Sheared bioconvection in a horizontal tube

The recent interest in using microorganisms for biofuels is motivation enough to study bioconvection and cell dispersion in tubes subject to imposed flow. To optimize light and nutrient uptake, many microorganisms swim in directions biased by environmental cues (e.g. phototaxis in algae and chemotaxis in bacteria). Such taxes inevitably lead to accumulations of cells, which, as many microorganisms have a density different to the fluid, can induce hydrodynamic instabilites. The large-scale fluid flow and spectacular patterns that arise are termed bioconvection. However, the extent to which bioconvection is affected or suppressed by an imposed fluid flow, and how bioconvection influences the mean flow profile and cell transport are open questions. This experimental study is the first to address these issues by quantifying the patterns due to suspensions of the gravitactic and gyrotactic green biflagellate alga Chlamydomonas in horizontal tubes subject to an imposed flow. With no flow, the dependence of the dominant pattern wavelength at pattern onset on cell concentration is established for three different tube diameters. For small imposed flows, the vertical plumes of cells are observed merely to bow in the direction of flow. For sufficiently high flow rates, the plumes progressively fragment into piecewise linear diagonal plumes, unexpectedly inclined at constant angles and translating at fixed speeds. The pattern wavelength generally grows with flow rate, with transitions at critical rates that depend on concentration. Even at high imposed flow rates, bioconvection is not wholly suppressed and perturbs the flow field.Comment: 19 pages, 9 figures, published version available at http://iopscience.iop.org/1478-3975/7/4/04600

Mechanistic modeling of sulfur-deprived photosynthesis and hydrogen production in suspensions of Chlamydomonas Reinhardtii

The ability of unicellular green algal species such as Chlamydomonas reinhardtii to produce hydrogen gas via iron-hydrogenase is well known. However, the oxygen-sensitive hydrogenase is closely linked to the photosynthetic chain in such a way that hydrogen and oxygen production need to be separated temporally for sustained photo-production. Under illumination, sulfur-deprivation has been shown to accommodate the production of hydrogen gas by partially-deactivating O2 evolution activity, leading to anaerobiosis in a sealed culture. As these facets are coupled, and the system complex, mathematical approaches potentially are of significant value since they may reveal improved or even optimal schemes for maximizing hydrogen production. Here, a mechanistic model of the system is constructed from consideration of the essential pathways and processes. The role of sulfur in photosynthesis (via PSII) and the storage and catabolism of endogenous substrate, and thus growth and decay of culture density, are explicitly modeled in order to describe and explore the complex interactions that lead to H2 production during sulfur-deprivation. As far as possible, functional forms and parameter values are determined or estimated from experimental data. The model is compared with published experimental studies and, encouragingly, qualitative agreement for trends in hydrogen yield and initiation time are found. It is then employed to probe optimal external sulfur and illumination conditions for hydrogen production, which are found to differ depending on whether a maximum yield of gas or initial production rate is required. The model constitutes a powerful theoretical tool for investigating novel sulfur cycling regimes that may ultimately be used to improve the commercial viability of hydrogen gas production from microorganism

Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow

The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity

Chemoconvection patterns in the methylene-blue–glucose system: weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments

Dynamics of a structured slug population model in the absence of seasonal variation

We develop a novel, nonlinear structured population model for the slug Deroceras reticulatum, a highly significant agricultural pest of great economic impact, in both organic and non-organic settings. In the absence of seasonal variations, we numerically explore the effect of life history traits that are dependent on an individual's size and measures of population biomass. We conduct a systematic exploration of parameter space and highlight the main mechanisms and implications of model design. A major conclusion of this work is that strong size dependent predation significantly adjusts the competitive balance, leading to non-monotonic steady state solutions and slowly decaying transients consisting of distinct generational cycles. Furthermore, we demonstrate how a simple ratio of adult to juvenile biomass can act as a useful diagnostic to distinguish between predated and non-predated environments, and may be useful in agricultural settings

Dispersion of biased swimming microorganisms in a fluid flowing through a tube

Classical Taylor-Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments, and compared with an approximation a la Taylor. As in the Taylor-Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming microorganisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.Comment: 20 pages, 4 figures. Published version available at http://rspa.royalsocietypublishing.org/content/early/2010/02/09/rspa.2009.0606.short?rss=

Extensive Chaos in the Lorenz-96 Model

We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Edward Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and decreases non-monotonically with increasing system size. The length scale describing the deviations from extensivity and the natural chaotic length scale are approximately equal in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. As the forcing is increased at constant system size the fractal dimension exhibits a power-law dependence. The power-law behavior is independent of the system size and quantifies the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.Comment: 12 pages, 20 figure

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.Comment: 11 pages, 8 figure

Enhanced sedimentation of elongated plankton in simple flows

Negatively buoyant phytoplankton play an important role in the sequestration of CO_2 from the atmo-sphere and are fundamental to the health of the world’s fisheries. However, there is still much to discoveron transport mechanisms from the upper photosynthetic regions to the deep ocean. In contrast to intuitive expectations that mixing increases plankton residence time in light-rich regions, recent experimental and computational evidence suggests that turbulence can actually enhance sedimentation of negatively buoyant diatoms. Motivated by these studies we dissect the enhanced sedimentation mechanisms using the simplest possible two-dimensional flows, avoiding expensive computations and obfuscation. In particular, we find that in vertical shear, preferential flow alignment and aggregation in down-welling regions both increase sedimentation, whereas horizontal shear reduces the sedimentation due only to alignment. However the magnitude of the shear does not affect the sedimentation rate. In simple vertical Kolmogorov flow elongated particles also have an enhanced sedimentation speed as they spend more time in down-welling regions of the flow with vertically aligned orientation, an effect that increases with the magnitude of shear. An additional feature is identified in horizontal Kolomogorov flow, whereby the impact of shear-dependent sedimentation speed is to cause aggregation in regions of high-shear where the sedimentation speed is minimum. In cellular flow, there is an increase in mean sedimentation speed with aspect ratio and shear strength associated with aggregation in down-welling regions. Furthermore, spatially projected trajectories can intersect and give rise to chaotic dynamics, which is associated with a depletion of particles within so called retention zones