Thesis defense of Felix Sebastian Kratz

Capsules and their properties have provoked an increasing interest in several fields of the sciences and industry. In the sciences, several relevant biological system are modeled as a liquid core encapsulated by a skin of some sort, e.g. red blood cells. In industry, capsules are usually used the other way around – not to model nature, but rather to design for functionality, e.g. in medical application or the food industry. Given their ubiquitous application, we discuss and investigate the solution of shape equations for freely pendant droplets, capsules and derive a method to incorporate viscous dissipation for time dependent deformation sequences. These theoretical investigations are supplemented with a novel numerical framework which allows us to solve the shape equations, fit them to experimental images, and therefore infer information from experiments. We apply the theoretical and numerical insights gained during the course of this work to investigate the properties of complex interfaces, such as multi-layer systems.
While an individual capsule has interesting applications, the reality often is that a capsule can not be isolated from other capsules or some constraining boundaries. We therefore investigate – for the first time in literature – the contact problem of a pressurized, bending-stiff, adhesive, elastic capsule under an external force both with a solid wall and with another capsule of this kind. The resulting shape equations give us access to the shape-parameter diagram and allow us to understand the contact problem without performing any experiment. We rather integrate the shape equations numerically and find the solutions nature realizes, together with all relevant derived quantities, such as the contact force. Additionally, we design a meta-material (theoretically) from an elastic capsule unit-cell by extending the contact theory to a columnar structure.
Several problems encountered in physics, especially in inverse problems, can be considered ill-conditioned. An ill-conditioned problem reacts sensitive to perturbations of the input data and usually needs to be regularized or otherwise constrained to produce stable predictions or results. In this thesis we explore the potential of machine learning approaches for exactly this task. With liquid droplet and elastic capsule shape fitting, as well as traction force microscopy, as example problems, we convincingly show that machine learning approaches for these ill-conditioned problems are suitable and outperform conventional methods by orders of magnitude in speed, allowing for a entirely new applications.