A new approach for the detection of particle interactions for large-inertia and colloidal particles in a turbulent flow

The purpose of the paper is to present a new principle and a new algorithm for the direct numerical simulation of particle interactions within a turbulent flow. This approach has been developed in order to be able to compute agglomeration kernels with a numerical method which can still be applied at reasonable costs for very small colloidal particles. In this paper, classical algorithms are first tested and analyzed. They are shown to yield correct results but to require the use of time steps that are so small that they become intractable for colloidal particles. Their direct applications using large steps with respect to the relaxation time scale of the smallest particles reveal drastic errors that increase with the time step and with decreasing particle diameters. The new principle introduces the notion of continuous relative trajectories between possible collision partners and evaluates the exact probability for this trajectory to reach the minimum distance where two particles actually collide. Based on this new physical point of view and on the use of a probabilistic approach, a novel algorithm has been devised and numerical outcomes confirm that accurate predictions for the collision kernel are obtained independently of the particle diameter and for very large time steps. It is believed that the present ideas open interesting possibilities for the simulation of particle interactions over a whole range of particle behavior, from a ballistic to a diffusive regime, and can be extended to take into account new phenomena. Although present developments arise in the context of a numerical study, the new ideas that are introduced in this paper rely on the use of continuous stochastic bridges and, in that respect, propose a new approach to address physical issues of two-phase flow modeling.