The Collision Rate of Nonspherical Particles and Aggregates for all Diffusive Knudsen Numbers

We examine theoretically and numerically collisions of arbitrarily shaped particles in the mass transfer transition regime, where ambiguities remain regarding the collision rate coefficient (collision kernel). Specifically, we show that the dimensionless collision kernel for arbitrarily shaped particles, H, depends solely on a correctly defined diffusive Knudsen number (Kn(D), in contrast with the traditional Knudsen number), and to determine the diffusive Knudsen number, it is necessary to calculate two combined size parameters for the colliding particles: the Smoluchowski radius, which defines the collision rate in the continuum (Kn(D) -> 0 ) regime, and the projected area, which defines the collision rate in the free molecular (Kn(D) -> infinity) regime. Algorithms are provided to compute these parameters. Using mean first passage time calculations with computationally generated quasifractal (statistically fractal) aggregates, we find that with correct definitions of H and Kn(D), the H(Kn(D)) relationship found valid for sphere-sphere collisions predicts the collision kernel for aggregates extremely well (to within +/- 5%). We also show that it is critical to calculate combined size parameters for colliding particles, that is, a collision size/radius cannot necessarily be defined for a nonspherical particle without foreknowledge of the geometry of its collision partner. Specifically for sequentially produced model aggregates, expressions are developed through regression to evaluate all parameters necessary to predict the transition regime collision kernel directly from fractal descriptors.