Influence of a low-viscosity layer between rigid inclusion and viscous matrix on inclusion rotation and matrix flow: A numerical study

We have used 2-D finite element modelling to investigate the influence of a permanent low-viscosity layer between matrix and inclusion on matrix flow and inclusion rotation under viscous simple shear flow. Rigid inclusions of different shape (circle, square, ellipse, lozenge, rectangle and skewed rectangles) and aspect ratio (R) were used. The calculated matrix flow pattern is neither bow tie nor eye-shaped. It is a new flow pattern that we call cat eyes-shaped, which is characterized by: (i) straight streamlines that slightly bend inwards at the inclusion's crests; (ii) elongate eye-shaped streamlines on each side of the inclusion; (iii) stagnation points in the centre of the eyes; (iv) absence of closed streamlines surrounding the inclusion; (v) changes in flow configuration with inclusion orientation; the lines of flow reversal bend and tilt, closed streamline circuits may disappear, and streamlines may bend outwards at the inclusion's crests.Concerning inclusion rotation, the numerical results show that: (i) a low-viscosity layer (LVL) makes inclusions with R = 1 rotate synthetically, but the rotation rate depends upon shape (circle or square) and orientation. Therefore, shape matters in the slipping mode. (ii) All studied shapes with R > 1 rotate antithetically when starting with the greatest principal axis (e₁) parallel to the shear direction ( = 0°); (iii) rotation is limited because there is a stable equilibrium orientation (_se) for all studied shapes with R > 1. (iii) There is also an unstable equilibrium orientation (_ue), and both _se and _ue depend upon inclusion's R and shape.The present numerical results closely agree with previous results of analogue experiments with a permanent low viscosity interface. Only minor deviations related with small shape differences were detected.