Modelling and simulation of cell migration in heterogeneous media

Cell motility is a complex process comprising, among others, cytoskeletal remodelling and growth, active force generation, chemical transport and reaction of multiple substances inside and outside the cell as well as on the cell membrane, anisotropic material behavior of the cell and of the extracellular matrix (ECM), and proteolytic cleavage of the ECM. We are working on an evolving finite element based computational framework that is able to incorporate models and methods for all the key features of cell motility. The approach exploits a mesoscopic point of view and aims at a comprehensive 3D model allowing for the simulation of cell motility at reasonable computational costs. In the presentation we will first sketch the overall framework, addressing all the respective models and methods, and will then focus on some essential subunits

Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions