HYDRODYNAMIC PAIR DIFFUSION IN ISOTROPIC RANDOM VELOCITY-FIELDS WITH APPLICATION TO TURBULENT COAGULATION

Diffusion and coagulation are investigated in a random, isotropic flow in the presence of hydrodynamic interactions, interparticle forces, a nd Brownian diffusion. Different strain and rotation rate time scales characterize the velocity field and the particles are assumed small co mpared with the characteristic length of the flow, so that the velocit y field is linear in the vicinity of the particles. The pair probabili ty equation for the relative motion of two particles is written in ter ms of a diffusion tensor and a drift velocity. This technique is valid in the limit of small strain, i.e., when the product of the character istic velocity gradient and time scale of the fluctuating velocity gra dient is small. A consequence of the drift velocity is that, at steady state in a noncoagulating system, the pair probability distribution i s nonuniform when hydrodynamic interactions are included, and there is a higher probability of particle pairs at close proximity. The pair p robability conservation equation is used to determine the coagulation rate both without and with consideration of interparticle interactions . The stability factor, W, is the ratio of the coagulation rate in the absence and presence of interparticle forces, and W is calculated num erically for different size particles influenced by van der Waals attr action, electrostatic repulsion, hydrodynamic interactions, and Browni an motion. A semi-analytical expression is derived that is valid for l arge particles that are not influenced by Brownian motion and that exp erience weak van der Waals attraction. The analysis shows that colloid al stability increases with increasing particle size and shear rate as a result of the hydrodynamic resistance to particle-particle collisio n. Double layer repulsion can lead to stable colloidal suspensions, bu t increasing the fluid shear can reduce this effect. Colloid stability for the randomly varying flow considered here is comparable to that o btained for steady linear flows, such as simple shear when only van de r Waals attraction is considered. Compared with the steady linear flow s, double layer repulsion imparts additional resistance to aggregation in the randomly varying flow. The relevance of applying this analysis to coagulation in isotropic turbulent flows is discussed. (C) 1997 Am erican Institute of Physics.