High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by Multi-step Differential Transformation Method

In this study, coupled equations of particleʹs motion in Couette fluid flow are solved by Multi-step Differential Transformation Method (Ms-DTM) considering the rotation and shear effects on lift force and neglecting gravity. The precious achievement of the present work is introducing a new, fast and efficient analytical technique for spherical particles in plane Couette fluid flow over the previous numerical and analytical results in the literature. Also, obtained values are compared with numerical solution and HPM–Pade which recently are done by Torabi et al. It is shown that presented method gives approximations with a high degree of accuracy and least computational effort for studying particle motion in Couette fluid flow without the need for any linearization, discretization or perturbation against the previous work. Also, the acceleration profiles of the particle are presented and positions of the particle in each 1 s time step are depicted graphically in the current study.