Kaiserslautern NETIAM Report
The full report of the NETIAM workshop on "Challenges in visualization, simulation and design for virtual porous materials" may be downloaded in pdf format by using the link at the bottom of this page. The executive summary of the report is given below.
Through a series of five workshops at different venues across Europe, the European FRAMEWORK 6 project NETIAM (New and Emerging Themes in Industrial and Applied Mathematics), aims to use mathematics in the formulation of unexplored multidisciplinary challenges, to increase awareness of this role across academic disciplines and end-users, and to identify strengthening mechanisms for multidisciplinary collaboration.
In its third Thematic Workshop, held in Kaiserslautern, Germany on 29-30 September 2004, the NETIAM project explored opportunities for multidisciplinary research under the title ‘Challenges in visualization, simulation and design for virtual porous materials’. The workshop was attended by some 27 researchers from 8 countries, including physicists, computer scientists, and mathematicians.
There were six opening presentations: Visualisation of very large data sets, Ventilation, material transport and separation in the human lung, Numerical rocks, Material geometry: physics and shape of spatially complex matter, Parallel algorithms for complex materials, and Textiles and non-wovens.
There were many possible areas within this large area of basic science upon which the breakout groups could have focused. Of the two which emerged, one covered a broad range of applications and the other a broad area of basic mathematical methodology.
Micromechanics of future filtration devices
The classical theory of filters classifies their mechanics according to certain key mechanical chemical and thermodynamic parameters which emerge from paradigm studies of single particle impact on a simple filter element. The applicability of such ideas depends considerably on the ability of scientists to scale up their predictions to practical filters with all their complex geometry. Modern methodology offers the promise of predicting filter performance far more precisely by using
However, there is one basic gap in scientific understanding that needs to be addressed before this strategy can be considered to be reliable. This concerns the microscale impact mechanics of the particle (which may be minute) with the filter matrix. This inevitably involves delicate fluid mechanics and surface adhesion mechanics and may also involve electrostatics, coating properties and surface chemistry.
There are also theoretical challenges concerning coupling the particle motion (including coagulation) to the fluid motion, especially when there is a filter cake, or when clogging needs to be predicted.
If these scientific issues can be resolved, there are really exciting applications in prospect ranging from ultrafilters, tissue engineering, catalysis and fuel cells to the preservation of our architectural heritage and to the trapping of bacteria and perhaps even viruses.
From microgeometry of porous media to macro material properties
This is the fundamental multiscale problem of all porous media and it is one where the methodologies cited above pave the way. It is axiomatic (and provable) that fluid flow through a porous medium at the pore scale averages or homogenises itself to Darcy flow in many parameter regimes. It is already possible to explore new regimes by using CFD codes that apply when the Navier-Stokes equations contain inertial terms. However, as flow rates increase, the accuracy of the geometrical representation must be increased, and new codes must be written to compute macroscopic thermodynamic or electromagnetic properties, rather than flow per se. This challenge is waiting to be met because the code predictions can immediately be tested against known homogenised models (Darcy or Biot) and then used to search for new correlations and scaling laws between the microgeometry measures and the macroscale properties. (For Darcy flow the porosity and tortuosity are the principal ones to have been identified.)
This experimental research programme should receive all the quality control it can receive from the burgeoning mathematical theories of homogenisation, computational geometry and stochastic partial differential equations, this last being vital in the presence of uncertain tomographic data.
It is even possible that this research could lead to fundamental advances in image processing because it is clear that state-of-the-art voxel visualisations are inadequate to represent porous media with strong inhomogeneities such as fractures. There is a great need for the discretised visualisation to contain geometrical elements which are physically plausible for the porous media under consideration. The problem of making such elements is waiting to be addressed.
It is certain that this research theme will have really strong links with one of the principal NETIAM themes, namely network modelling. At the moment in the oil and filtration industries the passage from microgeometry to macroproperties can only be realised by constructing intermediate scale networks of elements that are believed to provide a reliable stepping-stone between the two scales. The design and reliability of such networks has never been subject to mathematical scrutiny.
The programme of each of the NETIAM workshops is highly flexible, interactive, and responsive to emergent ideas, so distinguishing them from more traditional conference and seminar events. The Firenze and Ventspils workshops have provided insight into the mechanisms and challenges in stimulating ideas for novel multidisciplinary research topics and collaborations; these aspects will be addressed more fully in the subsequent capstone Plenary Workshop in March 2005.
The proceedings and output from the Kaiserslautern workshop are recorded in this report for dissemination amongst the workshop participants and the wider public and research communities. The report is intended as a resource of ideas for future multidisciplinary research activity on the topic of Challenges in visualisation, simulation and design of virtual porous materials and related areas. It is also the third of four Thematic Workshop reports which will form the basis of the final Plenary Workshop in March 2005, in which the ideas emerging from the Thematic Workshops will be integrated into substantial themes and collaborations for novel and multidisciplinary research.
The full report from the Kaiserslautern workshop can be downloaded here, or a shorter version (not including workshop presentations) is also available.