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5.6 · Microscopic Shear Sense Indicators in Mylonite 137

Box 5.4 Rigid objects in a ductile matrix – theory
Research into development of porphyroclasts and mineral fish is of rigid objects is mostly dependent on their length-width ratio,
still in progress. This section aims to give an overview of the fac- and much less on their actual rectangular, rhomboid or elliptical
tors that are presently thought to play a role in their development shape (Jeffery 1922; Ghost and Ramberg 1976; Arbaret et al. 2001).
(Passchier and Simpson 1986; vandenDriessche and Brun 1987; Even if objects do not obtain a true stationary position, the vari-
Passchier et al. 1993; Passchier 1994; Pennacchioni et al. 2000; able rotation rate may cause a statistical preferred orientation of
Biermeier et al. 2001; Ceriani et al. 2003). elongate objects with orientation and strength that depend on fi-
A spherical rigid object with perfect bonding between object nite strain and vorticity number (Fig. B.5.3; Passchier 1987; Masuda
and a homogeneous extensive matrix in a non-coaxial flow will et al. 1995c; Piazolo et al. 2002; Marques and Coelho 2003).
rotate with respect to flow-ISA with an angular velocity of half An additional complication arises when rigid objects are close
the shear strain rate, just as a paddle wheel inserted in a flowing together, or are close to a non-deforming wall rock. In that case,
river (Jeffery 1922; Fig. B.2.3). However, even if the strain rate and objects may rotate more slowly, become irrotational or even show
vorticity of the flow are constant, the angular velocity of a rigid antithetic rotation (Marques and Coelho 2001; Biermeier et al.
object will be fluctuating if the object is not a sphere (Fig. B.5.1, 2001). Series of objects can also become stationary in a tiling ar-
×Video B.5.1a,b; Ghosh and Ramberg 1976; Passchier 1987b). rangement (Fig. 5.48; Ildefonse et al. 1992a,b; Tikoff and Teyssier
Elongate objects will accelerate and decelerate with changing ori- 1994; Mulchrone et al. 2005).
entation and, if the vorticity number is between that for pure and Another scenario is that the central object has higher viscos-
simple shear, may even become stationary in the flow when they ity than the matrix, but is not rigid. In such cases, the central
exceed a critical aspect ratio (Figs. B.5.1, B.5.2, B.5.6, ×Video B.5.2; object may be deforming while it rotates, which can lead to com-
Ghosh and Ramberg 1976; Freeman 1985; Passchier 1987b; Jezek plex rotational behaviour and either permanent or pulsating
et al. 1994; ten Brink 1996; Arbaret et al. 2001). In simple shear, deformation of the central object (Passchier and Sokoutis 1993;
however, all rigid objects with perfect bonding to the matrix ex- Piazolo and Passchier 2002a; Fig. B.5.4). The same applies to
cept material lines rotate permanently. The rotational behaviour an object that is weaker than the matrix (Treagus and Lan 2003),

Fig. B.5.1. Rotational behaviour of rigid objects in simple shear flow and several types of general flow. Shear strain component of the
deformation γ is given on the horizontal axis, orientation of the objects on the vertical axis. With increasing aspect ratio (R), objects
show increasingly oscillating angular velocity in simple shear. In general flow, objects with an aspect ratio higher than a critical value
can reach a stable position and rotate no further. W k is the kinematic vorticity number (Sect. 2.5.2). (Calculations by Sara Coelho)