4- Conclusions

\label{conclusions}
A new wet particle collision technique i.e. Simplified Spring Collision Method (SSCM), is developed in order to model collision of particles with arbitrary shapes. The method defines an overlapping function based on the distance from the particle interface which helps to find the collision parameters. These include the collision point, degree of overlapping, the local relative velocity and the local curvature at the collision point. Moreover, SSCM by adjusting the spring stiffness coefficient after the maximum overlapping happens, applies the collision damping forces without using a dashpot. SSCM instead of using the expensive lubrication forces, implements the restitution coefficient obtained from the local relative velocity at the collision point. Therefore, there is no need for extra grid refinement to solve the lubrication forces during the collision which results in significant saving in the computational costs.
SSCM was validated with the experiment and shown to be valid over a wide range of Stokes numbers for the case of falling sphere. The study of the effect of the collision course as the only unknown parameter shows that for \(0.05D_{p}<\sigma<0.3D_{p}\), the error in the results is not significant. The capability of the method also was tested for elliptical and rectangular shapes. Furthermore, the accuracy of the tangential component of SSCM was validated for a spherical particle exposed to the shear flow. The accuracy method also was compared with the benchmarks for the situation of two particles in the case of drafting, kissing and tumbling. The results shows the overall agreement of the results. However, there is an error in the velocity during the collision phase due to the soft collision method and the diffuse nature of the interface.