Drop coalescence simulation using phase field method with discrete exterior calculus discretization*

We present two spherical drops coalescence simulations by using the phase field method with

discrete exterior calculus (DEC) discretization. Motivated by the fact that two spherical drops

coalescence phenomena are axisymmetric, we extend our previous work, DEC scheme for

2D two-phase incompressible Navier-Stokes equations (Wang et al., 2022), to axisymmetric

incompressible two-phase flow. In our simulation, two drops are stationary and touch each

other initially, and they coalesce rapidly, due to large interface curvature and surface tension

force in the neck region formed upon coalescence. Several drop coalescence simulations are

presented to investigate its interface evolution under various Ohnesorge numbers Oh. The

evolution of the drop neck radius R yields two well-known power-law scaling in viscous and

inertial regimes, respectively, and our simulations reproduce these two power-law scalings.

For the inertial regime (high Oh), the neck radius evolution has the 1/2 power-law scaling, and

the inertial regime transition to the viscous regime by increasing Oh, in which the neck radius

evolution has linear scaling.