Engineering topics

Pedley, T. J.

Publications and source records attributed to Pedley, T. J..

3 records

NASA NTRS1995

The development of concentration gradients in a suspension of chemotactic bacteria

When a suspension of bacterial cells of the species Bacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e., they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development when N and C depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.

NASA Discipline Cell Biology↗

NASA NTRS1993

The heart works against gravity

The circulatory systems of vertebrate animals are closed, and blood leaves and returns to the heart at the same level. It is often concluded, therefore, that the heart works only against the viscous resistance of the system, not against gravity, even in vascular loops above the heart in which the siphon principle operates. However, we argue that the siphon principle does not assist blood flow in superior vascular loops if any of the descending vasculature is collapsible. If central arterial blood pressure is insufficient to support a blood column between the heart and the head, blood flow ceases because of vascular collapse. Furthermore, the siphon principle does not assist the heart even when a continuous stream of blood is flowing in a superior loop. The potential energy gained by blood as it is pumped to the head is lost to friction in partially collapsed descending vessels and thus is not regained. Application of the Poiseuille equation to flow in collapsible vessels is limited; resistance depends on flow rate in partially collapsed vessels with no transmural pressure difference, but flow rate is independent of resistance. Thus the pressure developed by the heart to establish a given flow rate is independent of the resistance occurring in the partially collapsed vessels. The pressure depends only on the height of the blood column and the resistance in the noncollapsed parts of the system. Simple laboratory models, involving water flow in collapsible tubing, dispel the idea that the siphon principle facilitates blood flow and suggest that previously published results may have been affected by experimental artifact.

Review, Tutorial↗

NASA NTRS1990

A new continuum model for suspensions of gyrotactic micro-organisms

A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.

NASA Discipline Number 28-20↗