The motion of rigid particles embedded in a viscous fluid during pure shear deformation of the fluid

Abstract

Equations are derived to describe the motion of rigid, ellipsoidal particles, which are embedded in a viscous fluid matrix, during pure shear deformation of the particle-matrix system. The equations show that ellipsoids aligned parallel to either of the pure shear axes will not change their orientation during deformation, though they may increase or decrease in plunge. Particles in any other position will rotate towards the direction of elongation of the strain. Simultaneous with this rotation, the plunge of the major axis of the ellipsoid will increase until the ellipsoid is aligned at 45° to the strain axis, after which it will decrease. The rates of change of plunge and orientation increase with increasing particle eccentricity.