When some fluid components are absent from N (N $\ge$ 2) immiscible fluids, the reduction-consistent property should be guaranteed. In phase-field theory, the evolution of fluid–fluid interface in N immiscible fluids can be captured by a reduction-consistent Cahn–Hilliard equation (CHE), which has a variable dependent mobility. However, it is difficult for lattice Boltzmann equation (LBE) method to solve this kind of CHE with variable mobility. To eliminate this issue, in this paper, a reduction-consistent LBE is proposed for N immiscible fluids. In the model, the reduction-consistent formulation of fluid–fluid interface force is reformulated into a chemical potential form, which can be implemented by a force term in LBE, while a source term treatment is used to achieve the reduction-consistent property for CHE. Numerical simulations of spreading of a liquid lens, spinodal decomposition, and dynamic interaction of drops are carried out to validate present LBE, and the results show the accuracy and capability of present phase-field based LBE for $N$ ($N\ge 2$) immiscible fluids.

当N（N $\ge$2）不混溶的流体，应保证还原一致性。在相场理论中，N-不混溶流体中流体-流体界面的演化可以通过还原一致的Cahn-Hilliard方程（CHE）捕获，该方程具有随变量变化的迁移率。然而，晶格玻尔兹曼方程（LBE）方法很难解决这种具有可变迁移率的CHE。为了消除这个问题，在本文中，针对N提出了一个还原一致的LBE。不混溶的液体。在该模型中，将流体-流体界面力的折减一致公式化为化学势形式，可以通过LBE中的力项来实现，同时使用源项处理来实现CHE的折减一致属性。 。进行了液体透镜散布，旋节线分解和液滴动态相互作用的数值模拟，以验证当前的LBE，结果表明，基于当前相场的LBE的准确性和能力$ñ$ （$ñ\ge \mathrm{2个}$）不混溶的液体。