arXiv subjects

M. K. Panda

Publications and source records attributed to M. K. Panda.

12 recordsLinked to original sources

arXiv2025

Thermal-phototactic bioconvection in a forward scattering algal suspension

Bioconvection induced by phototaxis and thermal gradients in an anisotropic (forward) scattering algal suspension is investigated in this article. The suspension is illuminated by collimated irradiation from above and heated either from top or bottom. The linear theory is deployed on the steady state of the proposed bioconvective system and resulting eigen value problem is solved using fourth-order accurate finite-difference scheme based on Newton-Raphson-Kantorovich iteration. The results indicate that the forward scattering and heating from above (or cooling from below) in an algal suspension enhance bioconvective stability. On the other hand, heating from below enhance bioconvective instability for a fixed forward scattering coefficient.

physics.bio-ph↗

arXiv2025

Phototactic bioconvection under oblique collimated irradiation in a forward scattering suspension

Phototaxis, the process by which living organisms navigate toward optimal light conditions, is essential for motile photosynthetic microorganisms. Positive(negative) phototaxis denotes the motion directed towards(away from) the source of illumination. The main objective of this study is the numerical investigation of onset of bioconvection in a suspension of phototactic microorganisms illuminated by oblique collimated irradiation at the top. In this suspension, the algal cells absorb and anisotropically scatter incident light which influences the flow dynamics of the cells.

physics.bio-ph↗

arXiv2025

Thermal phototactic bioconvection in an isotropic porous medium heated from above

This study investigates thermal phototactic bioconvection in an isotropic porous medium using the Darcy-Brinkman model. The top boundary of the medium is exposed to normal collimated light and subjected to heating. A linear analysis of bio-thermal convection is performed using a fourth-order accurate finite difference scheme, employing Newton-Raphson-Kantorovich iterations for both rigid-free and rigid-rigid boundary conditions. The effects of the Lewis number, Darcy number, and thermal Rayleigh number on bioconvective processes are examined and presented graphically. The findings reveal that increasing the thermal Rayleigh number stabilizes the suspension, whereas a higher Lewis number enhances instability.

math.DS↗

arXiv2025

Effects of oblique collimated irradiation on the onset of phototaxis-driven bioconvection in an isotropic porous medium

In this study, we investigate the effects of oblique collimated irradiation on the onset of phototaxis-driven bioconvection in an isotropic porous medium. A linear stability analysis is conducted to assess the system's stability under fixed parameter values. The resulting eigenvalue problem is numerically solved using a fourth-order accurate finite difference scheme combined with Newton-Raphson-Kantorovich iterations. The results indicate that the system exhibits increased instability as the angle of incidence rises for a given Darcy number. Additionally, the critical Rayleigh number is found to be higher when a rigid top wall is considered compared to a stress-free top wall, suggesting that the suspension attains greater stability in the presence of a rigid top boundary.

cond-mat.soft↗

arXiv2024

Effect of oblique irradiation on the onset of thermal-phototactic-bioconvection in an isotropic scattering algal suspension

In this study, our focus is mainly to check the effect of light scattering on the onset of thermal-phototactic-bioconvection in an algal suspension where the suspension is illuminated by the collimated oblique irradiation from above while simultaneously applying heating or cooling from below. We conduct a numerical investigation into the linear stability of a suspension containing phototactic algae, focusing particularly on how the angle of incidence of oblique collimated irradiation influences the system. Our solutions reveal a transition of the most unstable mode from a stationary to an overstable state, or vice versa, under certain parameter configurations as the angle of incidence varies. Additionally, we frequently observe oscillatory instabilities in cases where the upper surface is rigid, particularly as the angle of incidence increases within the suspension.

math.DS↗

arXiv2024

Effect of oblique irradiation on the onset of thermal phototactic bioconvection in non-scattering medium

The linear stability of a suspension of phototactic algae is investigated numerically with particular emphasis on the effects of the angle of incidence of the illuminating oblique collimated irradiation with thermal effects. The suspension is illuminated by the oblique collimated irradiation from the top and heated/cooled from the bottom. The linear stability analysis shows that the suspension becomes more unstable as the angle of incidence increases.

math.DS↗

arXiv2024

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

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.

math.DS↗

arXiv2024

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

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.

math.DS↗

arXiv2023

Effect of heating or cooling in a suspension of phototactic algae with no-slip boundary conditions

In this study, we investigate the impact of heating or cooling in a suspension experiencing phototactic bioconvection. The suspension is illuminated by collimated irradiation from the top and subjected to heating or cooling from the bottom. The governing equations include the Navier Stokes equations with the Boussinesq approximation, the diffusion equation for motile microorganisms, and the energy equation for temperature. Employing linear perturbation theory, we analyse the linear stability of the suspension. The findings predict that the suspension undergoes destabilization when heated from below and stabilization when cooled from below. This suggests a sensitive dependence of the system's stability on the thermal conditions, providing valuable insights into the behavior of phototactic bioconvection under different heating or cooling scenarios.

math.DS↗

arXiv2023

Two dimensional penetrative phototactic bioconvection with periodic sidewalls

Light gradient can allow many motile photosynthetic microorganisms to bias their motion towards moderate light (positive phototaxis) or away from intense light (negative phototaxis). The proposed work presents the penetrative phototactic bioconvection in a non-scattering algal suspension. The suspension is confined by a stress-free top boundary, and rigid bottom and periodic lateral boundaries. The resulting bioconvective patterns of the problem strongly resemble to that of a spatially extended domain in the same vicinity. The bioconvection solution appears in the form of a two-rolls pattern (or any even number of rolls) due to the periodic lateral boundaries.

math.DS↗

arXiv2023

Phototactic bioconvection in a forward scattering suspension illuminated by both diffuse and oblique collimated flux

The onset of light-induced bioconvection via linear stability theory is investigated qualitatively for a suspension of phototactic algae. The forward scattering algal suspension is uniformly illuminated by both diffuse and oblique collimated flux. An unstable mode of disturbance at bioconvective instability transits from the stationary (overstable) to overstable (stationary) state at the variation in forward scattering coefficient for fixed parameters. Suspension becomes more stable as forward scattering coefficient increases.

math.DS↗

arXiv2023

Effects of both diffuse and collimated incident radiation on phototactic bioconvection

The linear stability of a finite-depth algal suspension is investigated numerically with particular emphasis on the effects of angle of incidence. The suspension of phototactic algae is uniformly illuminated by both diffuse and oblique collimated irradiation. The bioconvective solutions show a transition of the most unstable mode of disturbance from the stationary (overstable) to overstable (stationary) state at the variation in angle of incidence for fixed parameter ranges. Furthermore, a transition from mode 2 to mode 1 instability is noticed for some parameter values as the angle of incidence varies. Oscillatory modes of disturbance are also predicted at the increment in angle of incidence (or cell swimming speed)

math.DS↗