A computational approach to model gliding motion of an organism on a sticky slime layer over a solid substrate

Bacteria are microscopic single-celled microbes that can only be spotted via a microscope. They occur in a variety of shapes and sizes, and their dimensions are measured in micrometers (one-millionth of a meter). Bacterial categorization is based on a variety of features such as morphology, DNA sequencing, presence of flagella, cell structure, staining techniques, oxygen, and carbon-dioxide requirements. Due to these classifications, gliding bacteria are a miscellaneous class of rodlike microorganisms that cling and propel over ooze slime connected with a substrate. Without the assistance of flagella, which are essential parts of bacterial motility, the organism movement is adopted by waves streaming down the outer layer of this microorganism. To simulate the locomotion of such gliding microorganisms, a wavy sheet over Oldroyd-4 constant fluid is utilized. Under the long wavelength assumption, the equations regulating the flow of slime (modeled as Oldroyd-4 constant slime) beneath the cell/organism are developed. The quantities such as slime flow rate, cell speed, and propulsion power are computed by using bvp4c (MATLAB routine) integrated with the modified Newton-Rasphson technique. Furthermore, the flow patterns and velocity of the slime are graphically shown and thoroughly described using precise (calculated) values of the cell speed and velocity of the slime.