Multiphysics transport in Energy Materials

This is a course in modelling of transport phenomena in energy storage materials and devices. It is an excellent introduction to multiphysics problems for students interested in learning how one can simulate or model the coupling of heat, mass and electricity in the devices that drive the energy transition. Example of such devices are batteries, supercapacitors, hydrogen/ CO2 storage devices, or materials for heat storage. Many courses treat transport phenomena as separate subjects, while this course unifies different transport phenomena exploiting analogies between different transport fields, with an applied emphasis on energy materials.

The course is particularly suitable for student wishing to later specialize in numerical simulation of conservation laws (e.g. CFD courses such as Computational Fluid Dynamics for Engineers); for students with an interest in experimental, theoretical or simulation-based fluid dynamics (e.g. as a foundation for the Turbulence, Rheology or Multiphase Flow courses) and who wish to learn about the coupling of momentum and species transport ; or for students who seek a solid preparation to face confidently the study of coupled transport theories used in the modelling of electrochemical and heat transfer systems, see e.g. the EFPT Electrochemical Energy Storage course.

Different from other transport phenomena courses within the EFPT curriculum, this course covers the modelling of diffusive and convective transport of generic species in materials that are not homogeneous, but are made of different phases in the form of compacted dry powders, solid foams, inks, slurries etc. For example, the course covers how to estimate the effective electrical or heat conductivity of materials used as battery electrodes, a key issue when modelling batteries.

Among other topics, the courses will give a practical introduction to Comsol Multiphysics, probably one of the most widespread software for the simulation of general multiphysics problems.

Topics include:

• MATHEMATICAL MODELLING: Mathematical analogies between conservation laws for heat, mass, electrons, ions and electric fields; Modes of microscopic transport: diffusion, convection, reaction/adsorption and their microscale modelling; From micro to macro: upscaling microscopic fluxes to the macroscale; the science behind engineering correlations; Extract general constitute laws for multiphysics fields: the most important ideas; Averaging of linear and non-linear equations; Bounds on transport properties for statistically homogeneous, periodic or percolating fields; effective conductivities of composites

• MICRO/NANOPHYSICS: Coupling of mass, momentum or heat transport with electric fields: electrokinetic transport in bulk and at interfaces; Upscaling adsorption in porous media: application to hydrogen and CO2 adsorption; How to analyse images, e.g. Scanning Electron Microscope images, to estimate transport properties in mesoporous materials

• NUMERICAL SIMULATIONS: How to use commercial codes (e.g. Comsol or Fluent) to compute experimentally testable transport properties; basic approaches to the discretizations of coupled multiphysics problems

• APPLICATIONS: use of the theory in practical case studies: battery electrodes, high-surface-area capacitors, hydrogen storage media, membranes for CO2 sequestration, multicomponent/multiphase heat storage materials