Despite the linearity of the Stokes equations, nonlinearity is prevalent at zero Reynolds number due to the presence of interfaces, elastic structures and polymers, chemical concentrations, and electric fields, all of which have ramifications across many industrial and biological processes. In recent years, especially with the development of new experimental techniques for exploring microscale physics, there has been significant interest in understanding and categorising how these sources of nonlinearity interact with the long-ranged, configuration dependent, and non-local flows present at zero Reynolds number. In fact, instabilities that arise as a result of these mechanisms are responsible for important phenomena such as inertia-free mixing and transport in microscale devices, spontaneous force-free motion of colloidal particles and droplets, the generation of intra- and extracellular flow fields in organisms, as well as curious turbulence-like phenomena exhibited by active suspensions.
The focus of this colloquium will be on nonlinearities that arise in the absence of inertia due to couplings with elastic structures and primarily elastic filaments, and coupling with chemical fields leading to phenomena such as phoretic motion. We aim for our colloquium to attract and invite both theoreticians and experimentalists in these exciting and sometimes connected areas. An important dimension of the colloquium is to provide a forum of an exchange of techniques and methodologies (computational dynamical systems, asymptotic analysis, experimental and simulation techniques) between researchers on these different topics, as well as explore the commonalities and differences between the mechanisms of instabilities that are encountered.