A modified Nukiyama–Tanasawa distribution function and a Rosin–Rammler model for the particle-size-distribution analysis

No fundamental mechanism or model enables a theory on particle-size distribution to be built. Consequently, a wide variety of empirical models or equations have been proposed to characterize experimental particle-size distributions, such as the Rosin–Rammler model. Because the Nukiyama–Tanasawa equation uses four parameters to simulate differential distribution frequencies for particle-size diameters, the distribution function is not easy to apply in order to fit experimental data. In this paper, a modification of the Nukiyama–Tanasawa model with only two parameters has been proposed to fit the data on a particle-size distribution (PSD). The proposed normalized distribution function has been applied successfully to the PSD analysis (cork granulate and spray atomization droplets).

A modification of the Nukiyama–Tanasawa equation with only two parameters has been proposed to fit the data on particle-size distribution (PSD). The proposed normalized distribution function has been applied successfully to the PSD analysis of experimental data.fN(D)=nDVSΓ(p+1n)(Γ(p+4n)Γ(p+3n))p+1(DDVS)pexp(-(Γ(p+4n)Γ(p+3n))n(DDVS)n)fM(D)=nDVSΓ(p+4n)(Γ(p+4n)Γ(p+3n))p+4(DDVS)p+3exp(-(Γ(p+4n)Γ(p+3n))n(DDVS)n)