A further discussion on basic equations for two-phase flow: On collision stress of solid phase

The following points are argued: (i) there are two independent kinds of interaction on interfaces, i.e. the interaction between phases and the collision interaction, and the jump relations on interfaces can accordingly be resolved; (ii) the stress in a particle can also be divided into background stress and collision stress corresponding to the two kinds of interaction on interfaces respectively; (iii) the collision stress, in fact, has no jump on interface, so the averaged value of its derivative is equal to the derivative of its averaged value; (iv) the stress of solid phase in the basic equations for two\|phase flow should include the collision stress, while the stress in the expression of the inter\|phase force contains the background one only. Based on the arguments, the strict method for deriving the equations for two\|phase flow developed by Drew, Ishii et al. is generalized to the dense two\|phase flow, which involves the effect of collision stress.