Extension of the hard-sphere particle-wall collision model to account for particle deposition

Abstract

Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results.

An extension of the hard-sphere particle–particle collision model to study agglomeration

“…This loss of mechanical energy may lead to the particles not managing to escape the potential well after the collision. While for the collision of a particle with a wall we know that the particle has to rise from the wall to escape after the collision, and the condition for agglomeration can thus be written in terms of the vertical component of the particle's impulse [23], it is not so clear-cut for a particle-particle collision, or for the collision between a particle and an asperity on a wall.…”

“…In fact, as long as the particles are of similar sizes, it seems intuitively reasonable to formulate the criterion for agglomeration in terms of the resultant of the relative velocity of the particles after the collision rather than only the component normal to the plane of collision. We grant, however, that in the limit of a very small particle colliding with a very large one, the agglomeration criterion should in principle be the same as that for a particle-wall collision, which is in terms of the normal component of the velocity [23].…”

“…The same argument was made for a particle-wall collision in ref. [23]. Substituting the expressions for J n and J t in Eq.…”

“…This is described in more detail in Section 3. Note that we used subscript t to denote the adhesive force in a previous paper [23] on particle-wall interaction. However, in this paper the subscript t is reserved to denote "tangential".…”

“…In our previous paper, [23], we made use of an approximation making it possible to carry out the change of variables in Equation (28), namely that the force F n,c is constant and equal to the average value of the Hamaker force over the surface separation interval in which the Hamaker force is significant.…”