We numerically study the dynamics of axisymmetric compound liquid threads with a phase-field model. Compound threads consist of a middle annular thread enclosing an inner core liquid and surrounded by an outer immiscible liquid. The model is composed of the Navier–Stokes equation, including a surface tension force term, and the convective ternary Cahn–Hilliard system. The finite difference method is used to discretize the governing equations and the resulting discrete equations are solved by using a multigrid method. A variety of numerical tests are performed to investigate the effects of inner and middle liquid radii, viscosity ratio, surface tension ratio, initial amplitude, and evolution mode on the dynamics of the axisymmetric compound liquid threads. We find that a larger inner fluid radius delays the evolution, a larger middle fluid radius suppresses the formation of double droplets, the evolution of compound liquid threads is delayed if we increase the viscosity ratio or surface tension ratio. Furthermore, a squeezing mode produces a more complex evolution process than a stretching mode.

我们用相场模型数值研究了轴对称复合液体线的动力学。复合线由中间的环形线组成，其中包含内核液体并被外部不混溶液体包围。该模型由 Navier-Stokes 方程（包括表面张力项）和对流三元 Cahn-Hilliard 系统组成。有限差分法用于离散化控制方程，所得离散方程使用多重网格法求解。进行了各种数值试验，以研究内外液体半径、粘度比、表面张力比、初始振幅和演化模式对轴对称复合液体线动力学的影响。我们发现较大的内部流体半径会延迟演化，较大的中间流体半径抑制双液滴的形成，如果我们增加粘度比或表面张力比，则复合液体线的演化会延迟。此外，挤压模式比拉伸模式产生更复杂的演化过程。