Influence of Strain-Rate on Coagulation Kinetics

Abstract

The nature of hydrodynamically induced particle collisions in orthokinetic coagulation is examined. For a discrete region of fluid that is exposed to linear velocity-gradients the frequency of collisions between particles is shown to be a function of the strain rates acting on the volume element of fluid containing the particles. Through transformation of the strain-rate tensor by diagonalization into principal components, a new scalar value is obtained that accurately estimates the total collision rate. This value, the absolute maximum principal strain-rate, is used in conjunction with a new collision-frequency function derived for the normal strain rates to yield an accurate relation for orthokinetic coagulation. The new method is contrasted with estimates of a global average velocity-gradient based on energy dissipation and power input to the fluid system. It is also shown that the square root of the dissipation function is not directly proportional to the velocity-gradient and that a global average of the energy dissipation function does not represent a mean-square velocity-gradient.