Diffuse Interface Surface Tension Models in an Expanding Flow
نویسندگان
چکیده
We consider a diffusive interface surface tension model under compressible flow. The equation of interest is the Cahn-Hilliard or Allen-Cahn equation with advection by a non-divergence free velocity field. These are two reduced models which show important properties of the full-scale surface tension model. We prove that both model problems are well-posed. We are especially interested in the behavior of solutions with respect to droplet breakup phenomena. Numerical simulations of 1, 2, and 3D all illustrate that the Cahn-Hilliard model is much more effective for droplet breakup. Using asymptotic methods we correctly predict the breakup condition for the Cahn-Hilliard model. Moreover, we prove that the Allen-Cahn model will not break up under certain circumstances due to a maximum principle.
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