The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

Developing scaffolds that mimic the architecture of tissue at the nanoscale is one of the major challenges in the field of tissue engineering. The development of nanofibers has greatly enhanced the scope for fabricating scaffolds that can potentially meet this challenge. Currently, there are three techniques available for the synthesis of nanofibers: electrospinning, self-assembly, and phase separation. Of these techniques, electrospinning is the most widely studied technique and has also demonstrated the most promising results in terms of tissue engineering applications. The availability of a wide range of natural and synthetic biomaterials has broadened the scope for development of nanofibrous scaffolds, especially using the electrospinning technique. The three dimensional synthetic biodegradable scaffolds designed using nanofibers serve as an excellent framework for cell adhesion, proliferation, and differentiation. Therefore, nanofibers, irrespective of their method of synthesis, have been used as scaffolds for musculoskeletal tissue engineering (including bone, cartilage, ligament, and skeletal muscle), skin tissue engineering, vascular tissue engineering, neural tissue engineering, and as carriers for the controlled delivery of drugs, proteins, and DNA. This review summarizes the currently available techniques for nanofiber synthesis and discusses the use of nanofibers in tissue engineering and drug delivery applications.

http://www.science-open.com/document_file/c62aa1b5-c0e5-4c3c-a44e-b4945a253176/PubMedCentral/c62aa1b5-c0e5-4c3c-a44e-b4945a253176.pdf

Nanofibers and their applications in tissue engineering.

流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Journal of Fluid Mechanics创刊50周年

This article reviews linear instability analysis of flows over or through complex two-dimensional (2D) and 3D geometries. In the three decades since it first appeared in the literature, global instability analysis, based on the solution of the multidimensional eigenvalue and/or initial value problem, is continuously broadening both in scope and in depth. To date it has dealt successfully with a wide range of applications arising in aerospace engineering, physiological flows, food processing, and nuclear-reactor safety. In recent years, nonmodal analysis has complemented the more traditional modal approach and increased knowledge of flow instability physics. Recent highlights delivered by the application of either modal or nonmodal global analysis are briefly discussed. A conscious effort is made to demystify both the tools currently utilized and the jargon employed to describe them, demonstrating the simplicity of the analysis. Hopefully this will provide new impulses for the creation of next-generation algorithms capable of coping with the main open research areas in which step-change progress can be expected by the application of the theory: instability analysis of fully inhomogeneous, 3D flows and control thereof.

Global Linear Instability

The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei-Eotvos plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions.

/pdf/dynamics-of-an-initially-spherical-bubble-rising-in-1zrsdzjsvo.pdf

Dynamics of an initially spherical bubble rising in quiescent liquid

This review highlights the profound and unexpected ways in which viscosity varying in space and time can affect flow. The most striking manifestations are through alterations of flow stability, as established in model shear flows and industrial applications. Future studies are needed to address the important effect of viscosity stratification in such diverse environments as Earth's core, the Sun, blood vessels, and the re-entry of spacecraft.

Instabilities in Viscosity-Stratified Flow

In this chapter, our objective is twofold: (1) to describe common physical mechanisms which cause flows to become unstable, and (2) to introduce recent viewpoints on the subject. In the former, we present some well-known instabilities, and also discuss how surface tension and viscosity can act as both stabilisers and destabilisers. The field has gone through a somewhat large upheaval over the last two decades, with the understanding of algebraic growth of disturbances, and of absolute instability. In the latter part we touch upon these aspects.

An Introduction to Hydrodynamic Stability

Effect of miscibility on the linear instability of two-fluid channel flow

The linear stability of variable viscosity, miscible core-annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed. A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/28FDFF2D9477D2036D079888073FD92B/S0022112007008269a.pdf/div-class-title-stability-of-miscible-core-annular-flows-with-viscosity-stratification-div.pdf

Rama Govindarajan

Papers

Dynamics of an initially spherical bubble rising in quiescent liquid

Instabilities in Viscosity-Stratified Flow

An Introduction to Hydrodynamic Stability

Effect of miscibility on the linear instability of two-fluid channel flow

Stability of miscible core–annular flows with viscosity stratification