Chrysikopoulos ConstantinosΧρυσικοπουλος ΚωνσταντινοςScottC.James2024-10-312024-10-3120012015-09-18S. C.James, C. V. Chrysikopoulos , "An e cient particle tracking equation with speci%ed spatial step for the solution of the diffusion equation ", Chem.Engin. Sc,.vol. 56,no.23 ,pp. 6535–6543, 2001.doi :10.1016/S0009-2509(01)00344-Xhttps://dspace.library.tuc.gr/handle/123456789/1005The traditional di(usive particle tracking equation provides an updated particle location as a function of its previous location and molecular di(usion coe cient while maintaining a constant time step. A smaller time step yields an increasingly accurate, yet more computationally demanding solution. Selection of this time step becomes an important consideration and, depending on the complexity of the problem, a single optimum value may not exist. The characteristics of the system under consideration may be such that a constant time step may yield solutions with insu cient accuracy in some portions of the domain and excess computation time for others. In this work, new particle tracking equations speci%cally designed for the solution of problems associated with di(usion processes in one, two, and three dimensions are presented. Instead of a constant time step, the proposed equations employ a constant spatial step. Using a traditional particle tracking algorithm, the travel time necessary for a particle with a di(usion coe cient inversely proportional to its diameter to achieve a pre-speci%ed distance was determined. Because the size of a particle a(ects how it di(uses in a quiescent 8uid, it is expected that two di(erently sized particles would require di(erent travel times to move a given distance. The probability densities of travel times for plumes of monodisperse particles were consistently found to be log-normal in shape. The parameters describing this log-normal distribution, i.e., mean and standard deviation, are functions of the distance speci%ed for travel and the di(usion coe cient of the particles. Thus, a random number selected from this distribution approximates the time required for a given particle to travel a speci%ed distance. The new equations are straightforward and may be easily incorporated into appropriate particle tracking algorithms. In addition, the new particle tracking equations are as accurate and often more computationally e cient than the traditional particle tracking equation9 pagesenhttp://creativecommons.org/licenses/by/4.0/Peer-Reviewed Journal Publication