Tian Fang-Bao
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia.
Comput Math Methods Med. 2016;2016:7981386. doi: 10.1155/2016/7981386. Epub 2016 Oct 19.
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
一种用于涉及非牛顿流体（如幂律流体）的流固相互作用的浸入边界 - 格子玻尔兹曼方法被开发出来。在该方法中，通过使用浸入边界法将柔性结构（如胶囊）动力学与流体动力学耦合起来。通过求解格子玻尔兹曼方程获得不可压缩粘性幂律流体的运动。在格子玻尔兹曼方法中使用与剪切速率相关的弛豫时间来实现非牛顿流变学。然后通过考虑直通道中的幂律流动来验证非牛顿流动求解器，这是验证内部求解器的基准问题之一。对于幂律指数的各种值，数值结果与解析解呈现出良好的一致性。最后，我们应用该方法通过改变雷诺数从0.025到0.1、无量纲剪切速率从0.004到0.1以及幂律指数从0.2到1.8来研究幂律剪切流中胶囊的变形。研究发现，对于不同的雷诺数和无量纲剪切速率，胶囊的变形随着幂律指数的增加而增大。此外，在所考虑的流动区域中，雷诺数对胶囊变形没有显著影响。而且，与较小值相比，幂律指数效应在较大的无量纲剪切速率下更强。
