A New Method of Moments for the Bimodal Particle System in the Stokes Regime

Abstract

The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM) should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for $m_0$ and 4% for $m_2$. The detailed distribution of each submodal could also be investigated through current model.