Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms
Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms
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非牛顿流体在不同波形的扩流管中的蠕动输送
DOI：
10.1016/j.mcm.2007.10.018
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
R. Banerjee
中科院分区：
文献类型：
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作者：
P. Hariharan;V. Seshadri;R. Banerjee
本文研究了非牛顿流体在扩张管中的蠕动输运，模型为幂律流体和宾汉流体，壁面波形分别为正弦波、多正弦波、三角波、梯形波和方波。采用傅里叶级数的方法，得到了时间和空间相关的壁面形状的表达式。计算了不同振幅比、φ、幂律指数n、屈服应力τ0和波形下的时间平均压力上升-流量关系的解。结果表明，φ和n在微扰中起着重要作用。当正弦波的φ从0.6增加到0.8时，最大压力上升，[公式：见正文]增加了10倍。将n从0.6增加到1，[公式：见正文]增加了3倍。对于φ=0.5的宾汉流体，当τ0从1（非牛顿流体）减小到0（牛顿流体）时，ΔPL_（max）增加25%。在所考虑的所有波形中，所得到的[公式：见正文]对于方波最大，对于三角波最小（取决于φ，小4-15倍）。最后，追踪无质量粒子的轨迹线来研究回流的发生。据观察，即使在零流速，回流发生在管壁附近，回流区的厚度和形状强烈地依赖于φ，n和蠕动波的形状。
The present study investigates the peristaltic transport of non-Newtonian fluid, modeled as power law and Bingham fluid, in a diverging tube with different wall wave forms: sinusoidal, multi-sinusoidal, triangular, trapezoidal and square waves. Fourier series is employed to get the expressions for temporal and spatial dependent wall shapes. Solutions for time average pressure rise — flow rate relationship are computed for different amplitude ratios, φ, power law indices, n, yield stresses, τ0, and wave shapes. Results indicate that φ and n play a vital role in peristalsis. When φ of the sinusoidal wave is increased from 0.6 to 0.8, the maximum pressure rise, [Formula: see text] increased by a factor of 10. Increasing n from 0.6 to 1 increased the [Formula: see text] by a factor of 3. For Bingham fluid with φ=0.5, a 25% increase in ΔPL,maxis obtained when τ0, is reduced from 1 (non-Newtonian) to 0 (Newtonian). Of all the wave shapes considered, [Formula: see text] obtained is maximum for the square wave and minimum for the triangular wave (4–15 times less depending on φ). Finally, pathlines of massless particles are traced to investigate the occurrence of reflux. It is observed that, even for zero flow rate, reflux occurs near the tube wall and the thickness and shape of the reflux region strongly depends on φ, n, and shape of the peristaltic waves.