Here we present the results of the newly developed Eulerian-Lagrangian model to simulate both the primary and the secondary phases coupled in a transient analysis. A set of two a-dimensional, transient linear shear flow at low Reynolds numbers was considered, and the effect of shearing rate on a suspended buoyant spherical solid particle was analyzed. The rotation and displacement of the solid particle are considered in the model, and the effect of the secondary phase on the primary phase is also evaluated at each time step without any simplification. In order to overcome the existing discontinuity at the interface between secondary and primary phases in this Eulerian-Lagrangian approach, the interface between the solid particle and the fluid phase is replaced by a kernel function creating a smooth profile from the solid into the liquid with a predefined thickness. Several simulations were performed, and the reliability of the developed model was assessed. The global deviation grid convergence index (GCI) approach was employed to perform solution verification. The observed order of accuracy of the primary phase solver approaches 2, consistent with the formal order of accuracy of the applied discretization scheme. The obtained velocity profiles from the computational analyses show excellent agreement with the analytical solution confirming the reliability of the single-phase flow solver. To validate the computational results for the multiphase flow solver, we used the experimental data from our newly developed linear shear flow apparatus with suspended buoyant particles.