Partitioning of vorticity in bimineralic rocks

A model for the rotational behaviour of flow in bimineralic rocks based on the concept of a multiphase continuum is developed here. An additive relation with respect to the vorticity is assumed. The ideal linear viscous bimineralic rocks are defined such that (i) both the bulk rock and the constituent phases have linear viscous rheology, (ii) the phases are uniformly mixed and distributed in the rock, and (iii) no segregation occurs during the deformation. The model reveals the partitioning of vorticity between the two phases in the ideal linear viscous bimineralic rocks. The model shows that there are two modes of flow behaviour. In mode 1 there is neither partitioning of strain rate nor vorticity; in mode 2 partitioning occurs for strain rate and vorticity. Mode 1 behaviour corresponds to upper bound behaviour and mode 2 to the lower bound behaviour. There are two solutions for the partitioning of vorticity in mode 2: type 1 and type 2 partitioning. In the type 1 partitioning the more viscous phase is more rotational than the less viscous phase, while in the type 2 partitioning the former is less rotational than the latter. In a special case where flow occurs by simple shearing and where the more viscous phase behaves as rigid particles, the following two cases occur: (1) the more viscous phase rotates at twice the rate of the bulk rock (type 1 partitioning), (2) the more viscous phase does not rotate at all with respect to the external reference coordinate (type 2 partitioning). The present model alone cannot predict which type will occur and further theoretical and experimental work is needed.