FENE-P fluid flow generated by self-propelling bacteria with slip effects.

It is hypothesized that gliding bacteria move by producing waves on their own surface and leave an adhesive slime trail. Slime is basically a viscoelastic slippery material. Based on these observations, we use a mathematical model (of undulating sheet) to examine the locomotion of gliding bacteria over a layer of non-Newtonian slime. The constitutive equations of FENE-P model are employed to characterize the rheological behavior of the non-Newtonian slime. Moreover, substratum beneath the slime is approximated by a multi-sinusoidal sheet. A hybrid computational technique to solve the second order DE with a system of algebraic equations is presented. The speed of organism, flow rate and energy loss at larger values of the involved parameters are simulated using bvp5c in conjunction with a modified Newton-Raphson technique (MNRT). The comparison of soft and rigid substrate, slip and no-slip boundary conditions, Newtonian and non-Newtonian slime is displayed in several figures. Streamlines pattern and velocity of the slime are also drawn for the realistic pairs of speed and flow rate and are thoroughly explained.

Controlling kinetics of self-propelled rod-like swimmers near multi sinusoidal substrate.

Motility is defined as the movement of cells by some form of self-propulsion. Some organisms motile by using long flagella that quickly rotate to propel them over various surfaces (in swarming and swimming mechanism), while few motile without the aid of flagella (in twitching, sliding and gliding mechanism). Among these modes, gliding motility is adopted by a rod-shaped organism famously known as gliding bacteria. It is hypothesized that in such type of motility, organism motile under their own power by secreting a layer of slime on the substrate. In this study, an active wall is considered as a substrate and a two-dimensional wavy sheet as an organism. Slip effects are also employed in the current work. The physical properties of the slime are governed by a suitable constitutive equation of couple stress model. A sixth order BVP is obtained by utilizing lubrication assumption. For an appropriate fixed pair of flow rate and organism speed the BVP is solved by MATLAB built-in function bvp-5c. This solution is utilized in the mechanical equilibrium conditions which are obviously not satisfied yet. To satisfy these conditions, the pair of flow rate and gliding speed is refined by a root finding algorithm (modified Newton-Raphson method). By employing this numerical scheme, various figures are shown to demonstrate the effect of several associated parameters on organism speed, flow rate, energy expended by the glider, streamlines and longitudinal velocity. It is observed from the graphical results that organism speed and energy consumption is directly proportional to the couple stress parameter and slip effects.

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.