2022, Schamberger, Barbara, Ziege, Ricardo, Anselme, Karine, Ben Amar, Martine, Bykowski, Michał, Castro, André P. G., Cipitria, Amaia, Coles, Rhoslyn A., Dimova, Rumiana, Eder, Michaela, Ehrig, Sebastian, Escudero, Luis M., Evans, Myfanwy E., Fernandes, Paulo R., Fratzl, Peter, Geris, Liesbet, Gierlinger, Notburga, Hannezo, Edouard, Iglič, Aleš, Kirkensgaard, Jacob J. K., Kollmannsberger, Philip, Kowalewska, Łucja, Kurniawan, Nicholas A., Papantoniou, Ioannis, Pieuchot, Laurent, Pires, Tiago H. V., Renner, Lars D., Sageman‐Furnas, Andrew O., Schröder‐Turk, Gerd E., Sengupta, Anupam, Sharma, Vikas R., Tagua, Antonio, Tomba, Caterina, Trepat, Xavier, Waters, Sarah L., Yeo, Edwina F., Roschger, Andreas, Bidan, Cécile M., Dunlop, John W. C.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

2020, Hennessy, Matthew G., Celora, Giulia L., Münch, Andreas, Waters, Sarah L., Wagner, Barbara

An asymptotic framework is developed to study electric double layers that form at the inter-face between a solvent bath and a polyelectrolyte gel that can undergo phase separation. The kinetic model for the gel accounts for the finite strain of polyelectrolyte chains, free energy ofinternal interfaces, and Stefan?Maxwell diffusion. By assuming that the thickness of the doublelayer is small compared to the typical size of the gel, matched asymptotic expansions are used toderive electroneutral models with consistent jump conditions across the gel-bath interface in two-dimensional plane-strain as well as fully three-dimensional settings. The asymptotic frameworkis then applied to cylindrical gels that undergo volume phase transitions. The analysis indicatesthat Maxwell stresses are responsible for generating large compressive hoop stresses in the double layer of the gel when it is in the collapsed state, potentially leading to localised mechanicalinstabilities that cannot occur when the gel is in the swollen state. When the energy cost of in-ternal interfaces is sufficiently weak, a sharp transition between electrically neutral and chargedregions of the gel can occur. This transition truncates the double layer and causes it to have finitethickness. Moreover, phase separation within the double layer can occur. Both of these featuresare suppressed if the energy cost of internal interfaces is sufficiently high. Thus, interfacial freeenergy plays a critical role in controlling the structure of the double layer in the gel.

2020, Celora, Giulia L., Hennessy, Matthew G., Münch, Andreas, Wagner, Barbara, Waters, Sarah L.

In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multi-component transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.

2020, Celora, Giulia L., Hennessy, Matthew G., Münch, Andreas, Waters, Sarah L., Wagner, Barbara

The collapse of a polyelectrolyte gel in a (monovalent) salt solution is analysed using a new model that includes interfacial gradient energy to account for phase separation in the gel, finite elasticity and multicomponent transport. We carry out a linear stability analysis to determine the stable and unstable spatially homogeneous equilibrium states and how they phase separate into localized regions that eventually coarsen to a new stable state. We then investigate the problem of a collapsing gel as a response to increasing the salt concentration in the bath. A phase space analysis reveals that the collapse is obtained by a front moving through the gel that eventually ends in a new stable equilibrium. For some parameter ranges, these two routes to gel shrinking occur together.