Capsule rheology and machine learning
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Date
2024
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Abstract
apsules 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.
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Keywords
Rheology, Capsule, Interfaces, Bending, Elasticity, Contact, Traction force