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

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Logarithmic sensing in Bacillus subtilis aerotaxis

Aerotaxis, the directed migration along oxygen gradients, allows many microorganisms to locate favorable oxygen concentrations. Despite oxygen’s fundamental role for life, even key aspects of aerotaxis remain poorly understood. In Bacillus subtilis, for example, there is conflicting evidence of whether migration occurs to the maximal oxygen concentration available or to an optimal intermediate one, and how aerotaxis can be maintained over a broad range of conditions. Using precisely controlled oxygen gradients in a microfluidic device, spanning the full spectrum of conditions from quasi-anoxic to oxic (60 n mol/l–1 m mol/l), we resolved B. subtilis’ ‘oxygen preference conundrum’ by demonstrating consistent migration towards maximum oxygen concentrations (‘monotonic aerotaxis’). Surprisingly, the strength of aerotaxis was largely unchanged over three decades in oxygen concentration (131 n mol/l–196 μ mol/l). We discovered that in this range B. subtilis responds to the logarithm of the oxygen concentration gradient, a rescaling strategy called ‘log-sensing’ that affords organisms high sensitivity over a wide range of conditions. In these experiments, high-throughput single-cell imaging yielded the best signal-to-noise ratio of any microbial taxis study to date, enabling the robust identification of the first mathematical model for aerotaxis among a broad class of alternative models. The model passed the stringent test of predicting the transient aerotactic response despite being developed on steadystate data, and quantitatively captures both monotonic aerotaxis and log-sensing. Taken together, these results shed new light on the oxygen-seeking capabilities of B. subtilis and provide a blueprint for the quantitative investigation of the many other forms of microbial taxis

Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter (c2), thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter (Nt), Brownian motion parameter (Nb), Lewis number (Le), bioconvection Schmidt number (Sc), bioconvection constant (σ) and bioconvection Péclet number (Pe). Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter (c2) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter (c4) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter (c6) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent (m), skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter (c8) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes

Bioconvection

Bioconvection patterns are usually observed in the laboratory in shallow suspensions of randomly, but on average upwardly, swimming micro-organisms which are a little denser than water, but have also been found in situ in micropatches of zooplankton [Kils (1993), 1993. Bull. Mar. Sci. 53, 160–169]. The mechanism of upswimming differs between bottom-heavy algae and oxytactic bacteria. Rational continuum models have been formulated and analysed in each of these cases for low cell volume fraction. These will be described, as will new theoretical and experimental developments, including nonlinear analysis of the patterns, dispersion in shear flows, measurements of algal cell swimming behaviour, and new attempts to set up a model for more concentrated suspensions. The paper will review all work in this area since 1992, the year of the publication of the article "Hydrodynamic phenomena in suspensions of swimming micro-organisms" by Pedley and Kessler [1992b. Annu. Rev. Fluid Mech. 24, 313–358]