The behaviour of deformable and non-deformable inclusions in viscous flow

Many are the situations in Geology in which non-deformable and deformable inclusions are carried about in suspension by the motion of a fluid, or a rock behaving like a fluid. Therefore, it is of crucial importance to Geosciences to understand the rotational behaviour of inclusions in viscous flow, and the effects in the matrix deformation. A major step was given by Jeffery (1922), who provided approximate analytical solutions that have been extensively used to describe how rigid spheroids rotate in homogeneous flows. He considered isolated inclusions in no-slip contact with an infinite width matrix. However, in a great variety of geological processes, flow can be confined, the inclusion can deform, the inclusion/matrix interface can be slipping, or inclusions can interact with neighbours. By analytical, experimental analogue, and numerical modelling it has been shown how inclusions rotate, how the surrounding matrix flows, how pressure and velocity control rigid inclusion behaviour, and how the models can be applied to geological processes. Modelling has shown that: (1) for wide channels (ratio Wr of channel width over inclusion least axis length > 10) and non-slipping interface, results agree with Jefferyʹs model, while for narrow channels (Wr < 5) or slipping interface the results deviate greatly from Jefferyʹs model. (2) For narrow channels or slipping interface, inclusions with aspect ratio Ar (greatest over least principle axis) > 1 can rotate backwards (antithetic rotation, against flow vorticity) from an initial orientation ϕ = 0° (greatest principle axis parallel to the shear plane), in great contrast to Jefferyʹs model. (3) Back rotation is limited because inclusions reach a stable equilibrium orientation (ϕse) at shallow positive angles (0° ≤ ϕ < 90°). (4) There is also an unstable equilibrium orientation (ϕue), which defines an antithetic rotation field with ϕse, and both ϕse and ϕue depend on confinement and inclusion aspect ratio and shape. (5) The flow around rigid inclusions is greatly perturbed by confinement or slipping interface, and a new flow pattern (cat eyes-shaped) has been described. (6) The numerical models provide detailed and coherent information about the physical parameters involved in the process (e.g. pressure and velocity distributions within the model), which helps to explain inclusion behaviour. (7) The existing models can be used to quantify important parameters that characterise ductile shear zones.