DEM-SIMULATION OF THE MAGNETIC FIELD ENHANCED CAKE FILTRATION Christian Eichholz 1 , Fei Chen 2 , T. Alan Hatton 2 , Hermann Nirschl 1 1 Institute for Mechanical Engineering and Mechanics, University of Karlsruhe (Karlsruhe Institute of Technology), 2 Department of Chemical Engineering, Massachusetts Institute of Technology, USA Abstract: This paper presents a numerical study of the cake formation and growth in the magnetic field enhanced cake filtration by means of the Discrete Element Method (DEM). The process of magnetic field enhanced cake filtration results from the combination of classical cake filtration and magnetic field driven separation. Experimental results prove that different magnetic field effects influence the filtration process positively. In the present paper the DEM-Simulation gives further insight in the mechanisms of structuring effects of the filter cake and especially the interaction of magnetic, hydrodynamic and mass forces. The motion of the discrete particles is obtained by applying the three-dimensional Newton’s laws of motion to every single particle. Beside external forces particle interactions are calculated using the modified DLVO-theory. Liquid phase flow is assumed as one-dimensional. Although the simulation results only represent a small cut-out the numerical results can be assigned to the same regimes of liquid flow and magnetic field effects that are observed experimentally. Keywords: Solid-Liquid-Separation, Cake Filtration, Magnetic Separation, Simulation, Discrete Element Method 1. INTRODUCTION The basic idea of the Discrete Element Method (DEM) is to solve the Newton’s laws of motion for all N discrete elements of the system for all degrees of freedom to describe the motion of all particles individually. Occurring forces are categorized into primary and secondary forces. Primary forces are external and interaction forces between pairs of particles. Secondary forces are contact forces which describe the effect of particle collisions (Johnson 1985; Deen et al. 2007). The time depending integration of Newton’s laws has to be accomplished numerically. Independently from the integration method the time step has to be chosen in a manner that in each iteration step constant forces can be assumed. Two different approaches for describing the particle contact can be found in literature. The hard-sphere approach as a quite fast method can be used for diluted systems. Only binary collisions can be regarded one after the other although they might occur simultaneously. The conditions after an impact are calculated according to the Hertz contact theory. For multi body contacts the soft-sphere approach has turned out to be more helpful. Collisions are not calculated immediately but tracked over the whole time step. This way several contacts of one particle can be treated. The collision is described by a virtual overlapping of the spheres. Only after detecting all particle contacts in one time step the Newton equations are integrated. The process of magnetic field enhanced cake filtration results from the combination of classical cake filtration and magnetic field driven separation. Experimental results prove that different magnetic field effects influence the filtration process positively (Fuchs et al. 2006; Eichholz et al. 2008). In inhomogeneous magnetic fields magnetic particles experience a magnetic force. That gives the possibility to decouple solid and liquid phase motion. In case of counter wise orientation of differential pressure and magnetic force this leads to a decrease of the rate of cake formation, implying a smaller packed bed that the liquid phase has to drain and thus a reduction in filtration resistance. If the field strength is high enough even the prevention of cake formation at the beginning of a filtration process is possible. Thereby the filter media is kept free of particles and the filtrate can run through the filter media almost without resistance. Only after the outflow of the excess water the particles deposit on the filter media.