Lattice Boltzmann simulation of multiphase flows

Multiphase flows are of great importance in many technical applications and natural occurrences. This includes the phenomena investigated in this project in the transport of discrete solid particles in liquids or gases. Prominent examples are suspensions of small, possibly nanoscale particles in liquids and in gases (dust) or the transport of granular materials, e.g. in water. Depending on their size, the movement of the particles is dominated by thermal fluctuations (Brownian motion) or by viscous interactions with the surrounding fluid. Depending on the volume fraction of the particles, the rheological properties of the system are determined by interactions between particles or by the properties of the continuous phase. The modeling of these processes on a macroscopic level thus requires understanding and quantification on a microscopic level.

Numerical simulations can make a significant contribution to the clarification of these mechanisms if these processes are modeled on a particulate scale and on fundamental physical assumptions. However, this requires that suitable numerical methods are used to model the motion and interactions of a representative number of particles with sufficient accuracy. This requirement is met by the lattice-Boltzmann method [1], which is based on an efficient discretization of the phase space of the Boltzmann equation. The resulting equations are linear and first order and can be solved with a simple algorithm. Together with the efficient formulation of boundary conditions, flows through very complex regions of static or moving solids can be simulated. The modeling of the motion and the interactions between particles is based on Newton's equations of motion.

In the project, suspensions of microscale particles are investigated under the influence of external fields or shear forces. The basis for the modeling is Ladd's method [2,3].