Ahmed Aftab, Siddique J I, Mahmood Asif
a Department of Mathematics , Capital University of Science and Technology , Islamabad , Pakistan .
b Department of Mathematics , Penn State University , York , PA , USA .
Comput Methods Biomech Biomed Engin. 2017 Oct;20(13):1464-1473. doi: 10.1080/10255842.2017.1376323. Epub 2017 Sep 28.
We investigate the behavior of a spherical cavity in a soft biological tissue modeled as a deformable porous material during an injection of non-Newtonian fluid that follows a power law model. Fluid flows into the neighboring tissue due to high cavity pressure where it is absorbed by capillaries and lymphatics at a rate proportional to the local pressure. Power law fluid pressure and displacement of a solid in the tissue are computed as function of radial distance and time. Numerical solutions indicate that shear thickening fluids exhibit less fluid pressure and induce small solid deformation as compared to shear thinning fluids. Absorption in the biological tissue increases as a consequence of flow-induced deformation for power law fluids. In most cases non-Newtonian results are compared with the viscous fluid case to magnify the differences.
我们研究了在注射遵循幂律模型的非牛顿流体过程中，被建模为可变形多孔材料的柔软生物组织中的球形腔的行为。由于腔压力高，流体流入相邻组织，并在那里以与局部压力成比例的速率被毛细血管和淋巴管吸收。幂律流体压力和组织中固体的位移作为径向距离和时间的函数进行计算。数值解表明，与剪切稀化流体相比，剪切增稠流体表现出较低的流体压力并引起较小的固体变形。对于幂律流体，生物组织中的吸收由于流动诱导的变形而增加。在大多数情况下，将非牛顿结果与粘性流体情况进行比较以放大差异。
