This work presents a numerical study of the simulation of bi-phasic flow for a bubble rising in the viscous liquid. A 2D model is employed via Smoothed Particle Hydrodynamics (SPH). The liquid/bubble capillary interaction must be taken into account, implementing adequate properties of density, viscosity, and surface tension at the interface. Likewise, the simulation results are evaluated with numerical and experimental measurements from the literature in terms of terminal bubble morphology. These results are characterized by the variation of the dynamic parameters, such as the Reynold number (Re), Eötvös number (Eo200), density ratio, SPH resolution size, and the ratio between cavity width and the bubble diameter. Consequently, it is explored the independence of sidewalls on a single bubble rising, these results display different shapes and vortex regimes between the circular, ellipsoidal, and cap morphologies. Furthermore, The behavior of the bubble deformations during the high or low influence of sidewall is shown throughout cases with lateral instabilities, such as tails, break-up, and satellite bubble formation. Finally, It is demonstrated that the bi-phase SPH algorithm is robust enough, providing qualitative and quantitative information about global typical characteristics of a single rising bubble.
