Sochi Taha
a Department of Physics & Astronomy , University College London , Gower Street, London WC1E 6BT , UK.
Comput Methods Biomech Biomed Engin. 2016 Feb;19(3):324-329. doi: 10.1080/10255842.2015.1024666. Epub 2015 Apr 24.
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
使用基于残差的孔隙尺度网络建模方法并采用新推导的公式，研究了幂律流体（包括剪切变稀和剪切变稠流体，牛顿流体作为特殊情况包含在内）在相互连接的弹性管网络中的流动。在这些公式的推导过程中，考虑了两个描述弹性可扩张管中局部压力与局部横截面积之间力学相互作用的关系式。该模型可用于描述主要为粘性性质的剪切依赖流动。通过在一些特殊和极限情况下的多项测试验证了所提出模型的行为，在这些情况下结果可以进行定量或定性验证。该模型是同类模型中的首个，包含了对应于流体流变学和管道力学性质的多个主要非线性因素，即非牛顿效应和管道可扩张性。其公式推导、实现过程和性能表明，该模型相对于现有模型具有某些优势，例如在模型所基于的限制假设范围内是精确的、易于实现、计算成本低、可靠性高且收敛平稳。因此，所提出的模型可以用作现有牛顿可扩张模型的替代方案；此外，它扩展了现有建模方法的能力，以涵盖非牛顿流变学。
