Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat and mass transport at high and low Reynolds numbers. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain solutions that are due either to geometric simplifications, or large or small values of dimensionless parameters. The author emphasizes setting up problems and extracting as much information as possible short of obtaining detailed solutions of differential equations. The book also focuses on the solutions of representative problems. This reflects the book's goal of teaching readers to think about the solution of transport problems.

The effects of surface-active agents on drop deformation and breakup in extensional flows at low Reynolds numbers are described. In this free-boundary problem, determination of the interfacial velocity requires knowledge of the distribution of surfactant, which, in turn, requires knowledge of the interfacial velocity field. We account for this explicit coupling of the unknown drop shape and the evolving surfactant distribution. An analytical result valid for nearly spherical distortions is presented first. Finite drop deformation is studied numerically using the boundary-integral method in conjunction with the time-dependent convective–diffusion equation for surfactant transport. This procedure accurately follows interfacial tension variations, produced by non-uniform surfactant distribution, on the evolving interface. The numerical method allows for an arbitrary equation of state relating interfacial tension to the local concentration of surfactant, although calculations are presented only for the common linear equation of state. Also, only the case of insoluble surfactant is studied.The analytical and numerical results indicate that at low capillary numbers the presence of surfactant causes larger deformation than would occur for a drop with a constant interfacial tension equal to the initial equilibrium value. The increased deformation occurs owing to surfactant being swept to the end of the drop where it acts to locally lower the interfacial tension, which therefore requires increased deformation to satisfy the normal stress balance. However, at larger capillary numbers and finite deformations, this convective effect competes with ‘dilution’ of the surfactant due to interfacial area increases. These two different effects of surface-active material are illustrated and discussed and their influence on the critical capillary number for breakup is presented.

In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup a t low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ' end-pinching ' behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed.

An experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows. To circumvent the problem of optical turbidity, the refractive indices of the solid and liquid phases are closely matched. The residual turbidity, owing to small mismatches of the refractive indices, as well as impurities in the particles, allows a Doppler signal to be detected when a particle passes through the scattering volume. By counting the number of Doppler signals in a period of time, the local volume fraction is also measured.This new technique is utilized to study concentrated suspension flows in a rectangular channel. The general behavior of the suspension is that the velocity profile is blunted while the concentration profile has a maximum near the centre. Comparisons are made with theoretical predictions based on the shear-induced particle migration theory.

I n this paper numerical results are presented for the buoyancy-driven rise of a deformable bubble through an unbounded quiescent fluid. Complete solutions, including the bubble shape, are obtained for Reynolds numbers in the range 1 < R 6 200 and for Weber numbers up to 20. For Reynolds numbers R < 20 the shape of the bubble changes from nearly spherical to oblate-ellipsoidal to spherical-cap dependingon Webernumber; at higher Reynoldsnumbers 'disk-like ' and 'saucer-like ' shapes appear a t W = O( 10). The present results show clearly that flow separation may occur at a smooth free surface at intermediate Reynolds numbers; this fact suggests a qualitative explanation of the often-observed irregular (zigzag or helical) paths of rising bubbles.