A model is proposed to model sinter bridges between monomers in aggregates and a toy simulation is shown.

## System of springs

We know that in fresh soot aggregates, monomers are connected with solid sinter bridges. They are not free to translate of rotate relative to each other. The whole aggregate can only move as one solid object. As aging occurs, stresses induced in the aggregate by liquid coatings can lead to breakage of necks. In order to simulate necked connections in DEM model, we insert a system of springs between monomers. One infinitesimal spring is inserted at the contact point between monomers and two (2D) or four (3D) lateral springs are inserted perpendicularly to the contact plane but at a distance from the contact point. The 2D system is illustrated in the figure below.

Motion of each spring attachment point is tracked explicitly. Let **s** be the position of a spring attachment point, **v** – the velocity, **ω** – the angular velocity, and **x** – the position of the corresponding particle. Then the change in position **s** can be described with the following equation:

\frac{d}{dt}\mathbf{s}=\mathbf{v}+\boldsymbol{\omega}\times\left(\mathbf{s}-\mathbf{x}\right)

\]

In response to displacement, the springs will stretch or compress and produce a force. That force will be applied to attachment points of the respective springs and may result in torque acting on the particle.

## Example simulation

In order to observe the behavior of a restructuring necked system, a neck breaking criterion is introduced. A neck is broken (and removed from the simulation) if its potential energy exceeds some critical potential energy, which is a constant specific to that neck.

An aggregate was generated where every monomer was initially connected to its neighbors with necks and neck strengths were normally distributed. To simulate a driving force for restructuring, a simplistic force field that pulls every monomer towards the center of mass of the aggregate was defined. This simulation provides qualitative insights into the soot restructuring and neck breakage process.