Wavelengths in bioconvection patterns

Unicellular bottom-heavy swimming microorganisms are usually denser than the fluid in which they swim. In shallow suspensions, the bottom heaviness results in a gravitational torque that orients the cells to swim vertically upwards in the absence of fluid flow. Swimming cells thus accumulate at the upper surface to form a concentrated layer of cells. When the cell concentration is high enough, the layer overturns to form bioconvection patterns. Thin concentrated plumes of cells descend rapidly and cells return to the upper surface in wide, slowly moving upwelling plumes. When there is fluid flow, a second viscous torque is exerted on the swimming cells. The balance between the local shear flow viscous and the gravitational torques determines the cells' swimming direction, (gyrotaxis). In this thesis, the wavelengths of bioconvection patterns are studied experimentally as well as theoretically as follow; First, in aquasystem it is rare to find one species lives individually and when they swim they can form complex patterns. Thus, a protocol for controlled experiments to mix two species of swimming algal cells of \emph{C. rienhardtii} and \emph{C. augustae} is systematically described and images of bioconvection patterns are captured. A method for analysing images using wavelets and extracting the local dominant wavelength in spatially varying patterns is developed. The variation of the patterns as a function of the total concentration and the relative concentration between two species is analysed. Second, the linear stability theory of bioconvection for a suspension of two mixed species is studied. The dispersion relationship is computed using Fourier modes in order to calculate the neutral curves as a function of wavenumbers $k$ and $m$. The neutral curves are plotted to compare the instability onset of the suspension of the two mixed species with the instability onset of each species individually. This study could help us to understand which species contributes the most in the process of pattern formation. Finally, predicting the most unstable wavelength was studied previously around a steady state equilibrium situation. Since assuming steady state equilibrium contradicts with reality, the pattern formation in a layer of finite depth of an evolving basic state is studied using the nonnormal modes approach. The nonnormal modes procedure identifies the optimal initial perturbation that can be obtained for a given time $t$ as well as a given set of parameters and wavenumber $k$. Then, we measure the size of the optimal perturbation as it grows with time considering a range of wavenumbers for the same set of parameters to be able to extract the most unstable wavelength.

Exploring redox-driven self-assembly of mixed metal polyoxometalates

How can we control the experimental conditions towards the isolation of specific structures? Why do particular architectures form? These are some challenging questions that synthetic chemists try to answer, specifically within polyoxometalate (POM) chemistry, where there is still much unknown regarding the synthesis of novel molecular structures in a controlled and predictive manner. This work covers a wide range of POM chemistry, exploring the redox self-assembly of polyoxometalate clusters, using both “one-pot”, flow and hydrothermal conditions. For this purpose, different vanadium, molybdenum and tungsten reagents, heteroatoms, inorganic salts and reducing agents have been used. The template effect of lone-pair containing pyramidal heteroatoms has been investigated. Efforts to synthesize new POM clusters displaying pyramidal heteroanions (XO32-, where X= S, Se, Te, P) are reported. The reaction of molybdenum with vanadium in the presence of XO32- heteroatoms is explored, showing how via the cation and experimental control it is possible to direct the self-assembly process and to isolate isostructural compounds. A series of four isostructural (two new, namely {Mo11V7P} and {Mo11V7Te} and two already known, namely {Mo11V7Se} and {Mo11V7S} disordered egg-shaped Polyoxometalates have been reported. The compounds were characterized by X-ray structural analysis, TGA, UV-Vis, FT-IR, Elemental and Flame Atomic Absorption Spectroscopy (FAAS) analysis and Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Cyclic Voltammetry measurements have been carried out in all four compounds showing the effect of the ionic density of the heteroatom on the potential. High-Resolution ESI-MS studies have revealed that the structures retain their integrity in solution. Efforts to synthesize new mixed-metal compounds led to isolation, structural, and electronic characterization of the theoretically predicted, but experimentally elusive δ-isomer of the Keggin polyoxometalate cluster anion, {H2W4V9O33(C6H13NO3)}, by the reaction of tungstate(VI) and vanadium(V) with triethanolammonium ions (TEAH), acting as a tripodal ligand grafted to the surface of the cluster. Control experiments (in the absence of the organic compound) have proven that the tripodal ligand plays crucial role on the formation of the isomer. The six vanadium metal centres, which consist the upper part of the cluster, are bonded to the “capping” TEA tripodal ligand. This metal-ligand bonding directs and stabilises the formation of the final product. The δ-Keggin species was characterized by single-crystal X-ray diffraction, FT-IR, UV-vis, NMR and ESI-MS spectrometry. Electronic structure and structure-stability correlations were evaluated by means of DFT calculations. The compounds exhibited photochromic properties by undergoing single-crystal-to-single-crystal (SC-SC) transformations and changing colour under light. Non-conventional synthetic approaches are also used for the synthesis of the POM clusters comparing the classical “one-pot” reaction conditions and exploring the synthetic parameters of the synthesis of POM compounds. Reactions under hydrothermal and flow conditions, where single crystals that depend on the solubility of the minerals under hot water and high pressure can be synthesized, resulted in the isolation of two isostructural compounds, namely, {Mo12V3Te5}. The compound isolated from a continuous processing method, crystallizes in a hexagonal crystal system, forming a 2D porous plane net, while the compound isolated using hard experimental conditions (high temperature and pressure) crystallizes in monoclinic system, resulting in a different packing configuration. Utilizing these alternative synthetic approaches, the most kinetically and thermodynamically compounds would possibly be isolated. These compounds were characterised by single-crystal X-ray diffraction, FT-IR and UV-vis spectroscopy. Finally, the redox-controlled driven oscillatory template exchange between phosphate (P) and vanadate (V) anions enclosed in an {M18O54(XO4)2} cluster is further investigated using UV-vis spectroscopy as a function of reaction time, showed that more than six complete oscillations interconverting the capsule species present in solution from {P2M18} to {V2M18} were possible, provided that a sufficient concentration of the TEA reducing agent was present in solution. In an effort to investigate the periodicity of the exchange of the phosphate and vanadate anions, time dependent Uv-vis measurements were performed for a period at a range of 170-550 hours. Different experimental conditions were also applied in order to investigate the role of the reducing agent, as well as the effect of other experimental variables on the oscillatory system.