Development and stability of gyrotactic plumes in bioconvection

Using the continuum model of Pedley, Hill and Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results

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

Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

We study the effects of imposed {three-dimensional flows} on the trajectories and mixing of gyrotactic swimming micro-organisms, and identify new phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor--Green and ABC flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical `plume-like' structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. \note{Furthermore, studies of Lyapunov exponents reveal that as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds

Study of cardiovascular function using a coupled left ventricle and systemic circulation model

To gain insight into cardio-arterial interactions, a coupled left ventricle-systemic artery (LV–SA) model is developed that incorporates a three-dimensional finite-strain left ventricle (LV), and a physiologically-based one-dimensional model for the systemic arteries (SA). The coupling of the LV model and the SA model is achieved by matching the pressure and the flow rate at the aortic root, i.e. the SA model feeds back the pressure as a boundary condition to the LV model, and the aortic flow rate from the LV model is used as the input for the SA model. The governing equations of the coupled system are solved using a combined immersed-boundary finite-element (IB/FE) method and a Lax–Wendroff scheme. A baseline case using physiological measurements of healthy subjects, and four exemplar cases based on different physiological and pathological scenarios are studied using the LV–SA model. The results of the baseline case agree well with published experimental data. The four exemplar cases predict varied pathological responses of the cardiovascular system, which are also supported by clinical observations. The new model can be used to gain insight into cardio-arterial interactions across a range of clinical applications

Correlation of mechanical factors and gallbladder pain

Acalculous biliary pain occurs in patients with no gallstones, but is similar to that experienced by patients with gallstones. Surgical removal of the gallbladder (GB) in these patients is only successful in providing relief of symptoms to about half of those operated on, so a reliable pain-prediction model is needed. In this paper, a mechanical model is developed for the human biliary system during the emptying phase, based on a clinical test in which GB volume changes are measured in response to a standard stimulus and a recorded pain profile. The model can describe the bile emptying behaviour, the flow resistance in the biliary ducts, the peak total stress, including the passive and active stresses experienced by the GB during emptying. This model is used to explore the potential link between GB pain and mechanical factors. It is found that the peak total normal stress may be used as an effective pain indicator for GB pain. When this model is applied to clinical data of volume changes due to Cholecystokinin stimulation and pain from 37 patients, it shows a promising success rate of 88.2% in positive pain prediction

First steps in the development of a water temperature model framework for refining the ecological Reserve in South African rivers

Ecological Reserve determination for rivers in South Africa presently does not include a water temperature component, in spite of its importance in determining species distribution patterns. To achieve this requires an understanding of how lotic thermographs from South African rivers differ from northern hemisphere rivers, to avoid mismanaging rivers based on incorrect regional assumptions. Hourly water temperatures from 20 sites in four river systems, representing a range of latitudes, altitudes and stream orders, were assessed using a range of metrics. These data were analysed using principal component analyses and multiple linear regressions to understand what variables a water temperature model for use in ecoregions within South Africa should include. While temperature data are generally lacking in low- and higher-order South African rivers, data suggest that South African rivers are warmer than northern hemisphere rivers. Water temperatures could be grouped into cool, warm and intermediate types. Based on temperature time series analyses, this paper argues that a suitable water-temperature model for use in ecological Reserve determinations should be dynamic, include flow and air temperature variables, and be adaptive through a heat exchange coefficient term. The inclusion of water temperature in the determination and management of river ecological Reserves would allow for more holistic application of the National Water Act’s ecological management provisions. Water temperature guidelines added to the ecological Reserve could be integrated into heuristic aquatic monitoring programmes within priority areas identified in regional conservation plans.Keywords: water temperatures, conservation planning, water temperature modelling, managemen

Sign-reversal of drag in bilayer systems with in-plane periodic potential modulation

We develop a theory for describing frictional drag in bilayer systems with in-plane periodic potential modulations, and use it to investigate the drag between bilayer systems in which one of the layers is modulated in one direction. At low temperatures, as the density of carriers in the modulated layer is changed, we show that the transresistivity component in the direction of modulation can change its sign. We also give a physical explanation for this behavior.Comment: 4 pages, 4 figure