Numerical Simulation of the Filtration of Colloidal Suspensions
H. Nirschl
Institute of Mechanical Process Engineering (MVM), Karlsruhe Institute of
Technology (KIT), 76131 Karlsruhe, Germany
(Email: hermann.nirschl@kit.edu)
Abstract
The simulation of the filtration of colloidal suspension is still a big challenge. In general for the filtration
of suspension commercial CFD codes are used which are in a lot of cases very limited in their use,
special when a high number of particles has to be treated or when the typical and all interactions of
the colloids have to be integrated. The paper will show alternative methods which try to overcome this
limitations.
Keywords: Numerical simulation, filtration, agglomeration
Introduction
Recently, many new processes and methods for the production of nanoscale particles have come into
the focus of current research and development. Thereby the synthesis of these products often takes
place in electrolyte solutions, where particles normally acquire a non-zero surface charge. This finally
results in the formation of an electric double layer. From the DLVO theory it is well known that the
electrostatic interactions have a main influence on the structure of agglomerates but also on the
behavior in the liquid, like the sedimentation velocity. In the present paper numerical simulations are
used to give further insight in the underlying physical principles.
Methods
For a small number of particles direct numerical simulation can be used, where the geometry of the
particles is fully resolved by a overlay grid technique. To take into account the effects of the electrical
double layer it is necessary not only to consider the Navier-Stokes equations for the fluid flow, but also
a Poisson equation for the electric potential as well as the Nernst-Planck equation that describes the
ion transport in the electrolyte. In this way all nonlinear interactions between the particles are included
in the simulation. Especially we investigate the electrokinetic interactions in periodic cubic arrays of
spheres and in random suspensions.
By increasing the particle number it is necessary to overcome the huge computational costs of a direct
numerical simulation. Therefore we use a combination of a stochastic rotation dynamics (SRD), which
is a coarse grained fluid description, and a discrete element method (DEM) including the DLVO
potential. We use our model to simulate a cake filtration and predict the permeability of the filter cakes
depending on a change of the compressive load, the particle size and the agglomeration of the
particles. The latter is thereby determined by the particle charge and the ionic strength of the
suspension. We show that our results agree qualitatively with experimental data obtained from
colloidal boehmite suspensions.
From the literature it is known that the permeability of the filter cake increases with decreasing particle
size and the mechanical dewatering becomes more and more difficult. One possibility to improve the
filtration kinetics is the process of magnetic field enhanced cake filtration, which 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. Therefore DEM
simulations are performed to give a deeper understanding in the mechanisms of structuring effects of
the filter cake and the interaction of magnetic, hydrodynamic and mass forces.
Results
The discussion will start with the investigation of the sedimentation of a single colloidal particle in an
electrolyte (figure 1). There, the Stokes equation was coupled with the Nernst-Planck equation which
helps to resolve the deformation of the electrical double layer. The figure shows the sedimentation
velocity related to the Stokes velocity. For a Reynolds number approaching to zero there are
significant deviations at high zeta potentials visible. The effect is even further increased when a huge
amount of particles is investigated.
Figure 1: Sedimentation velocity of a single particle depending on Reynolds number with the zetapotential as a parameter
The disadvantage of the methods based on the continuum theory is that the interactions cannot be
resolved down to the molecular level. For this reason a SRD method was implemented where the
agglomeration and the filtration of a colloidal suspension was simulated. Figure 2 shows a typical
result of such a simulation. The simulations have all been validated with experiments.
Figure 2: Porosity depending on zetapotential for the filtration of a colloidal suspension
Conclusion
The paper will show that there exist a branch of simulations tools which go far beyond the scope of
usual CFD codes. They help to understand the physical effects of the filtration and separation of fine
particles but they are not commercially available. This means that a lot of development effort is
necessary to get real and trustful results out of such simulations.
References
Schäfer B., Nirschl H. (2008) Physicochemical influences on electrochemical transport in compressible
packed beds of colloidal boehmite particles, Journal of Colloid and Interface Science 318, 457-462
Keller F., Feist M., Nirschl H., Doefler W. (2010) Investigation of the nonlinear effects during the
sedimentation process of a charged colloidal particle by direct numerical simulation, Journal of Colloid
and Interface Science 344, 228-236