The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms

‘Bioconvection’ is the name given to pattern-forming convective motions set up in suspensions of swimming micro-organisms. ‘Gyrotaxis’ describes the way the swimming is guided through a balance between the physical torques generated by viscous drag and by gravity operating on an asymmetric distribution of mass within the organism. When the organisms are heavier towards the rear, gyrotaxis turns them so that they swim towards regions of most rapid downflow. The presence of gyrotaxis means that bioconvective instability can develop from an initially uniform suspension, without an unstable density stratification. In this paper a continuum model for suspensions of gyrotactic micro-organisms is proposed and discussed; in particular, account is taken of the fact that the organisms of interest are non-spherical, so that their orientation is influenced by the strain rate in the ambient flow as well as the vorticity. This model is used to analyse the linear instability of a uniform suspension. It is shown that the suspension is unstable if the disturbance wavenumber is less than a critical value which, together with the wavenumber of the most rapidly growing disturbance, is calculated explicitly. The subsequent convection pattern is predicted to be three-dimensional (i.e. with variation in the vertical as well as the horizontal direction) if the cells are sufficiently elongated. Numerical results are given for suspensions of a particular algal species (Chlamydomonas nivalis); the predicted wavelength of the most rapidly growing disturbance is 5–6 times larger than the wavelength of steady-state patterns observed in experiments. The main reasons for the difference are probably that the analysis describes the onset of convection, not the final, nonlinear steady state, and that the experimental fluid layer has finite depth

Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.

PHASE TRANSITIONS OBSERVED ON WARMING FAST-QUENCHED MBBA

Si on refroidit rapidement la phase nématique du MBBA à la température de l'azote liquide, on obtient un solide vitreux où la structure nématique a été gelée, ainsi que le montre la diffraction des rayons X. On réchauffe ensuite le MBBA et on étudie son évolution par diffraction des rayons X et par analyse thermique différentielle. Un solide cristallin apparaît vers -14 °C, qui se transforme ensuite en la phase nématique par l'intermédiaire d'une autre phase qui pourrait être soit la phase cristalline stable, soit une phase smectique. On propose d'appeler anotropiques les transitions monotropiques qui apparaissent quand on chauffe.When the nematic phase of MBBA is rapidly cooled by exposure to liquid nitrogen a glassy solid is formed which, X-ray diffraction studies indicate, has the nematic ordering quenchedin. The sequence of events which occur upon reheating this glass was monitored using X-ray diffraction and a differential thermal technique. A transition to a metastable crystalline phase occurs at about -14 °C and this phase converts into the nematic phase via some other phase, possibly the stable crystalline phase or a smectic mesophase. We propose the name anofropic for monotropic transitions that occur on heating