Math2Market Technical Reports

In the present paper, we propose a novel single-fiber model which exploits a description of fibers as a sequence of bond and torsion angles. Using the Frenet-Serret formulas, this representation can be translated into 3D space and vice-versa. While the precise locations of points along a fiber do not directly convey information about inner material properties of the fiber, the distribution of bond and torsion angles may be related to various material characteristics and, thus, our model may form…

The precise simulation of filtration characteristics of a filter element at the macro scale, i.e. complete filter with housing, is of importance to continuously increasing requirements in the filtration market. For this reason, several key parameters are essential as input data, which are obtained from the filter media scale. These main input parameters for the macro-scale simulation are: permeability of the media, maximum particle packing density and maximum flow resistivity for both the depth…

In this paper, detailed insights are given into the computation of fiber diameters from discretized binary images, for example a segmented CT-scan of a fiber reinforced composite. Similar methods can be used to predict the pore size distribution of a digital rock or the grain size distribution for a FIB-SEM image of a battery electrode. The explored methods make use of the Euclidean Distance Transform.

Several key parameters are essential as input data to precisely simulate the filtration characteristics of a filter element at macro scale, e.g. simulating the particle filtration through a pleated filter. Boundary and flow conditions, as well as input parameters related to the nano/microstructure of the media, should be defined. The main input parameters for the macro-scale simulation, which are related to the nano/microstructure of the media, are: permeability of the media, maximum particle…

Nonwoven are used in many industries, for example for liquid and gas filtration, glass-fiber reinforced plastics or carbon-fiber reinforced plastics, or gas-diffusion layers in fuel cells. The study of the micro-structure of nonwoven is also the starting point to understand, analyze and optimize filters. We propose to base this process on computer simulations. The first step consists of processing μCT-scans of existing filter media to prepare detailed 3D micro-structure models or statistical…

Type of weave, wire diameter, and mesh counts are geometrical characteristics with an enormous impact on the specific flow and filtration properties of a wire cloth. HAVER & BOECKER uses GeoDict (Math2Market GmbH) to input these parameters and depict the structure of single-layer and multiple-layer cloths as a real 3D model (Fig. 1). Geometric parameters such as pore size distribution and bubble point are determined with GeoDict.

Nanofibers are attractive to use in air filtration due to the high surface-to-volume ratio, low flow resistance and enhanced filtration performance. However, the cost of nanofibers and slowing down in production process when using them leads to the desire to use as few nanofibers as possible. We treat such optimization issues by simulating filter media and filtration processes resolving the smallest scale.

We present a particle/continuum approach for a reactive transport simulation which can be carried out with the scientific software GeoDict® on a state of the art desktop workstation. The presented model allows running simulations directly on real rock structures of representative size (REV). Using a very simple model for the chemical reaction, we can achieve comparable phenomenological dissolution patterns, similar to published results.

3D imaging methods, such as micro Computed Tomography (μCT) or focused ion beam scanning electron microscopy (FIB-SEM), allow deep insights into the three-dimensional structure of porous materials. The resulting 3D data sets are very large, often exceeding 2000³ or 8 billion volume elements called voxels. Researchers and engineers are interested in determining effective homogenized material properties based on these data sets to understand existing materials or to design new man-made materials.…