Habilitation

Elasticity, Multi-phase Flow and Geophysical Pattern Formation

Habilitation thesis, Georg-August-Universität Göttingen, 2015.

In the German academic tradition a Habilitation thesis is prepared as proof of research accomplishments, during a review process that leads to a professional certification to teach at a German university (i.e. a prerequisite for permanent professorship). Typically, this consists of a cumulative thesis (also called a postdoctoral thesis, or second thesis) of a number of papers, forwarded by a general introduction to the research topic. This introduction can be downloaded by the above link.

Superficially, I study what happens as paint dries, and mud cracks. Colloids, clays, gels and polymer solutions belong to a class of soft materials that are composed of more than one phase of matter, mixed together in a potentially complex arrangement. The properties and dynamics of such mixtures depend intimately on the physics of its different parts, which may consist of a solid-like phase, and a liquid-like phase, and their interactions. More formally, my research looks into a number of instabilities and questions involving elasticity and multi-phase flow in such soft materials. These questions are interdisciplinary, and often take some inspiration from patterns that we can see directly around us, mostly from geological settings. However, some of the questions that have sprung from these origins also involve a mixture of soft matter physics with chemistry, materials science, and biology. What unifies these topics are the methods used -- models constructed of strict mass, momentum, and energy balance of the various interacting parts -- and the types of fundamental questions asked, which involve the relationship between microscopic dynamics and macroscopic response, as well as an attempt to understand the types of instabilities that can develop. This thesis summarises my work, over the past six years, of experimental research in this field.

Some highlights include:

•The use of sheared polymers to understand the scaling and formation of billion-year old fossil wrinkle structures, which have been a century-old mystery to science.
•Modelling of the vast polygonal permafrost patterns of polar Earth and Mars with the cyclic drying of clay in a Petri dish
•The discovery of wavy cracks in thin colloidal films and their use in developing an energy-based model for crack path prediction
•Identification of plastic relaxation mechanisms that can toughen a paint film when, counter-intuitively, the adhesion between its constituent particles is weakened
•Finding a general route of solidification from disordered liquid, to ordered repulsive solid, to an attractive hard solid, as charged colloids dry

Although these results are diverse the work here all focusses on the mechanical interactions and responses of multi-phase materials. In the work collected in this thesis three main topics emerge. The first involves the application of laboratory techniques to geophysical problems of pattern formation, where the inhuman timescales or distances involve can make direct field verification of ideas difficult, or impossible. Much of this work, including my earlier studies on columnar joints (which are not included here) turn on fundamental questions of crack growth and propagation in brittle materials. From this, I became interested in the question of how to predict the behaviour of a growing crack, or how a crack interacts with other nearby cracks or an uneven environment. This serves as the second main topic here -- the physics of crack interaction and growth in brittle thin films. Or, simply put, how do you predict the path that a crack will take? Finally, as these cracks are driven by the evaporation of water from soft materials, I became interested in the basic problem of how a multi-phase material dries, and solidifies. This has lead to a series of studies on structure formation and the dynamics of drying in soils and colloidal materials (such as the precursors of latex paints).