Integrating effects of Carreau–Yasuda slime on bacterial hydrodynamics

Abstract

This work deals with gliding motion of bacteria over a non-Newtonian slime layer attached to a solid substrate. The surface of a glider is approximated with a simple wavy two-dimensional sheet while the sticky slime is modeled as Carreau–Yasuda fluid. The classical Navier–Stokes equations are transformed by using Galilean transformation and dimensionless variables. Flow beneath the organism is creeping and the lubrication assumption is also valid in this scenario, hence the equation is reduced to fourth-order BVP in terms of stream function. The basic purpose is to compute the gliding speed and flow rate of the slime which are present in the boundary conditions. MATLAB built-in bvp5c solver is utilized to calculate the numerical solution of the stream function. Further, unknowns (flow rate and cell speed) are refined by using modified Newton–Raphson method (MNRT). Further, these pairs are employed in the formula of energy expended. Velocity and stream function is also plotted for these computed pairs. This study is motivated by scientific interest and the desire to understand the dynamics of gliding bacteria. The findings of this study are thought to be beneficial in the development of artificial crawlers.