Designing plant to sterilise two-phase food mixtures in flow is complicated by velocity gradients in the liquid and slip velocities between solid and liquid. The model of Mankad et al. (1995 Chem. Engng Sci. 50, 1323-1336) for the effect of particle-liquid slip on a homogeneous food flow has been extended to the case of heterogeneous flows. It has been used to model a stratified flow through a combination of a heating and holding tube over a range of process conditions : flows where velocity differences are minimised appear best in terms of minimal process time. More data on the behaviour of real flows are needed.