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 Methods Programs Biomed. 2020 Jun;189:105313. doi: 10.1016/j.cmpb.2020.105313. Epub 2020 Jan 11.
The swimming mechanism of self-propelling organisms has been imitated by biomedical engineers to design the mechanical micro bots. The interaction of these swimmers with surrounding environment is another important aspect. The present swimming problem integrates Taylor sheet model with couple stress fluid model. The thin passage containing micro-swimmers and mucus is approximated as a rigid (passive) two-dimensional channel. The spermatozoa forms a pack quite similar as a complex wavy sheet.
Swimming problem with couple stress cervical liquid (at low Reynolds number) leads to a linear sixth order differential equation. The boundary value problem (BVP) is solved analytically with two unknowns i.e. speed of complex wavy sheet and flow rate of couple stress mucus. After utilizing this solution into equilibrium conditions these unknowns can be computed via Newton-Raphson algorithm. Furthermore, the pairs of numerically calculated organism speed and flow rate are utilized in the expression of power dissipation.
This work describes that the speed of micro-swimmers can be enhanced by suitable rheology of the surrounding liquid. The usage of couple stress fluid as compared to Newtonian fluid enhances the energy dissipation and reduces the flow rate. On the other hand complex wavy surface also aids the organisms to swim faster.
生物医学工程师模仿自推进生物的游泳机制来设计机械微型机器人。这些游泳者与周围环境的相互作用是另一个重要方面。本研究将泰勒片模型与偶应力流模型相结合，来解决微型游泳者的游泳问题。含有微型游泳者和黏液的薄通道被近似为刚性（被动）二维通道。精子形成了一种类似于复杂波浪片的包。
在低雷诺数下，偶应力颈液的游泳问题导致了一个线性六阶微分方程。边界值问题（BVP）通过两个未知量（即复杂波浪片的速度和偶应力黏液的流量）进行解析求解。利用这个解到平衡条件，就可以通过牛顿-拉普森算法计算这些未知量。此外，通过数值计算得到的生物体速度和流量对被用来表达能量耗散。
本研究表明，通过适当改变周围液体的流变学性质，可以提高微型游泳者的速度。与牛顿流体相比，偶应力流体的使用可以增强能量耗散并降低流量。另一方面，复杂的波浪表面也有助于生物体更快地游泳。
