Phototactic bioconvection in an algal suspension with a free top wall due to diffuse flux in the absence of direct collimated flux

Abstract

In this article, the effect of diffuse flux in the absence of direct collimated flux on the onset of phototactic bioconvection is investigated. The main effect of diffuse flux in the absence of collimated flux is on the swimming behaviour of microorganisms in the suspension. At higher diffuse flux, the horizontal component of swimming orientation exhibits a higher magnitude, which slows the rate of pattern formation in the suspension. Also, the linear stability of the suspension predicts that the most unstable mode of disturbance transits from stationary (oscillatory) to oscillatory (stationary) at the variation in the magnitude of diffuse flux for some fixed parameters. The overstable nature of disturbance is mostly observed at the high value of swimming speed and extinction coefficient. Moreover, the suspension shows a more stable behaviour at the higher magnitude of diffuse flux.

Figures (17)

• Figure 1: Formation of sublayer inside the suspension at a depth where $G=G_c$.
• Figure 2: Alteration in the total intensity for a homogeneous suspension at different values of $B$, while $k=0.5$, and $\omega=0.7$.
• Figure 3: (a) Photo-response curve for $G_c=1.0$, and (b) basic profiles of cell concentration for different sets of values of diffuse flux $B$, where $V_c=20$, $\kappa_H=0.5$, and $\omega=0.7$.
• Figure 4: (a) The variation in total intensity in a uniform suspension for two different values of $B$ and, (b) corresponding basic profiles of cell concentration in the suspension for the same values of $B$. The parameters $S_c$, $V_c$, $\kappa_H$, and $\omega$ are held constant at $20$, 20, $0.5$, and $1$, respectively.
• Figure 5: (a) The basic profiles of cell concentration at steady state, (b) corresponding marginal stability curves. Here the upper surface is stress-free, and the parameter values $V_c=20$, $k_H=0.5$, and $\omega=0.7$.