The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

Abstract

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection-diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection-diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection-diffusion model to apply. We also use a simple twodimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the 'break-down' regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection-diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel

“…The generalised Taylor dispersion theory would be a good starting point in this regard as it has recently been shown to provide a reliable prediction for self-propelling particles with a constant rotational diffusivity (e.g. Bearon et al 2011;Croze et al 2013). However, it is not evident yet whether it would also provide a good description for the dispersion of 'real' cells.…”

“…Bearon et al 2012;Croze et al 2013). It can be improved by the generalised Taylor dispersion theory as recently addressed (Hill & Bees 2002;Malena & Frankel 2003;Bearon et al 2011). However, it should also be pointed out that it is not evident yet whether the generalised Taylor dispersion theory itself would provide a good quantitative prediction for D * T in 'real' cell suspensions.…”

Swim stress, motion, and deformation of active matter: effect of an external field

“…14-18 Manela and Frankel 17 analyzed the effective translational diffusivity of dipolar swimmers subjected to a simple shear ow and an external eld, and Bearon and coworkers 19,20 extended the analysis to different ow conditions. Owing to slow numerical convergence, most studies have focused on weak external elds; in practice, however, active particles may be exposed to strong external elds, be it a chemical or thermal gradient eld.…”

Gyrotactic bioconvection at pycnoclines

“…To overcome this difficulty, Hill & Bees (2002) and Manela & Frankel (2003) calculated the diffusion tensor using the generalized Taylor dispersion theory which accounts for shear-induced contributions in both the cells' position and orientation. This approach has been employed to simulate suspensions of swimming micro-organisms subjected to a range of shear strengths in planar (Bearon, Hazel & Thorn 2011) and axisymmetric pipe flows (Bearon, Bees & Croze 2012) and the corresponding results exhibit good agreement with those obtained via individual-level biased random walk simulations.…”