FreeForm Parametric Fitting of Van der Waals Binodal and Spinodal Curves with Bat Algorithm This paper concerns the Van der Waals (VdW) equation of state, originally conceived to be a generalization of the ideal gas law. For practical use, it is often necessary to compute two characteristic curves of VdW, called binodal and spinodal curves. They are usually constructed through polynomial fitting from a collection of 2D points in the pressurevolume plane by using standard numerical procedures. However, the resulting models are still limited and can be further enhanced. In this paper, we carry out this task through leastsquares approximation of sets of 2D points using freeform Bezier curves. This requires to perform data parameterization in addition to computing the poles of the curves. To this aim, we apply a powerful natureinspired swarm intelligence method for continuous optimization called the bat algorithm. To test the performance of this new approach, it has been applied to real data of a gas. Our experimental results show that the method can reconstruct the characteristic curves with very good accuracy. In addition, the computing times are also very good, given the complexity of this problem. These remarkable features make this approach very promising in the field. Furthermore, it is actually ready to be applied to realworld instances of chemical components and mixtures.

An accurate and efficient algorithm to model the agglomeration of macroscopic particles Abstract   The agglomeration of particles during the handling of powders results in caking, lumping or the local accumulation of electrostatic energy which represents a serious hazard to the operational safety of industrial facilities. In the case of dry powders the attraction inbetween particles can be mainly attributed to van der Waals and electrostatic forces. Nonetheless, due to the challenges related to the small size and distance of relevant particles and the optical density of powder flows the detailed physical mechanisms of their interaction are so far little investigated. In this paper we present a novel numerical approach which is based on an algorithm developed by Erleben  1  in the field of computer graphics. This algorithm is extended to compute binary and multiple particle interaction with each other and solid surfaces. Therein, besides van der Waals and electrostatic forces also collisional forces and plastic particle deformation is accounted for. The herein presented results demonstrate that this algorithm allows to predict accurately and efficiently whether particles agglomerate or separate depending on their kinetic parameters. In particular, the imposed constrain forces prevent spurious velocity fluctuations and potential particle overlapping in statically overdetermined systems. Simulated test cases reveal how electrostatic and van der Waals forces lead to the growth of structures in case the particle restitution coefficient is sufficiently low.