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In this paper, we propose and analyze a diffuse interface model forinductionless magnetohydrodynamic fluids. The model couples a convectiveCahn-Hilliard equation for the evolution of the interface, the Navier-Stokessystem for fluid flow and the possion quation for electrostatics. The model isderived from Onsager's variational principle and conservation lawssystematically. We perform formally matched asymptotic expansions and developseveral sharp interface models in the limit when the interfacial thicknesstends to zero. It is shown that the sharp interface limit of the models are thestandard incompressible inductionless magnetohydrodynamic equations coupledwith several different interface conditions for different choice of themobilities. Numerical results verify the convergence of the diffuse interfacemodel with different mobilitiess.

Sharp-interface limits of the diffuse interface model for two-phase inductionless magnetohydrodynamic fluids