Microhydrodynamics and complex fluids
The central subject of this book for graduate students is the low Reynolds number flow in hydrodynamics. The text is divided into 11 chapters.NEWLINENEWLINEIn Chapter 1, the author deals with basic principles of hydrodynamics. The equations governing fluid flows have been introduced, together with numerical data about the viscosity of water. The dimensional analysis, which is the backbone of various approximations in this fascinating branch, has also been introduced here.NEWLINENEWLINEChapter 2 substantiates the requirement of small Reynolds and Stokes numbers. Steady-state Stokes equations have been explained and used to discuss a simple problem. The concepts of linearity, uniqueness, minimum energy dissipation have been included. The author demonstrates that the Stokes flow dissipates less energy than a general flow.NEWLINENEWLINEChapter 3 examines two-dimensional Stokes flows in Cartesian and cylindrical coordinates. These flows have been illustrated by the flow past a wedge. Particular cases of moving boundaries and large and small wedge angles have been included. The study of flows past wedges presents a mathematically rigorous analysis of a difficult problem for streamlined corners.NEWLINENEWLINEChapter 4 discusses applications to lubrication in mechanics, bio-mechanics and microfluidic networks. The lubrication hypothesis has been formulated by using dimensional and order-of-magnitude analyses. Two-dimensional and three-dimensional Reynolds equations are key concepts in lubrication theory. The author considers here applications to slider bearing, squeezing a drop, Hele-Shaw flow, microfluidic channels and porous media. The problems at the end of the chapter are very interesting.NEWLINENEWLINEIn Chapter 5, the concept of thin fluid films introduced in the previous chapter has been extended to films with free surface. The author examines the interfaces between two immiscible fluids, the gravity spreading of a fluid on a horizontal plane, and the stability of a film flowing down an inclined plane. The effect of surface tension on free surface films also finds its place. In the reviewer's opinion, the introduction of the companion concept of wetting dynamics would have been welcome in this chapter.NEWLINENEWLINEChapter 6 describes the motion of a solid particle in a quiescent fluid. The particular case of isotropic particles has been derived from the general equations. This has been extended to include the flow past a sphere. These flows have important applications in mechanics and bio-mechanics. Towards the end of this chapter, a discussion for the flow past slender particles has also been given.NEWLINENEWLINEChapter 7 studies the flows of bubbles and droplets. They are modeled as flows of deformable particle suspended inside the fluid. The complications arise due to the presence of a deformable interface of unknown geometry. The author enunciates the difficulties arising in these problems, and introduces interesting topics like the bubble shape and the stability of Stokes solution. Various necessary techniques have been listed.NEWLINENEWLINEChapter 8 presents the general solution of the Stokes equations. Various techniques and transformations to handle this general solution are mentioned, and the method of singularities for the integral form of Stokes equations is discussed in detail.NEWLINENEWLINEChapter 9, titled ``Introduction to suspension mechanics'' contains the basic concepts of suspension mechanics along with the analysis in complex domains and possible applications. Some open problems are suggested.NEWLINENEWLINEChapter 10 improves the approximation by using full Navier-Stokes equations. The required correction has been made by using Oseen' approximation. The process has been explained in a concise manner. This is necessary for the reader to understand the order of correction required in realistic situations. The flow past a cylinder illustrates the theory.NEWLINENEWLINEThe last Chapter 11 provides a brief description of non-Newtonian fluids. The basic concepts of these fluids along with their classification provide a bird's eye-view of this fascinating branch of fluid dynamics. Within the limited space, the author has done a magnificent job.NEWLINENEWLINEThe book has been made self-sufficient by including useful appendices on mathematical preliminaries and curvilinear coordinates. The symbols used in the text have been explained from the beginning. The text is very well written, and the concepts are pesented with clarity. The emphasis is on the reader to appreciate the subject rather than to dazzle.
scientific article; zbMATH DE number 6044791