Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant
Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant
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DOI：
10.1007/s11433-010-0171-5
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发表时间：
2010-05
期刊：
影响因子：
--
通讯作者：
X. Sun;Jie Peng;K. Zhu
中科院分区：
文献类型：
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作者：
X. Sun;Jie Peng;K. Zhu
通过线性稳定性分析，考虑了剪切变稀对两种不互溶幂律流体核-环空流动稳定性的影响。流动由直管中的轴向压力梯度驱动，两种流体之间的界面由不溶性表面活性剂占据。给出了这种核-环布置的基本流动，并根据幂律流体模型得到了解析解。推导了无穷小扰动演化的线性化方程，将稳定性问题转化为广义矩阵特征值问题，并采用基于QZ算法的Matlab软件包求解。剪切变稀特性对幂律流体核-环空流动稳定性有显著的影响，这种影响体现在多个方面。首先，毛细管不稳定性被剪切变稀特性放大，这可能导致幂律流体和牛顿流体流动之间的本质区别。特别是当界面靠近管壁时，幂律流体流动可能不稳定，而牛顿流体流动稳定。第二，在界面扰动下，界面处出现速度不连续性，这对流动是不稳定的。幂律指数的大小决定了这种速度间断的大小，从而影响了流动的稳定性。此外，剪切变稀特性可能导致新的稳定模式，不出现在牛顿流体流动。流动稳定性与界面位置密切相关，而界面位置的作用在以往的研究中被忽略。当界面靠近管壁时，剪切变稀流体流动对长波扰动更不稳定，而当界面靠近管中心线时，牛顿流体流动对长波扰动更不稳定。但界面活性剂的加入改变了这一趋势，使幂律流体的流动更加稳定，无论界面在何处。
The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability analysis. The flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble surfactant. Given the basic flow for this core-annular arrangement, the analytical solution is obtained with respect to the power-law fluid model. The linearized equations for the evolution of infinitesimal disturbances are derived and the stability problem is formulated as a generalized matrix eigenvalue problem, which is solved by using the software package Matlab based on the QZ algorithm. The shear-thinning property is found to have marked influence on the power-law fluid core-annular flow stability, which is reflected in various aspects. First, the capillary instability is magnified by the shear-thinning property, which may lead to an essential difference between power-law and Newtonian fluid flows. Especially when the interface is close to the pipe wall, the power-law fluid flow may be unstable while the Newtonian fluid flow is stable. Second, under disturbances to the interface a velocity discontinuity at the interface appears which is destabilizing to the flow. The magnitude of this velocity discontinuity is affected by the power-law index and the flow stability is influenced correspondingly. Besides, the shear-thinning property may induce new stability modes which do not appear in the Newtonian fluid flow. The flow stability shows much dependence on the interface location, the role of which was neglected in most previous studies. The shear-thinning fluid flow is more unstable to long wave disturbances when the interface is close to the pipe wall, while the Newtonian fluid flow is more unstable when the interface is close to the pipe centerline. But this trend is changed by the addition of interfacial surfactant, for which the power-law fluid flow is more stable no matter where the interface is located.