On the basis of phase-field theory, we develop a lattice Boltzmann model for ternary fluids containing solid. We develop a modified bounce-back method to describe the interactions between the solid and N-phase $(N\ge 2)$ fluids. We derive a wetting boundary condition for three-phase flows from the point of mass conservation and propose a scheme for implementing the wetting condition on curved boundaries. We develop a diffuse interface method to compute the capillary force acting on the moving solid objects at the ternary fluids-sold contact lines. In addition, this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. We test the modified bounce-back scheme, wetting boundary condition, and capillary force model in three different cases, and the numerical results agree well with the analytical solutions. Finally, we apply the model to two three-dimensional problems to assess its numerical accuracy and stability.

中文翻译：

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具有固体颗粒的三元流体的Lattice Boltzmann模型

基于相场理论，我们针对包含固体的三元流体建立了格子Boltzmann模型。我们开发了一种改进的反跳方法来描述固相和N相之间的相互作用$（ñ\ge 2）$液体。我们从质量守恒的角度推导了三相流的润湿边界条件，并提出了在弯曲边界上实施润湿条件的方案。我们开发了一种扩散界面方法来计算作用在三元流体-售出接触线上的移动固体物体上的毛细作用力。另外，该模型可以处理涉及高密度和粘度对比的问题。通过几个测试案例对提出的方法进行了研究。我们在三种不同情况下测试了修改后的反弹方案，润湿边界条件和毛细作用力模型，数值结果与解析解吻合得很好。最后，我们将该模型应用于两个三维问题，以评估其数值准确性和稳定性。