Effects of forward scattering on the onset of phototactic bioconvection in an algal suspension under diffuse flux without collimated flux

Abstract

Phototaxis refers to the directed swimming response influenced by the sensed light intensity in microorganisms. Positive phototaxis involves motion toward the light source, while negative phototaxis entails motion away from it. This study explores the phototactic bioconvection in a suspension of anisotropic scattering phototactic algae, illuminated by diffuse flux without direct collimated flux. The basic state is characterized by zero fluid flow, with the balance between upward and downward swimming due to positive and negative phototaxis, respectively, counteracted by microorganism diffusion. The paper conducts a thorough numerical analysis of linear stability, placing particular emphasis on the impact of forward scattering. The onset of bioconvection manifests either through a stationary mode or an oscillatory mode. The transition between these modes is observed with varying anisotropic coefficients for specific parameter values.

Figures (18)

• Figure 1: Formation of sublayer inside the suspension of phototactic algae at a depth where $G=G_c$.
• Figure 2: Exploring the impact of the forward scattering coefficient $A_1$ on the total intensity, $G_s$, within a uniform suspension while maintaining a fixed values $\omega=0.7$ and $\tau_H=0.5$. Various scenarios are considered with different values of B: $A_1=0 (-)$, $A_1=0.4 (---)$, and $A_1=0.8 (-\cdot-\cdot-)$.
• Figure 3: (a) The photo-response curve featuring a critical intensity value of $G_c=1.0$, and (b) The influence of the forward scattering coefficient, $A_1$, on the fundamental concentration profiles while maintaining a constant $\omega=0.7$, with varied values of B: A$=0 (-)$, A$=0.4 (---)$, and A$=0.8 (-\cdot-\cdot-)$. The parameters $V_c=20$ and $\tau_H=0.5$ are held constant.
• Figure 4: (a) Examining how the linearly anisotropic scattering coefficient $A_1$, impacts the profiles of base concentration, and (b) exploring the corresponding neutral curves. Here, the parameters that remain fixed are as follows: $V_c = 20$, $\omega = 0.7$, $\tau_H = 0.5$, $B = 0.5$, and $G_c = 1$.
• Figure 5: (a) Examining how the linearly anisotropic scattering coefficient $A_1$, impacts the profiles of base concentration, and (b) exploring the corresponding neutral curves. The parameters that remain fixed are as follows: $V_c = 20$, $\omega = 0.7$, $\tau_H = 0.5$, $B = 0.62$, and $G_c = 1$.