Macroscopic model discovery of complex fluids using sparsity promoting techniques
The development of smart responsive materials such as magnetorheological fluids, liquid crystals, hydrogels and shape memory alloys is the driving force behind global technological progress. Theoretical modeling allows us to predict the behavior of a material under various external stimuli without actually conducting expensive experiments. Using macroscopic dynamics, which is a symmetry-based approach, consistent macroscopic equations can be extracted. However, these models introduce a variety of unknown phenomenological parameters that need to be measured experimentally. Furthermore, microscopic details cannot be included in the theory. On the other hand, microscopic simulations can include these details, but are computationally too expensive for engineering applications.
Machine learning methods are becoming increasingly popular as a means of discovering a reduced model directly from data. Most of these are applied to simple low-dimensional nonlinear dynamical systems. The aim of this project is to discover macroscopic laws directly from simulation data of microscopic dynamics. These methods are so far unexplored with regards to particle simulation data. As an example of a complex material, we will study magnetorheological fluids, which consist of micron sized magnetic parts suspended in a fluid. Manetorheological fluids have a large market share in the automotive industry and are used as active dampers, clutches or brakes. Columns of particles are formed in the external field, which cause a huge effective increase in viscosity and the existence of static and dynamic stresses. In the project, we will first implement a model of magnetorheological fluids based on dissipative particle dynamics and perform some non-equilibrium numerical experiments. From the data of these simulations, we will extract a macroscopic model and perhaps also the connections between macroscopic parameters and microscopic details of the magnetic system.
Detailed implementation plan
The project is divided into three work packages (WP):
In WP1 a mesoscopic model of micron sized particles suspended in a simple fluid solvent will be constructed using dissipative particle dynamics (DPD). Basic solvent properties, such as viscosity and shear modulus will be measured to gain reference values for subsequent WPs.
In WP2 we will couple the mesoscopic method constructed in WP1 with dynamics of the magnetic degree of freedom, which will be added to each magnetic particle. Here a magnetic dipolar interaction will be added between magnetic particles. We will also consider different models for the magnetic susceptibility of the particles. We will perform nonequilibrium simulation experiments, i.e. shear and pressure driven flows and study the pattern formation of MRFs under external fields.
In WP3, which represents the core of the project, we will first coarse-grain the microscopic states of the nonequilibrium simulations performed in WP2 into fields of density, velocity and magnetization and possibly concentration of magnetic particles. We will set-up the sparse regression algorithm to extract the underlying macroscopic equations of the magnetorheological fluid model.
Composition of the project team
Duration of the project
1.10.2023-30.9.2026
Funding
The project is co-financed by ARIS.