In this paper we computationally examine the motion of a dilute suspension of slightly non-neutrally buoyant solid spheres as they migrate across the curved fluid streamlines of a viscous cellular flow. This is done by incorporating particle-fluid interactions into a continuum-based Lagrangian advection model derived from the Basset–Boussinesq–Oseen (BBO) equation, where the flow field is mimicked by using a perturbed streamfunction. Although the purely regular cellular flow is able to capture maximum velocity and particle diameter effects that are observed experimentally, it has several shortcomings. Most significantly, it is unable to capture the secondary island structures that exist in many rotating flow systems, nor the impact that these structures are observed to have on particle migration. Our results in this work demonstrate significant interplay between the underlying fluid structure and the non-trivial equilibrium locations of the non-Brownian particles, in agreement with previous experimental work. We also evaluate the effect of the Saffman lift force on the lateral migration of the solid spheres.