Biomechanics of bacterial gliding motion with Oldroyd-4 constant slime

Microscale gliders are regularly affected by the local surrounding environment, such as liquid rheology and physical (nearby) boundaries. This article focuses on the numerical simulations of bacterial speed over a non-Newtonian slime and its power expenditure. The flow rate generated by the swimmer, slime speed, shear stress and level curves are also points of interest. To fulfill the purpose, Oldroyd-4 constant model is assumed over a rigid boundary. A complex undulating sheet is approximated as a bacterial surface. Since a slime (present below the undulating sheet) is a non-Newtonian fluid, a modeling approach of peristaltic flow problem is adopted, and dynamic equilibrium conditions are implemented for steady motion. Implicit finite difference method (FDM) is employed to calculate the numerical solution of reduced boundary value problem. To compute the flow rate and cell speed, Broyden’s root finding algorithm is integrated with FDM. These computed values are further utilized to perceive the behavior of work done, shear stress at the surface of bacteria, velocity of slime and streamlines.