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$\le 50$), Eötvös number (Eo$\le$200), density ratio ($\Phi \le 1000$), SPH resolution size ($\Delta x\le 1/500$), and the ratio between cavity width and the bubble diameter ($\beta \le 8$). 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.

这项工作提出了在粘性液体中气泡上升的两相流模拟的数值研究。通过平滑粒子流体动力学（SPH）使用2D模型。必须考虑液体/气泡的毛细管相互作用，在界面处实现足够的密度，粘度和表面张力特性。同样地，根据末端气泡形态，利用文献中的数值和实验测量值对仿真结果进行评估。这些结果的特征在于动态参数的变化，例如雷诺数（Reynold$\le 50$），Eötvös号码（Eo$\le$200），密度比（$\Phi \le 1000$），SPH分辨率大小（$\Delta X\le \mathrm{1个}/500$），以及腔体宽度与气泡直径之间的比率（$\beta \le 8$）。因此，探索了单个气泡上升时侧壁的独立性，这些结果显示了圆形，椭圆形和帽形之间的不同形状和涡旋状态。此外，在具有横向不稳定性（例如，尾部，破裂和卫星气泡形成）的所有情况下，都显示了在侧壁的高或低影响期间气泡变形的行为。最后，证明了双相SPH算法足够鲁棒，可以提供有关单个上升气泡的全局典型特征的定性和定量信息。