The microrheology of colloidal dispersions: IV. Pairs of interacting spheres in shear flow

Abstract

The effect of interaction forces on the trajectories of pairs of equal-sized spheres in shear flow is calculated. Depending on the functional form of the interaction potential there are three modes of behavior: (i) the spheres can collide and form a touching doublet, (ii) they can be captured in an energy minimum, orbiting around each other after capture, or (iii) the interactions are transitory and the spheres separate. For interactions determined jointly by van der Waals attraction and electrostatic repulsion, we have calculated the conditions under which (i) touching doublets from (i.e., in the so-called primary energy minimum) and the system coagulates, (ii) nontouching doublets form (in a secondary minimum) and the system flocculates, or (iii) no permanent doublets form and the system is stable. The results indicate that when Brownian motion can be neglected, dilute spherical sols can be unstable at low and high shear rates, but stable in between.