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The existing lattice Boltzmann models for incompressible multiphase flows aremostly constructed with two distribution functions, one is the order parameterdistribution function, which is used to track the interface between differentphases, and the other is the pressure distribution function for solving thevelocity field. In this brief report, it is shown that in these models therecovered momentum equation is inconsistent with the target one: an additionalinterfacial force is included in the recovered momentum equation. The effectsof the additional force are investigated by numerical simulations of dropletsplashing on a thin liquid film and falling droplet under gravity. In theformer test, it is found that the formation and evolution of secondary dropletsare greatly affected, while in the latter the additional force is found toincrease the falling velocity and limit the stretch of the droplet.

Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows