Virtual Material Design and Air Filtration Simulation
Techniques inside GeoDict and FilterDict

Andreas Wiegmann, PhD, Stefan Rief and PD Dr. Arnulf Latz

Faunhofer Institut Techno- und Wirtschaftsmathematik
Kaiserslautern, Germany

In case of depth filtration in fibrous filter media, pressure drop, 
permeability, filter efficiency, and filter lifetime depend strongly 
on the micro structure. In addition to the filter mechanisms which are 
present already for a single fiber we also simulate sieving effects and 
electrostatic forces that are highly dependent on the geometry of the 
material. The procedure decouples into several steps: First individual 
layers of the fibrous filter media are modeled and then stacked into a 
random three-dimensional representation with given mean properties such 
as porosity, fiber types and fiber directions. Next, the air flow through 
the media is computed by solving the steady Stokes equations, and the 
electric field given by surface charges on the fibers is computed by solving 
a Poisson problem with singular source terms and appropriate boundary 
conditions. Then, a stochastic ordinary differential equation models Brownian 
motion, friction with the air, inertia of particles due to mass, as well as 
attraction or repulsion due to electric forces. Particles may collide with 
fibers and stick due to adhesion or bounce off if they have enough energy. 
They may also be sieved by being stuck between three or more fibers. By iterating 
this procedure, and computing new flow fields after significant amounts of 
particles were filtered, even filtration by previously filtered particles is 
simulated and the clogging and pressure drop of filters can be estimated.

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