Rigid Particles in Simple Shear Flow: Is Their Preferred Orientation Periodic or Steady-State ?

Abstract

The theory of the rotation of isolated rigid particles within a linearly viscous fluid deforming in progressive simple shear is often invoked in models of Shape Preferred Orientations (SPO) of crystals in igneous rocks. A classical result of the theoretical model is that the SPO should rotate and pulsate with increasing strain, with a periodicity equal to that of the rotation of an individual particle. However, the initial theoretical model makes a large number of assumptions, many of which are unlikely to be satisfied by actual crystalline suspensions in magmatic melts. The purpose of this note is to review three of the reasons why periodicity of rigid particle SPO may not really be expected in igneous rocks: (i) SPO in igneous rocks are generally defined by suspensions of crystals that are concentrated enough to allow mechanical interactions between the crystals; (ii) the porphyroblast/matrix interface may not always be coherent; and (iii) the aspect ratios of the crystals defining the SPO are unlikely to be unique and constant, as assumed in the model. The last point is discussed on the basis of some 2D simple calculations of the development of SPO defined by different types of heterogeneous populations of particles. The combined effects of these deviations from the standard model point to two fundamental conclusions: (i) there is no simple relationship between fabric and finite strain, and (ii) the SPO in magmatic rocks may be considered as good markers of the flow, whatever the significance of the inferred flow pattern in terms of geodynamics and/or emplacement processes.