This work presents a new experimental-numerical method combining PIV (particle image velocimetry), digital image analysis, and FEM (finite element method) to obtain gas and particle motion around bubbles in a 2D freely bubbling fluidized bed. The bubble geometry is captured with a high speed video camera while the particle velocity is measured using a PIV technique. These experimental data are exported to a finite element software where the pressure and gas velocity fields are obtained numerically. The flow equations proposed by Davidson's model have been chosen to exemplify the application of the method presented in this paper. Different bubble types have been analyzed: slow and fast bubbles but also erupting and interacting bubbles. The effect on the gas flow of bubbles with a nonzero horizontal velocity component has also been analyzed, and it is shown how such bubbles interchange gas with the main stream. In addition, the Darcy's law included in Davidson's model has been extended including a quadratic term (i.e., Ergun's equation) to take into account non-Darcy effects and the PIV results have been used to evaluate the error committed when voidage variation around bubbles is neglected. The results obtained including non-Darcy effects show differences in the gas velocity magnitude in regions near the nose and the wake of the bubble, where the gas velocity and, consequently, the local Reynolds number are higher. Nevertheless, these local differences give no significante difference in the gas streamlines around bubbles. Finally, the study of the voidage variation around bubbles shows that this variation is important only in a region,of small thickness adjacent to the bubble.