Project 2). "Bioconvection: hydrogen production and high concentrations"

GENERAL
Single celled green algae can be found growing and swimming in most naturally occurring bodies of water on Earth. They are small - 10,000 could fit on a pinhead - and they tend to swim in particular directions, such as towards light or away from gravity, to improve their chances of survival.  Indeed, a red form is responsible for the pink sheen that you can sometimes see on melting snow.  When they accumulate in upper regions of the fluid, the mostly high density of the cell rich fluid above less dense fluid can lead to overturning and amazingly intricate self-perpetuating patterns in just tens of seconds. Physicists and mathematicians, including myself, have been studying these so-called bioconvection patterns in dilute suspensions for some years and have come up with ways to predict some aspects of the patterns that occur.  One minor aspect of this proposal is to study other statistical properties of the patterns with geometric image processing techniques that I hope to develop using curvature.  The system is a great example of how simple rules for individuals can scale up to produce structure many times the individuals' size, and the same methods can be used with other organisms such as bacteria.

It turns out that green algae have other tricks up their sleeves. When they are starved of sulphur, a new circuit internal to each cell kicks in to convert spare electrons from photosynthesis together with protons to hydrogen. This would be fantastic news, for it might ultimately provide a pollution-free and competitive source of hydrogen fuel, were it not for the fact that this circuit is extremely sensitive to oxygen, which is another product of photosynthesis.  In order to produce hydrogen you also need to starve the culture of oxygen.  This works well for a while, as all the oxygen released from photosynthesis gets used up by the respiration circuitry.  As well as producing hydrogen, the cells change shape and structure, and thus their behavioural response to the environment, which means that the algae produce different types of large-scale pattern and this in turn effects the amount of photosynthesis and hydrogen that each cell produces.  However, after some hours the cells begin to starve and they shut down.  Sulphur and oxygen are required to bring the algae back to their original condition.  Actually there are fine balances between starving the cells, the patterns produced and hydrogen production.  It's reasonable to predict that a better understanding of the system can produce better yields of hydrogen.  To understand the whole process we must make mathematical models of each aspect and to glue them together so that they make sense.  My recent research papers have concentrated on the patterns produced by dilute suspensions of cells, but I now have a number of ideas on how to deal with the range of behaviour from individual cell dynamics to large scale patterns in dilute suspensions, through simple cell-to-cell interactions to very concentrated cultures.  Techniques from probability and the study of fluids and porous structures shall be employed.  I also have set up a laboratory where mechanisms can be explored and mathematical theories can be tested to make sure that they are fully consistent with reality.  The hope is that one day we may have cars fuelled by hydrogen produced in an environmentally friendly way using green algae, but the methods and results produced from this research will undoubtedly have application in many other systems from pharmaceuticals to fisheries.

OBJECTIVES FOR PHD PROJECT (PLUS OPTIONAL OPPORTUNITIES FOR EXPERIMENTAL WORK)

Each student should pick 2 of the 4 main objectives outlined here (i.e. first the major then the minor).  For example, a PhD project might investigate objectives B & C, B & D, or A & B.

A) To develop multiscale analysis of hydrogen production in dilute suspensions of green algae.
a) To develop a model of intracellular dynamics for the interplay between photosynthesis, respiration, electron transport, the iron-hydrogenase sub-system and catabolism of endogenous substrate, consistent with existing experimental measurements.
b) To experimentally measure morphological and structural changes (e.g. cell eccentricity, centre-of-mass offset) of individual algae in response to sulphur and oxygen limitation.
c) To develop theoretical descriptions, in concert with experimental measurement, of individual behavioural changes in response to the above environmental stresses (e.g. effects on phototaxis & gyrotaxis).
d) To extend the application of generalized Taylor dispersion theory for swimming micro-organisms to encapsulate extra internal degrees of freedom (such as due to phototaxis or hydrogen induced changes in cell eccentricity and centre-of-mass offset).
e) To experimentally measure hydrogen production induced changes in bioconvection patterns using Fourier analysis and pattern analysis as in D).
f) To theoretically predict instability length scales or pattern type employing continuum models and items a) to d), to compare with and to aid e).

B) To model physical cell-to-cell interactions
a) To explore fluid flow interactions of two interacting flagellated spheroids developing (and comparing) either
i) existing resistive force theory for individuals, and/or
ii) slender body theory and computation, with rational placement of Stokelets and stresslets, and/or
iii) full numerical simulation, exploring boundary integral or immersed boundary methods.
b) To develop experimental apparatus and imaging techniques to track cell-to-cell interactions in a plane for comparison with a).

C) To design and develop models for very concentrated suspensions
a) To model concentrated suspensions using developments of two-phase flow or otherwise (for example, incorporating a leading order stresslet representation of swimming cells in an effective porous medium).
b) To experimentally track individual motile algae in very concentrated suspensions in a shallow layer, to lead and compare with a).

D) To investigate topological and geometric measures of bioconvection pattern type that are invariant to experimental
setup.
To develop differential and integral geometric methods for morphological characterization of bioconvection patterns, incorporating a novel and unique curvature thresholding technique, and to compare these with statistical techniques (e.g. for the quantification of regularity) and Fourier/wavelet methods.