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 one of the driving forces of global technological progress. Materials science is largely focused on developing materials with a specific set of properties, that are most suitable for a given application. Theoretical modeling gives us a way to predict the behavior of the material under various external stimuli without actually performing costly experiments. Since most of the applications of these fluids are on large spatial and time-scales, a macroscopic description of the statics as well as the dynamics of the system is of paramount importance for modeling these materials. Using macroscopic dynamics, which is a symmetry based approach, one can derive consistent macroscopic equations. However, these models introduce a number of unknown phenomenological parameters that have to be measured experimentally. Moreover, microscopic details cannot be included into this theory. On the other hand, microscopic simulations can incorporate these details, but are computationally too expensive for engineering applications. A bottom-up coarse-graining of microscopic dynamics is usually performed to achieve larger (mesoscopic) spatial and time-scales. These methods typically match certain structural properties of the system, but disregard the dynamic properties of the system, which are crucial for macroscopic rheological behavior. Data-driven techniques are becoming increasingly popular to discover a reduced model directly from data. Most of these methods have been applied to simple low-dimensional nonlinear dynamical systems. This project aims to discover macroscopic laws directly from simulation data on a smaller scale. As a showcase of a complex material we will study magnetorheological fluids (MRFs), which consist of micron sized magnetizable particles suspended in a carrier fluid. MRFs have a large market share in automotive industry and are utilized as active dampers, clutches or breaks. In an external field, columnar structures are formed which cause a huge increase in the effective viscosity as well as the existence of a static and dynamic yield stress. The proposed project is divided into three work packages (WPs): WP1: A mesoscopic model of micron sized particles suspended in a simple fluid solvent will be constructed using dissipative particle dynamics (DPD). We will also measure certain thermodynamic properties to gain reference values for subsequent WPs. 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. We will perform nonequilibrium simulation experiments, i.e. shear and pressure driven flows and study the pattern formation of MRFs under external fields. WP3: 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. Although there are several macroscopic models of MRFs, some mechanisms which are present in nonequilbrium situations are still poorly understood and not captured by current models. With this project, we aim to extract a model of MRFs and possibly shed some light on these mechanisms. The results could open up a new field of data-driven model discovery from microscopic simulations.