Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia; NUTECH, School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan.
Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan.
Comput Biol Med. 2023 Feb;153:106386. doi: 10.1016/j.compbiomed.2022.106386. Epub 2022 Nov 30.
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.
据推测，滑行细菌通过在自身表面产生波来移动，并留下粘性的粘液痕迹。粘液基本上是一种粘弹性的光滑材料。基于这些观察，我们使用数学模型（波动片）来研究在非牛顿粘液层上滑行细菌的运动。使用 FENE-P 模型的本构方程来描述非牛顿粘液的流变行为。此外，粘液下面的基底近似为多正弦片。提出了一种混合计算技术，用于求解具有代数方程组的二阶 DE。使用 bvp5c 结合改进的牛顿-拉普森技术（MNRT）模拟了所涉及参数较大时的生物速度、流速和能量损耗。在几个图中显示了软质和硬质基底、滑动和不滑动边界条件、牛顿和非牛顿粘液的比较。还为实际的速度和流速对绘制了粘液的流线模式和速度，并进行了详细解释。
