A numerical framework for modeling the dynamics of micro-organism movement on Carreau-Yasuda layer

The gliding motility is widely observed in rod-shaped bacteria known as gliding bacteria, which produce waves on their surfaces and leaves a sticky layer of ooze slime. In the current analysis, we utilize a hydrodynamic complex wavy model to analyze the movement of gliding bacteria over a layer of Carreau-Yasuda (C.Y) fluid. After using lubrication and creeping flow assumption, the resultant fourth-order differential equation of the gliding model is solved numerically with two different techniques, i.e., implicit finite difference method (IFDM) and MATLAB's function Bvp-5c. The convergent solution is obtained for appropriate gliding gaits, slime parameters, and certain guesses of flow rate (Q) and glider speed (Vg/c). Unknowns are refined by the modified secant method in such a way that they will satisfy the mechanical equilibrium condition. Excellent agreement between two different computational approaches and outstanding benchmarking is attained. Power required (P), level curves and velocity profiles are plotted for calculated pair from the said procedure. The key verdict of this present examination is that the bacterial speed and slime velocity can be controlled via five different rheological parameters and two gliding gaits.

Automated summary

In this study, we used a complex wavy model to analyze the gliding motion of bacteria on a layer of Carreau-Yasuda fluid. By solving the fourth-order differential equation of the gliding model numerically using two different techniques, i.e., implicit finite difference method (IFDM) and MATLAB's function Bvp-5c, we obtained convergent solutions. The results showed that the speed of bacteria and slime velocity can be controlled by five rheological parameters and two gliding gaits.