(354d) The Ideal Collision Rate and Effective Aspect Ratio of Cylindrical Particles in Simple Shear Flow

The collision of particles influences the behavior of suspension through the formation of aggregates of adhesive particles or the contributions of solid-body contacts to the stress in non-adhesive particles. The simplest estimate of the collision rate, termed the ideal collision rate, is obtained when particles translate and rotate with the flow but have no hydrodynamic or colloidal interactions. Smoluchowski calculated the ideal collision frequency of spherical particles in 1917. In this work we calculate the ideal collision rate for cylindrical particles over a broad range of particle aspect ratios r defined as the ratio of length to diameter. Monte Carlo simulations are performed with initial relative positions and orientations that model the rate of approach of non-interacting particles following Jeffery orbits with several choices of the orbit distribution. It is shown that the ratio of the collision rate of cylinders to those of spheres that circumscribe the cylinders is proportional to 1/rr_e and r_e for r>>1 and rr_e is the effective aspect ratio defined as the aspect ratio of a spheroid having the same period of rotation as the cylinder. The effective aspect ratio of the cylindrical particles was determined using finite element (COMSOL) calculations of the torque on non-rotating cylinders with their axes parallel to the velocity and velocity gradient directions. A boundary integral formulation for the limiting case of thin disks shows that the effective aspect ratio of a cylinder is proportional to r^1/2 for rr are in good agreement with the asymptotic scalings for both effective aspect ratio and collision rate. In addition to deriving the total collision rate, we categorize collisions as side-side, edge-side and face-edge based on the initial point of contact. In the limit of high aspect ratio, most collisions are found to be side-face suggesting that if particles stick at the point of first contact nonlinear aggregates will develop.