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

Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent

Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes. The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method. Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow

Growing spherulitic calcite grains in saline, hyperalkaline lakes: experimental evaluation of the effects of Mg-clays and organic acids

The origin of spherical-radial calcite bodies – spherulites – in sublacustrine, hyperalkaline and saline systems is unclear, and therefore their palaeoenvironmental significance as allochems is disputed. Here, we experimentally investigate two hypotheses concerning the origin of spherulites. The first is that spherulites precipitate from solutions super-saturated with respect to magnesium-silicate clays, such as stevensite. The second is that spherulite precipitation happens in the presence of dissolved, organic acid molecules. In both cases, experiments were performed under sterile conditions using large batches of a synthetic and cell-free solution replicating waters found in hyperalkaline, saline lakes (such as Mono Lake, California). Our experimental results show that a highly alkaline and highly saline solution supersaturated with respect to calcite (control solution) will precipitate euhedral to subhedral rhombic and trigonal bladed calcite crystals. The same solution supersaturated with respect to stevensite precipitates sheet-like stevensite crystals rather than a gel, and calcite precipitation is reduced by ~ 50% compared to the control solution, producing a mixture of patchy prismatic subhedral to euhedral, and minor needle-like, calcite crystals. Enhanced magnesium concentration in solution is the likely the cause of decreased volumes of calcite precipitation, as this raised equilibrium ion activity ratio in the solution. On the other hand, when alginic acid was present then the result was widespread development of micron-size calcium carbonate spherulite bodies. With further growth time, but falling supersaturation, these spherules fused into botryoidal-topped crusts made of micron-size fibro-radial calcite crystals. We conclude that the simplest tested mechanism to deposit significant spherical-radial calcite bodies is to begin with a strongly supersaturated solution that contains specific but environmentally-common organic acids. Furthermore, we found that this morphology is not a universal consequence of having organic acids dissolved in the solution, but rather spherulite development requires specific binding behaviour. Finally, we found that the location of calcite precipitation was altered from the air:water interface to the surface of the glassware when organic acids were present, implying that attached calcite precipitates reflect precipitation via metal–organic intermediaries, rather than direct forcing via gas exchange

Periodic and Quasiperiodic Motion of an Elongated Microswimmer in Poiseuille Flow

We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow for different flow geometries. When moving between two parallel plates or in a cylindrical microchannel, the swimmer performs either periodic swinging or periodic tumbling motion. Although the trajectories of spherical and elongated swimmers are qualitatively similar, the swinging and tumbling frequency strongly depends on the aspect ratio of the swimmer. In channels with reduced symmetry the swimmers perform quasiperiodic motion which we demonstrate explicitely for swimming in a channel with elliptical cross section

The long-time dynamics of two hydrodynamically-coupled swimming cells

Swimming micro-organisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system - of dimension two - describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of $t\to\infty$, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations

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.

An Evaluation of Alternatives for Enhancing Anaerobic Digestion of Waste Activated Sludge

Waste activated sludge (WAS) is one of the largest by-products of biological wastewater treatment. Anaerobic digestion of WAS is beneficial for several reasons. In an ever increasingly energy conscientious world the production of renewable energy resources is becoming more important, and thus the production of methane has been seen as a valuable product. To achieve efficient conversion of organic matter to methane, the biomass in the digester must be provided optimal operating conditions, as well as adequate retention times, that will allow for substrate metabolism and prevent bacteria washout. Two approaches have been taken in this research to achieve improved biodegradation. Initially microwave pretreatment was employed to improve the biodegradability of the sludge, then the addition of a submerged hollow fibre membrane separation unit was used to allow for a longer SRT while maintaining the hydraulic residence time (HRT). The impact of microwave pretreatment on WAS characteristics was assessed for both the low temperature operations and the high temperature operations. An increase due to pretreatment on the filtered to total COD ratio when comparing the feed to the microwaved feed was established to be 200 % for low temperature operations and 254 % for high temperature operations. For the low temperature operations, CODT destruction, VS destruction, and organic nitrogen destruction were all higher for the test digester than the control digester indicating that the microwaving of the WAS increased the biodegradation in the anaerobic digester. For the high temperature operation, CODT destruction and organic nitrogen destruction were improved with microwave application, however VS destruction did not support this. The measured biogas data indicated that microwaving did influence the volume of biogas produced during anaerobic digestion of WAS for both the low and high temperature operations, and hence the VS destruction data for the high temperature operations was determined to be incorrect. For the membrane operations both the CODT and the VS destruction calculations indicated that at the same SRT the test digester was capable of more biodegradation than the control digester. The control digester organic nitrogen reduction was calculated to be higher than for the test digester, suggesting that the control digester removed more organic nitrogen than the test digester, however, these results were likely due to the lower HRT of the test digester compared to those of the control digester. A greater volume of biogas was produced by the test digester than the control digester; however, the composition of the gas from both digesters was similar, although the percentage of methane produced by the test digester was higher than that produced by the control digester. The higher destruction by the test digester indicated that the presence of the membrane unit and the decoupling of the HRT and SRT improved the biodegradation capability of the digesters. The results of the membrane performance study indicated that for a hollow fibre anaerobic membrane bioreactor, stable operations could be achieved with a total solids concentration of 2.01 %+/-0.34, an HRT of 15 days and an SRT of 30 days. With a constant flux of 14 L/m2-h +/-0.68 the average TMP was 0.079 kPa/min+/-0.08. No cleaning was required to achieve this, however the operations consisted of 20 minutes of permeation followed by 5 hours and 40 minutes of relaxation. The critical flux was determined to be in the range of 18 to 22 L/m2-h

A multi-center study on the attitudes of Malaysian emergency health care staff towards allowing family presence during resuscitation of adult patients

BACKGROUND The practice of allowing family members to witness on-going active resuscitation has been gaining ground in many developed countries since it was first introduced in the early 1990s. In many Asian countries, the acceptability of this practice has not been well studied. AIM We conducted a multi-center questionnaire study to determine the attitudes of health care professionals in Malaysia towards family presence to witness ongoing medical procedures during resuscitation. METHODS Using a bilingual questionnaire (in Malay and English language), we asked our respondents about their attitudes towards allowing family presence (FP) as well as their actual experience of requests from families to be allowed to witness resuscitations. Multiple logistic regression was used to analyze the association between the many variables and a positive attitude towards FP. RESULTS Out of 300 health care professionals who received forms, 270 responded (a 90% response rate). Generally only 15.8% of our respondents agreed to allow relatives to witness resuscitations, although more than twice the number (38.5%) agreed that relatives do have a right to be around during resuscitation. Health care providers are significantly more likely to allow FP if the procedures are perceived as likely to be successful (e.g., intravenous cannulation and blood taking as compared to chest tube insertion). Doctors were more than twice as likely as paramedics to agree to FP (p-value = 0.002). This is probably due to the Malaysian work culture in our health care systems in which paramedics usually adopt a 'follow-the-leader' attitude in their daily practice. CONCLUSION The concept of allowing FP is not well accepted among our Malaysian health care providers