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18 October 2017 Tablets & Capsules 3. Determine δ. From Figure 3b, δ equals 45.8 degrees (°). 4. Calculate ϕ'. From equations 4 to 13, σ 2 = 0.18 kPa, σ avg = 0.62 kPa, R = 0.45 kPa. The normal and shear stresses at the wall equal 0.72 kPa and 0.44 kPa, respec- tively, and ϕ' = 31.0°. 5. Select the mass-flow hopper angle. From equations 2 and 3, θ' = 9.2°. 6. Calculate H(θ'). From Equation 18, H(θ') = 2.14. 7. Update the flow factor. Using δ = 45.8°, ϕ' = 31.0°, and θ' = 9.2° in equations 13 to 15 gives ff = 1.26. 8. Determine the major consolidation stress at the intersection of the flow function and flow factor. The major consolidation stress σ 1 is equal to 1.12 kPa. 9. Update δ and ϕ'. From Figure 3b, δ = 45.7°; from equations 4 to 13, ϕ' = 30.7°. 10. Update the recommended mass-flow hopper angle. From equations 2 and 3, θ' = 9.5°. 11. Update H(θ') and flow factor. H(θ') = 2.15 and ff = 1.25. Solution has converged. 12. Calculate the critical stress; σ crit = 1.12/1.25 = 0.90 kPa. 13. Calculate the bulk density. From Figure 3c, ρ b = 804 kg/m 3 . 14. Calculate the critical outlet diameter. From Equation 20, B min = (2.15)(900)/[(804)(9.8)] = 0.24 meter (10 inches). The recommended hopper for reliable storage and handling the APAP-MCC-HPC formulation has a 10- inch-diameter outlet and conical walls fabricated from 304 stainless steel with a 2B finish sloped 9 degrees from vertical. Because such a design is impractical, the formula- tion must be altered to improve its flowability. Blends containing fumed silica at levels ranging from 0.25 to 0.75 percent and magnesium stearate levels between 0.5 and 1.0 percent were prepared. Flow property tests per- formed on the blend showed that an APAP-MCC-HPC blend containing 0.25 percent fumed silica and 1.0 percent magnesium stearate was the least cohesive and had the low- est wall friction. The flow properties of this formulation are shown in Figures 11 to 14. Additionally, the permeability of the formulation was determined to equal 0.0024 meter per second at its loose fill bulk density (652 kg/m 3 ). Design of a mass flow bin for this formulation is as follows: 1. Inspection of the material's flow function shows that it will lie below any flow factor if plotted together on the same graph. Therefore, choose a hopper outlet diameter that is appropriate for the downstream equipment. Set B = 2 inches (0.051 m). 2. Estimate the values of the wall friction angle and effective angle of friction. Based on Figures 12 and 14, choose δ = 37°, ϕ' = 20°. 3. Select the mass-flow hopper angle. From equations 2 to 3, θ' = 24.3°. 4. Determine the flow factor. From Equations 15 to 18, ff = 1.52. 5. Calculate H(θ'). From Equation 18, H(θ') = 2.37. 6. Calculate the outlet major consolidation stress σ 1 from Equation 19. (The bulk density ρb is determined from Figure 13.) Solving gives σ 1 = 0.21 kPa and ρ b = 664 kg/m 3 . 7. Update the effective angle of friction. From Figure 12, δ = 36.7°. 8. Determine the wall friction angle. From equations 4 to 13, ϕ' = 20.9°. 9. Update the mass-flow hopper angle. Equations 2 and 3a are solved to give θ' = 23.1°. 10. Update the flow factor and H(θ'). From equations 15 to 18, ff = 1.56; H(θ') = 2.35. 11. Update the estimate of the major consolidation stress and bulk density at the hopper outlet. σ 1 = 0. 22 kPa and ρ b = 664 kg/m 3 . 12. Update the effective angle of friction and angle of wall friction. δ = 36.7°; ϕ' = 20.6°. 13. Update the mass-flow hopper angle. θ' = 23.5°. 14. Update the flow factor and H(θ'). ff = 1.54. Solution has converged. A conical hopper with a 2-inch-diameter outlet and fab- ricated from 304 stainless steel with a 2B finish must have walls sloped 23.5 degrees or steeper to ensure mass flow. The maximum powder discharge rate will depend on the diameter of the cylinder and the height of the pow- der inside the cylinder. For a 24-inch- (0.61-m) diameter, 36-inch- (0.91-m) tall cylinder completely filled with the powder, the maximum major consolidation stress in the cylinder is calculated from the Janssen Equation: σ 1 = (690)(9.8)(0.61)/[(4)(0.4)tan(14°)]{1-exp[- (4)(0.4)(tan(14°)(0.91)/0.61]}/1000 = 4.6 kPa. From Figure 13, ρ bmax = 712 kg/m 3 . From Equation 22, the maximum solids discharge rate is = (652)π(0.058)2(0.0024)/[4(1-652/712)](3600) = 135 kg/hr This discharge rate is expected to meet the down- stream requirements. Figure 12 Effective angle of friction of APAP-MCC-HPC blend with 0.2 percent fumed silica and 1.0 percent magnesium stearate 0 2 4 6 8 10 Major consolidation stress (kPa) Effective angle of friction (deg) 50 45 40 35 30 25