Emergent Hydrodynamic-Mediated Behaviour in Micro-Organisms
Bring together applied mathematics, fluid mechanics, and biology, to show how minimal physical models can explain complex biological phenomena related to motile cilia at the microscale, while also pointing toward engineering applications such as biomimetic microswimmers, microfluidic pumps, and flow sensors.
This course will specifically cover examples where hydrodynamic interactions give rise to emergent, collective behaviour in microorganisms and ciliated systems - from synchronised beating and metachronal waves to swarming and optimised swimming strategies. At microscopic scales, viscous forces dominate over inertial forces (low Reynolds number), so fluid motion is governed by the linear Stokes equations. This regime permits powerful mathematical tools - such as singularity solutions (Stokeslets, rotlets, stresslets) - as the building blocks to model how swimming organisms generate and interact with surrounding flows. The course will show how these tools are used to study organisms ranging from swimming bacteria to Volvox colonies, and how advection can dominate diffusion in nutrient transport at high Péclet numbers.
A central theme is motile cilia, their biophysics and how this results in synchronised dynamics. Individual cilia, each performing a periodic power-and-recovery stroke, coordinate through hydrodynamic and elastic couplings to produce travelling metachronal waves that enhance fluid transport. Students will be introduced to the nonlinear-dynamics frameworks - including the Adler equation and the Kuramoto model - used to describe how coupling strength, noise, and spatial arrangement determine whether many interacting oscillators lock into coherent motion or remain to various extents disordered.
The course also connects microscale flow physics to physiology and technology. Examples include how ciliary arrays on coral surfaces drive three-dimensional flows that support oxygen and nutrient exchange, and how insights into flow sensing and ciliary control inform the design of artificial microswimmers, microfluidic devices, and hydrodynamic sensors.
- Fundamentals of low-Reynolds-number hydrodynamics and Stokes flow.
- Minimal singularity models of microbial swimming and propulsion.
- Motility and feeding in ciliates: individual and collective behaviour.
- Sensory and signalling processes associated with cilia.
- Flow sensing, active/passive responses, and soft-body dynamics in flows.
- Mechanisms and biophysics of motile cilia and cilia beating.
- Synchronisation theory: noisy oscillators, the Adler equation, and the Kuramoto model.
- Mass transport by ciliary arrays, including lungs and coral physiology as case studies.
- Control of ciliary coordination, from single cells to multicellular/animal systems.
The course is aimed at doctoral students, early-career and senior researchers, and R&D technologists working in microfluidics, biophysics, soft matter, applied mathematics, and biomedical or biomimetic engineering who wish to gain a rigorous, cross-disciplinary grounding in the hydrodynamics of microscale living systems.