the rate of coagulation is largely controlled by the rate of We consider a dilute homogeneous suspension of rigid spheridoublet formation, and it is this quantity that we seek to cal particles with different size and density in a motionless Newdetermine. tonian fluid. These particles are moving under gravity at low Significant progress has been made in the understanding Reynolds and Stokes numbers ( negligible fluid and particle inerof relative trajectories and rates of collision since Saffman tia ) and high Pe Β΄clet numbers ( negligible Brownian diffusion ) . and Turner (1) estimated the rate of gravity-induced coagu-Doublets are formed when two particles in relative motion are lation of rigid spheres neglecting both hydrodynamic interacbrought into contact by the action of the attractive van der Waals tion and interparticle forces other than a sticking force upon force. Trajectory calculations for particles with different densicontact. Hydrodynamic interaction and the van der Waals ties indicate that as the reduced density ratio increases above unity, the percentage of particles captured on the front hemi-force have been considered by Davis ( ), Melik and Fogler sphere decreases, and this generally results in smaller collision (3), and Han and Lawler (4), who calculated collision effiefficiencies. Furthermore, in contrast to the case of particles with ciencies between two rigid spherical particles using a trajecequal density, a maximum of the collision efficiency occurs for tory analysis. Similar results have been obtained by Wen and a particle size ratio smaller than unity. Above a critical value of Batchelor (5) and Wen et al. (6), who found an approximate the reduced density ratio, the occurrence of a closed region of analytical equation relating the pair-distribution function for relative trajectories confines the capture sites mostly to the a dilute dispersion to the collision efficiency. However, the ''rear'' hemisphere of each particle. As the reduced density ratio results given in these studies for noninertial particles of difincreases above the critical value, this region grows larger and ferent size are restricted to the case in which the particles the collision efficiency may be estimated by a closed-form asymphave the same density.
totic solution.