具有滑移边界的非牛顿流体电渗流问题应用研究

发布时间：2017-12-26 21:07

本文关键词：具有滑移边界的非牛顿流体电渗流问题应用研究　出处：《山东大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要研究微管道中具有滑移边界条件的非牛顿流体电渗流的流动机理。文章主要分为五个章节。第一章为绪论部分,简要介绍了非牛顿流体、电渗流、分数阶微积分、积分变换以及有限差分数值方法的基础知识。第二章研究在外加电场力和压力共同作用下,微平行管道内非牛顿流体-Eyring流体的电渗流动规律。在考虑微尺度效应,电场作用,非牛顿特性,滑移边界等情况下,建立Eyring流体在微平行管道内电渗流动的力学模型。通过求解线性Possion-Boltzmann方程和Cauchy动量方程,给出Eyring流体速度分布的精确解和近似解析解,并探讨了上述因素对电渗流动的影响。将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析,得到了一些有意义的结果。第三章研究了圆管中分数阶Oldroyd-B流体的瞬时电渗流动,线性Navier模型被用作滑移边界条件。利用Laplace变换和有限Hankel变换方法,给出电势分布和瞬时速度分布的精确解,其中,速度由稳定部分和不稳定部分组成。牛顿流体、分数阶Maxwell流体以及分数阶二阶流体相应的解都可以作为本部分的特解给出。最后我们利用数值Laplace逆变换得到了速度分布半解析解的图像,并分析了各个参数对速度分布的影响,得出了一些有用的结论。我们的结果将对微通道中粘弹性流体流动特性的预测有一定的参考意义,并且有利于微流体设备的设计。在第四章我们利用有限差分方法对圆管中分数阶Oldroyd-B流体的速度分布进行数值求解与拟合,并与构造的解析解做了对比,提出了一种有效的数值计算方法。最后,第五章梳理了本文的主要结论,同时对电渗流的研究和分数阶微积分的发展进行了展望。
[Abstract]:This paper mainly deals with the flow mechanism of non Newtonian fluid with slip boundary conditions in microtubule. The article is divided into five chapters. The first chapter is the introduction, which briefly introduces the basic knowledge of non Newtonian fluid, electroosmotic flow, fractional calculus, integral transformation and finite difference numerical method. In the second chapter, the law of electroosmotic flow of a non Newton fluid -Eyring fluid in a micro parallel pipeline is studied under the combined effect of applied electric field force and pressure. The mechanical model of the electroosmotic flow of the Eyring fluid in a micro parallel pipe is established in the case of the micro scale effect, the electric field action, the non Newtonian characteristics and the slip boundary. By solving the linear Possion-Boltzmann equation and the Cauchy momentum equation, the exact solution and approximate analytical solution of the velocity distribution of Eyring fluid are given, and the influence of the above factors on the electroosmotic flow is discussed. The effect of the electric field force and pressure on the velocity distribution of the electroosmotic flow of the Eyring fluid is compared and analyzed, and some meaningful results are obtained. In the third chapter, the transient electroosmotic flow of a fractional Oldroyd-B fluid in a circular tube is studied. The linear Navier model is used as a slip boundary condition. The exact solutions of potential distribution and instantaneous velocity distribution are given by means of Laplace transformation and finite Hankel transformation. The speed is composed of stable part and unstable part. The solutions of the Newton fluid, the fractional Maxwell fluid and the fractional order two order fluid can all be given as the special solutions of this part. Finally, we use the numerical Laplace inverse transformation to get the image of the semi analytical solution of velocity distribution, and analyze the influence of various parameters on velocity distribution, and draw some useful conclusions. Our results will be of reference to the prediction of the flow characteristics of the viscoelastic fluid in the microchannel, and will be beneficial to the design of the microfluidic equipment. In the fourth chapter, we use the finite difference method to solve numerically the velocity distribution of fractional Oldroyd-B fluid, and compare it with the analytical solution of the structure, and propose an effective numerical calculation method. Finally, the fifth chapter has combed the main conclusions of this paper. At the same time, the research of electroosmotic seepage and the development of fractional calculus are prospected.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O373

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