On IFDM simulation of Oldroyd 8-constant fluid flowing due to motile microorganisms

Abstract

This work studies the motion of bacteria on the Oldroyd 8-constant slime layer to determine the fundamental mechanism of bacterium gliding over immune system cells based on creeping flow and long wavelength approximation applicable to Stokes equations. Galilean transformation is also utilized to convert the problem from the lab to a wave frame. The bacterial gliding speed and the fluid flow rate are computed using an implicit finite difference method (IFDM), and a root-finding algorithm. These computed pairs are utilized to get power dissipation. Our results show that, due to the effect of slime rheology, characterized by relaxation time and retardation time, the gliding speed, flow rate of slime, and energy dissipation of bacteria are greatly modulated. Dynamic analysis shows that bacteria glide more quickly with reduced power dissipation when relaxation time is less than retardation time. On the other hand, relaxation time greater than the retardation time leads to slower bacterial swimming with increased energy consumption. The work presented here emphasizes that changes in the rheology of slime, specifically added time (relaxation and retardation time), can promote or inhibit bacterial motility. Additionally, the outcomes are confirmed using a separate technique based on bvp4c solver. A new comprehensive understanding of how this gliding happens (by controlling slime rheology and gliding gait) opens up possibilities for bio-inspired designs in the form of micro-robots or anti-fouling surfaces based on this work.