assume that this tensile strength force is equal to the sum of the adhesive forces at the contact point between each individual particle, each point equal to F H , which is proportional to the parti- cle diameter d, and let the number of contacts equal n, as shown in the following equation. σ T = nF H A The number of particle contacts is proportional to the platen area and inversely proportional to the square of the particle diameter. n ∝ A d 2 It then follows that σ T = nF H ∝ nF H ∝ d ∝ 1 A nd 2 d 2 d Although interparticle adhesive forces increase with particle diam- eter, the powder's cohesive strength decreases with increasing particle size. This is why size enlargement is often used to reduce the likeli- hood of unwanted agglomeration of powders. The technologies available for particle size enlargement include tumble-growth agglomeration, pressure agglomeration, and heat- ing or sintering agglomeration. 2 Tumble-growth agglomeration devices include pin mixers, pan pelletizers, and rotary drums. Pres- sure agglomeration devices include roller compactors and die com- FIGURE 2 The effect that a fertilizer's particle size has on the fertilizer's cohesive strength Cohesive strength (kPa) Time (days) 160 120 80 40 0 0 2 4 6 8 10 Particle size (μm) Consolidation stress (kPa) 10 2,500 500 2,500 10 5,000 500 5,000