A comprehensive numerical investigation of Carreau-Yasuda slime beneath complex bacterial wavy surface

Abstract Gliding motility often noticed in phylogenetically rod-shaped bacteria which locomote via dissipating their own energy. The said gliding motion via producing waves and secreting slime is generally witnessed in gram-negative bacteria. The influence of Inertia in slime layer beneath glider is also a significant feature to this mechanism. The propulsive microbe pushes the slime backwards, while reactive forces in the slime aids a forward movement of the propeller. Out of several motility modes the complex wavy gliding mechanism is considered here so one can approximate the glider’s surface by undulating two-dimensional sheet. Moreover, the nonNewtonian slime beneath the organism is taken as Carreau Yasuda fluid. Following a traditional approach of a fluid flow problem balance of mass and momentum is utilized. The x and y-component of momentum equation is combined and reduced into fourth order DE via lubrication and creeping flow assumption. For suitable values of rheological parameters, swimming gait and some initial values of gliding speed and flow rate, the BVP is solved via MATLAB build in routine bvp-5c. Modified Newton-Raphson algorithm is employed to simulate the unknowns present in the boundary conditions. Power required by the glider, velocity of the slime and level curves are also obtained with the aid of these realistic numerical pairs. The computed results are plotted in the latest available version of MATLAB (2021a) and discusses in detail.