The software to calculate flow field based on Stokes equation based on Eq. 21 shown in Fig. 2 and Supplementary Figure S4, based on the data of rho at the interface. You need to comple raw2txt.cc file with any C++ compiler, which generates sequential text file under text folder. The executable file i.e. a.out require one argument, which is supposedly *_v.raw file. This creates velocity profile at the interface. Then you have to run input.edp with FreeFEM++ version 4.8 Then the data under ./test/ will be automatically loaded as the velocity at the boundary of circular domain. The flow inside of the circular region is automatically created. This takes approximately 3 minutes.