BROWNIAN DYNAMICS SIMULATIONS OF A 2-D SUSPENSION OF CHARGED COLLOIDAL PLATES UNDER SHEAR

Numerical simulations of a 2-dimensional suspension of charged clay particles are presented. The plate-like particles, of dimension 2a x 2a and zero thickness, are confined to lie in a single monolayer, within a unit cell across which periodic boundary conditions are applied. Shear is imposed, and the hydrodynamic forces on each particle are the Stokes drag and couple on an isolated plate: hydrodynamic interactions between the plates are ignored. Inertia is assumed negligible: at each timestep the particle velocities are such that the hydrodynamic drag and couple balance the electrical double layer forces acting on each particle. Brownian motion is included via a simplified Brownian Dynamics algorithm. The charges on the plates are represented by a series of discrete charges, each surrounded by an electrical double layer with a Debye length kappa-1 (with kappa-1 = a). If these charges are all identical, the particles repel each other. Small liquid-crystal-like ordered domains are formed, and long-range ordering can be induced by shear. If the sign of the edge charge on each particle is reversed, the particles can flocculate to form a gel, which spans the unit cell. At low rates of shear a single shear band appears in the gel, and as the rate of shear is increased the typical floc size is reduced. The shear stress sigma(x,y) normal stress difference sigma(xx) - sigma(yy), and electrical free energy are studied as a function of the ratio of the viscous forces on each particle to the thermal and electrical forces. The results are generally in accord with intuitive expectations. However, the particles are confined to a monolayer, and points of contact between flocculated particles are freely hinged. The consequent absence of rigid 3-dimensional structures leads to weak flocs. These unravel to form linear structures, which align with the shear flow. Thus the flocculated gel rapidly shear-thins. The 2-dimensional model appears inadequate in this respect, and 3-dimensional simulations are required.