where s Γ
2r/(a i / a j ) is the dimensionless distance between the centers of the two spheres, while a i and a j are radii of sphere i and sphere j,
The rate of gravity-induced coagulation of a dilute polydisperse respectively. L(s) and M(s) are longitudinal and transverse scalar functions suspension of small particles is considered by incorporating graviof the relative gravitational velocity of the two spheres. G(s) is a longituditational and interparticle forces (both attractive and repulsive), nal scalar function of the relative Brownian diffusivity. L(s), M(s), and as well as hydrodynamic interactions. When electrostatic repulsion G(s) can be calculated by using the mobility functions obtained by Jeffrey is significant, particles can coagulate into either a primary or secand Onishi (4). Q ij Γ
pgDra 4 i (1 / l) 2 (1 0 l 2 )/3A describes the relative ondary minimum (as described by DLVO theory), or remain disimportance of gravitational to attractive forces, where g is the local accelera- persed. Spherical sols can be unstable at low and high gravitational tion of gravity, Dr is the density difference between the particles and the forces, but stable against gravity-induced coagulation at intermedisuspending medium, l Γ
a j /a i is the particle size ratio, and A is the compos- ate and higher values when Brownian motion can be neglected. ite Hamaker constant. N r Γ
1C 2 0 (a i / a j )/2A describes the relative impor-