Particle characteristics in a multi-phase Newtonian flow - Nzerem*†, F.E.; Ugorji*, H.C. (International Journal of Mathematical Analysis and Modelling, 2023)
The flow pattern associated with a multi-phase fluid is the fluid-mediated inter-particle collision, or the exertion of forces on the fluid by the colliding particles. The solid phase is reasonably dispersed but admits collision as a result of either some fluid behaviour or some spatial consideration or both. For some applicable purposes, there may be the need to track a particle’s instantaneous position as it is being buffeted during flow. The knowledge of the position, together with a collision history, is critical to predictions concerning the general behaviour of motion. The uncertainty in determining such leads to the recourse to the stochastic differential equation that governs the random stochastic dynamic system - the stable Ornstein-Uhlenbeck process (OUP). A given flow path characterized by the OUP is amenable to the dynamical equation that furnishes the instantaneous position of a particle that is being acted upon by surface forces. Therefore, this work relied on the provision of the equation, whose explicit solution relies on the Fokker-Plank equation that governs the evolution of the space-time probability current.