Controlled particle size distributions using Linear Programming

The sintering characteristics of powder blends are greatly influenced by the characteristics of the particle size distribution, typically well-modeled as lognormal. Some sintering processes combine individual powder batches of different sizes to produce a mixture with a specific mean, standard deviation and distribution. This work demonstrates how the technique of Linear Programming can be employed to produce accurate estimates of the proportions of the original manufactured powders that should be mixed in order to produce a final particle size distribution that closely matches a lognormal shape with a specific mean diameter and a specific diameter standard deviation. This approach is carried out using data describing the particle diameter distributions for eleven basic grades of alumina powder, and a Linear Programming formulation which uses the universally available Excel Solver spreadsheet software.