Wavelengths of Gyrotactic Plumes in Bioconvection

Abstract

Bioconvection occurs as the result of the collective behaviour of many microorganisms swimming in a fluid and is realized as patterns similar to those of thermal convection which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. The continuum model of Pedley et al. (1988, J. Fluid. Mech. 195, 223-237) is used to describe the suspension. 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. To examine the dependence of the horizontal pattern wavelengths on the parameters, we consider two-dimensional solutions in a wide chamber using rigid side walls. The wavelengths of the numerical computations are in good agreement with the experimental observations and we provide the first computational examples of the commonly seen 'bottom-standing' plumes.

Two-Dimensional Gravitactic Bioconvection in a Protozoan (Tetrahymena pyriformis) Culture

“…Numerical simulation by Ghorai and Hill (2000) was able to generate downward plumes that appeared very similar to those observed in the present study (Fig. 8).…”

“…In that model, the pattern is likely to be initiated by the migration of the cell population toward the center of the downward flow, which results from the balance between the hydrodynamic torque due to the spatial variation of the fluid velocity (vorticity) and the torque due to the separation of the center of gravity and the center of buoyancy within a bottom-heavy cell body (Kessler, 1985a(Kessler, , 1986. The gyrotactic property is also likely to be involved in the steady state pattern formation in the suspension of C. reinhardtii, as shown in a numerical simulation based on the gyrotactic behavior (Ghorai and Hill, 2000). Due to gyrotaxis, Chlamydomonas cells focus on the axis of downwardly directed Poiseuille flow and diverge from upward ones (Kessler, 1985a).…”

Bioconvective pattern formation ofTetrahymenaunder altered gravity

“…Although the linear stability analyses on the densityinstability model and the gyrotacticinstability model (Pedley et al, 1988) only predict the onset of patterns for suspensions for which the Rayleigh numbers are just above critical, the nonlinear numerical analyses on the basis of the same models showed the formation of steady state patterns well above critical values (Harashima et al, 1988;Ghorai and Hill, 2000). In the density-instability model, the wave number of the pattern arising at the onset of the convection is hypothesized to increase with increasing Rd/σ, where σ is a Schmidt number and given by σ=ν/κv .…”

Drastic reorganization of bioconvection pattern of Chlamydomonas: Quantitative analysis of the pattern transition response

“…Enhanced gyrotactic features may have forced the larger number of cells to be entrained to the downward plumes, which caused the cell population to shift downward. This may break down the SS1 pattern, and a new pattern may emerge from the disordered, quasistable state as the regular pattern, consisting of the 'bottomstanding' plumes with narrower spacing, which is characteristically obtained from the simulated bioconvection of gyrotactic organisms (Ghorai and Hill, 2000). The entrainment of the cell to the downward plume would be accelerated with increasing cell density of the suspension, and result in the shortening of the latent time to the initiation of the pattern transition response (Fig.…”