Numerical Simulation of Dispersed Magnetic Particles Combined with Adsorption Processes with Lattice Boltzmann Methods

Protein adsorption is an important phenomenon in chemistry, biology and medicine and is used in various applications in the biotechnology, pharmaceutical and chemical industries. The adsorption in combination with the high-gradient magnetic separation (HGMS) is a useful tool for the specific extraction of fermentation products, such as proteins, from a fermentation broth. In the process, the proteins bind to ligands on the surface of the functionalized magnetic particles, that are separable by magnetic forces. In another step the elution of the proteins takes place. The whole mechanism depends on the mixing of the components, the flow, the particle deposition and separation and the adsorption. In order to gain more knowledge over the HGMS, simulations of the particle deposition in the magnetic field are performed and combined with adsorption and flow processes. In the simulation, the fluids of the three-component flow (water, adsorptive and magnetic particles) are described by a Euler approach, the magnetic particles with a Lagrange approach. The Navier-Stokes equations model the flow behavior of the water, the calculation of the adsorptive is based on the convection-diffusion-reaction equation. The equations are coupled via the velocity field of the water and the computation is based on the Lattice-Boltzmann methods. The particles are regarded as point-shaped and are described with a discrete particle method. Resistive forces of the water, magnetic forces exerted by the magnetic field, and inter-particle dipole-dipole interactions act on them. The adsorption takes place on the surface of the particles and is represented by the reaction term in the convection-diffusion-reaction-equation. As a result, the concentration of the adsorbent in these regions is lowered. The simulation is performed with the Open Source Lattice Boltzmann code OpenLB (http://www.openlb.net)

The shape of the particle deposition in a magnetic field, here an inhomogeneous magnetic field generated by a magnetized cylindrical wire, is considered, and magnetic agglomerates arise from the magnetic particles’ dipole-dipole interactions. Both adsorption and magnetic particle simulations are validated by different physical experiments.