Abstract: The coagulation due to turbulent shear is the mainmechanism leading to the instability of micro- and nanoparticle-ladenmultiphase flows. The Smoluchowski mean-filed theory is considered to be agood selection for solving this problem since it can be coupled to someturbulent models. In this study, the Taylor-expansion method of moments(TEMOM) is first applied in micro- and nanoparticle coagulation due toturbulent shear mechanism in which the closure of Smoluchowski equation aswell as the relationship between the numerical accuracy and the order ofTaylor series expansion are emphatically investigated. The result show thepartial 4-order Taylor expansion method of moments can be applied to analyzethe problem involving micro- and nanoparticle turbulent shear coagulationwith high accuracy, and the pseudo self-preserving size distribution isfound in micro- and nanoparticle-laden multiphase systems dominated byturbulent shear mechanism.