Wangyi Liu, Andrea L. Bertozzi, Theodore Kolokolnikov
摘 要
We consider a diffusive interface surface tension model under compressible fl ow. The equation of interest is the Cahn-Hilliard or Allen-Cahn equation with advection by a non-divergence free velocity field. 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.
作 者
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