In this study, we approach a spherical particle in plane Couette fluid flow problem utilizing Adomian's decomposition method (ADM) as well as variational iteration method (VIM) to find a rapidly convergent power series solution. Equation of particle's motion in Couette flow considering the rotation and shear effects on lift force and neglecting gravity has been investigated by Vander Werff. The required time and distance for a spherical particle to reach terminal velocity trajectory of particle obtained which has application in transferring the medicine in blood in medical area or control of particles motion during spraying or injecting processes in industry. The precious contribution of the work is introducing a new fast and efficient solution of analytical methods in a spherical particle in plane Couette fluid flow over the previous numerical and analytical counterpart results in literature, while it is shown that both methods give approximations of a high degree of accuracy and least computational effort for studying particle motion in Couette fluid flow.

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