Specialist Lecture – Mathematical Modeling and Analysis of Active Suspensions

Complex fluids that have a “bio-active” microstructure — like suspensions of swimming bacteria or assemblies of immersed biopolymers and motor-proteins — are important examples of so-called active matter. These internally driven fluids can have strange mechanical properties, and show persistent activity-driven flows and self-organization. I will show how first-principles PDE models are derived through reciprocal coupling of the “active stresses” generated by collective microscopic activity to the fluid’s macroscopic flows. These PDEs have an interesting analytic structures and dynamics that agree qualitatively with experimental observations: they predict the transitions to flow instability and persistent mixing observed in bacterial suspensions, and for microtubule assemblies show the generation, propagation, and annihilation of disclination defects. I’ll discuss how these models might be used to study yet more complex biophysical systems.

Part of the 2015 AMSI-ANZIAM Lecture Tour