Abstract
This study presents an analytical model describing the transport of a single particle on a horizontal annular sieve subjected to harmonic rotational oscillations about a vertical axis. Unlike conventional models developed for linear or planar vibration trajectories, the proposed formulation captures the coupled radial–tangential motion induced by rotational excitation and centrifugal effects. The governing equations of the particle's relative motion are derived using a phase-based approach and reformulated in dimensionless form to reveal the balance between inertial driving forces and frictional resistance. A dimensionless criterion is established to predict the onset and cessation of sliding, demonstrating that single-particle transport occurs in a cyclic stick–slip regime. Closed-form analytical expressions for the particle's displacement, velocity, and trajectory are obtained using a stepwise integration method. An explicit analytical expression for the critical transport radius is derived, providing a direct design parameter for annular vibrating sieve systems. The model predicts a nonlinear increase in the particle transport velocity with oscillation frequency, oscillation amplitude, and radial position. Experimental validation demonstrates good agreement with the analytical predictions: for most operating conditions, the relative deviation does not exceed 10%, while the maximum observed deviation is about 16%. The proposed model provides a compact analytical framework for predicting single-particle transport and can serve as an efficient engineering tool for the analysis, design, and optimization of rotational vibrating screening systems.