Numerical simulations of the dynamics of axisymmetric compound liquid threads with a phase-field model

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.