Statistical evaluation of motile number in bio-convective swirling microorganism flow through a thin needle: Drug delivery system

In enhancing solutal transfer and flow stability in biomedical systems, the bioconvective transport of motile microorganisms has gained substantial attention. For the optimal design of drug delivery systems, needle-based injections and microorganism-driven convection within confined geometries are essential, where the control of nutrient and drug dispersion is required. Motivated by these applications, the current study shows a statistical evaluation of the motile number in a bio-convective flow of swirling microorganisms subjected to homogeneous and heterogeneous chemical reactions via a thin needle immersed in a permeable structure. Additionally, the impact of thermal radiation on the energy transport phenomenon is considered. The mathematical framework is based on the coupling behaviour of momentum, energy, solute concentration and microorganisms with various factors. Homogeneous and heterogeneous reactions are introduced for the realistic biochemical interactions during drug transport and release processes. The reduction of the governing dimensional model into dimensionless form is obtained by the utilization of appropriate similarity functions. The resulting system is handled numerically using a Runge-Kutta shooting scheme. A detailed statistical analysis of motile number is presented employing response surface methodology (RSM) adopting central composite design (CCD) and tested its validation utilizing analysis of variance (ANOVA). A three-factor design of motile number is presented for the impact of the solutal and bio-convective Lewis number with Peclet number. The results are reported briefly via their graphical illustration and presented in the discussion section. The observation shows that the enhanced bio-convective Lewis number due to variations in microorganism diffusivity has an opposite impact on the homogeneous and heterogeneous reactions. The quadratic model of the motile number using statistical optimization for the three-factor design lead to best fit model with high R 2 value.