Simulating Combined Translation and Rotation of Arbitrary Shaped Aerosol Particles using Hamilton's Quaternions
MRITTIKA ROY, Zhibo Liu, Ranganathan Gopalakrishnan,
University of Memphis Abstract Number: 626
Working Group: Aerosol Physics
AbstractWe simulate the trajectory of an arbitrary shaped aerosol particle made up of identical point-contacting spheres in three dimensions considering both translational and rotational degrees of freedom. To model motion in vacuum, we solve Newton’s second law of motion for translation and Euler’s equation for rigid body rotation. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to eight ordinary differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape, whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. The equations of combined rotation and translation are solved using the fourth-order Runge-Kutta scheme. For validation, computations of the orientation-averaged projected areas for agglomerate pairs are compared with the calculations of Thajudeen et al. (Aerosol Science and Technology, 46:11, 1174-1186). To include particle Brownian motion and hydrodynamic resistance when a particle moves in a gas, a Langevin formulation of the translation and rotation equations is used. We calculate the translational and rotational friction factors for an aerosol particle using the Extended Kirkwood-Risemann method developed by Corson et al. (Physical Review E 96(1): 013110, Physical Review E 95(1): 013103). Previously, Thajudeen et al. developed an expression for the coagulation rate constant between two agglomerates without explicitly considering rotation. Using the developed computational procedure, we are currently investigating the effect of particle rotation on coagulation dynamics.