A mixture model to take into account the flow of small carbon dioxide bubbles dissolved in a liquid is presented. The model describes the evolution of the velocity fields (mixture and gas), the pressure and the volume fraction of gas. The system of equations is derived from mass and momentum conservation of the mixture and gas.

Well-posedness is proved for a simplified problem when the volume fraction of gas is known and small. A priori error estimates are proved for a stabilized finite element approximation.

An industrial application pertaining to aluminium electrolysis is presented. Numerical results indicated that the effect of gas bubbles on the flow cannot be neglected.

提出了一种混合模型，该模型考虑了溶解在液体中的小二氧化碳气泡的流动。该模型描述了速度场（混合物和气体），压力和气体体积分数的变化。方程组源自混合物和气体的质量和动量守恒。

当气体的体积分数已知且很小时，就可以为简化的问题证明适定性。对于稳定的有限元逼近，证明了先验误差估计。

提出了与铝电解有关的工业应用。数值结果表明，气泡对流动的影响不可忽略。