Linear stability analysis of gyrotactic plumes

Abstract

Bioconvection occurs as the result of the collective behavior of many micro-organisms 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. Using the continuum model of Pedley et al. ͓"The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms," J. Fluid Mech. 195, 223 ͑1988͔͒, the linear stability of a gyrotactic plume ͑descending line of concentrated micro-organisms͒ is investigated. Linear stability analysis predicts that a plume is always unstable to both the varicose and meandering modes. The growth rates of these instability modes and their dependence on parameter values are investigated. Comparisons are made with the experimental and numerical results.

Advances in Bioconvection

“…The blip features observed in Figure 4e, f have been investigated experimentally (Denissenko & Lukaschuk 2007) and theoretically (Ghorai & Singh 2009, Hwang & Pedley 2014b. Notably, the steady plume solutions are subject to a varicose instability that has been found to be due principally to the horizontal gradient in cell orientation from nonuniform shear in alliance with the gyrotactic instability.…”

An overstability analysis of vertically vibrated suspension of active swimmers subjected to thermal stratification

“…(52) 1 = 52 (Pe) 3 + 528 (Pe) 5 (exp (Pe) − 1) − 4 (Pe) 2 + 264 (Pe) 4 (exp (Pe) + 1) (53) 2 = 16∕(Pe) + 192 (Pe) 3 (exp (Pe) − 1) − 96 (Pe) 2 (exp (Pe) + 1) (54) 3 = 72 (Pe) 5 + 720 (Pe) 7 (exp (Pe) − 1) − 6 (Pe) 4 + 360 (Pe) 6 (exp (Pe) + 1) For the limiting when Pe → 0 and G → 0 , the values of Λ 1i (i = 1, 2, ...7) defined in Eq. (50) are given as (74)…”

“…Bioconvection illustrates a mechanism for inducing the mass transfer mixing in the fluid micro-volumes and is potentially applicable in several pharmaceutical and bioengineering technologies [5,6]. A numerical computation for three dimensional gyrotactic plumes in a rectangular chamber with free-free sidewalls with their structural formations was scripted by Ghorai and Singh [7]. A classical linear stability theory is available on spheroidal orientations for uniform gyrotactic bioconvection [8].…”

Requirement of Volume of Dredging and Capacity Enhancement of Dredgers in India

“…If the light intensity is high, it dissipates steady patterns or intercepts pattern formation in well-stirred cultures. The intensity of light can also alter the shape and size of bioconvection patterns 10,11,16,17 . These changes can be due to several reasons, which can be described as follows.…”