Fluid dynamics of corals

Fundamental processes underpinning the health and function of corals such as nutrient uptake, oxygen exchange and bacterial infection occur at the microscale, yet we still largely lack a quantitative understanding of the governing transport processes. The cilia that corals use for feeding and cleansing also generate dramatic vortical flows, which affect mass transport and may provide a barrier against infection. My research investigates the nature and consequences of these active vortical flows. I use state of the art visualisation of flows, tracking of individual bacterial cells, and mathematical modelling to quantitatively understand the coupling between ciliary flows, nutrient and oxygen dynamics, and pathogen behaviour.

Microbial optimal foraging theories

My research focuses on the ecological consequences of spatial and temporal variability in the nutrient landscape and flow conditions. Microbial interactions in a heterogeneous environment are modelled using an optimal foraging framework, in which the effects of different nutrient landscapes, motility mechanisms, uptake kinetics and other phenotypes are explored. Through developing this holistic framework, we investigate the consequences of microscale heterogeneity on microbial ecology, and examine the extent to which microscale dynamics and nutrient uptake affect the macroscale nutrient flow in the ocean.

Synchronization of eukaryotic flagella

The flagellar dynamics of two micropipette-held somatic cells of Volvox carteri, with measurably different intrinsic beating frequencies, are studied by high-speed imaging as a function of their mutual separation and orientation. From analysis of beating time series we find that the interflagellar coupling, which is constrained by the lack of chemical and mechanical connections between the cells to be purely hydrodynamical, exhibits a spatial dependence that is consistent with theoretical predictions. We show unequivocally that flagella coupled solely through a fluid medium can achieve robust synchrony despite significant differences in their intrinsic properties. Accompanying this synchronization is a marked change in the beating waveform of the flagella, a key finding that lends support to models of synchronization that rely on waveform compliance to achieve phase-locking.

Metachronal waves

Microscale fluid flows generated by ensembles of beating eukaryotic flagella are crucial to fundamental processes such as development, motility and sensing. From unicellular ciliates to the respiratory epithelium, carpets of cilia display metachronal waves (MWs), long-wavelength phase modulations of the beating cycles, which theory suggests may arise from hydrodynamic coupling. Using time-resolved particle image velocimetry, we report the discovery of MWs on the surface of the colonial alga Volvox carteri , whose large size and ease of visualization make it an ideal model organism for these studies. An elastohydrodynamic model of weakly coupled compliant oscillators, recast as interacting phase oscillators, reveals that orbit compliance can produce fast, robust synchronization in a manner essentially independent of boundary conditions, and offers an intuitive understanding of a possible mechanism leading to the emergence of MWs.

Suspensions of swimming microorganisms

For ciliated organisms in which the appendages are sufficiently close together, the tips of the individual cilia may be considered to be joined by an effective no-slip "envelope". The periodic motion of cilia gives rise to small amplitude deformations of the spherical envelope, which facilitate locomotion. The forces and torques acting on two closely-separated spherical squirmers are calculated, through solving the Stokes equations to second-order. The lubrication analysis is used to assess the stability of a dense planar array of three-dimensional squirmers.

Nanoelectromechanical resonators in fluid

The ability to calculate flows generated by oscillating cylinders immersed in fluid is a cornerstone in micro- and nanodevice development. We undertake a detailed theoretical analysis of the hydrodynamic load experienced by an oscillating rigid cylinder, of arbitrary rectangular cross section, that is immersed in an unbounded viscous fluid. We also consider the formal limit of inviscid flow for which exact analytical and asymptotic solutions are derived. Due to its practical importance in application to the atomic force microscope and nanoelectromechanical systems, we conduct a detailed assessment of the dependence of this load on the cylinder thickness-to-width ratio.