Particles moving through the fluid phase may collide with the filter material. In the simulation, such a collision happens when the particle surface (modeled as spherical particle with a given diameter) touches the surface of a grid cell (voxel) that does not allow particles to enter. Such a grid cell may belong to

1. the solid filter material,
2. solid particles deposited in previous batches,
3. or porous grid cells which do not allow additional particles to enter.

When a particle collides with the surface of such a grid cell, it can stick to the current position and become a deposited particle or it can bounce off and continue moving in another direction. This behavior is defined in the Collision Model. FilterDict offers three different built-in collision models and the possibility to define your own models.

Caught on first touch

Caught on first touch is the simplest collision model in FilterDict. With this model, the particle sticks to the filter media as soon as it touches the filter surface.

Hamaker model

In the Hamaker model, the velocity of the particle is compared to the adhesive forces. The particle is caught by the filter if its velocity when touching the structure is sufficiently small. The condition on the velocity is

where is the adhesion (Hamaker constant), is the particle density, is the adhesion distance or equilibrium spacing between the particle and the surface (assumed to be the typical value of , and is the particle radius. See Krupp, 1967.

Adhesion (Hamaker constant) and, another parameter, restitution need to be fitted in FilterDict.

The restitution parameter determines the amount of kinetic energy conserved during the collision. The restitution value ranges from 0 to 1. If the restitution parameter is set to 1, the collision is perfectly elastic. Then, the particle is reflected with the same velocity it had before the collision.

For restitution values smaller than one, energy is absorbed by the collision and the particle slows down. For example, a 0.5 restitution value means that a particle loses half of its velocity in the collision and gets 50% slower.

Sieving

In the Sieving model, the particles never stick to the filter, but a particle is caught by the filter if it does not move anymore and touches the filter at two different points. The restitution parameter is used in the same way as in the Hamaker model.

User-Defined Collision Models

Additional collision models can be defined in user defined functions.