Jump Discontinuity Equations in Cake Filtration

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Abstract
Jump discontinuity balances in continuum theory are well known and are frequently applied in the literature for single-phase systems. Jump discontinuity balances between dispersed multiphase regions have been derived for multiphase volume averaging continuum theory. However, multiphase region jump balances have not received comparable attention in the literature in multiphase applications. In this work the continuum equations and jump balances are summarized and compared for the cake filtration and cake drainage processes under air pressure. The comparison shows the jump conditions for the fluid and solid phases are easily decoupled in cake filtration. On the other hand, during the drainage process the mass discontinuity balances for the gas and liquid phases are coupled if there is significant mass transfer between the phases at the drainage boundary. Furthermore, the momentum discontinuity balances are also coupled when the capillary forces are significant.

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