Foreword. Preface. Introduction. The Framework of Population Balances. Birth and Death Functions. The Solution of Population Balance Equations. Similarity Behavior of Population Balance Equations. Inverse Problems in Population Balances. The Statistical Foundation of Population Balances. Index.

Population Balances: Theory and Applications to Particulate Systems in Engineering

A literature review of theoretical models for drop and bubble breakup in turbulent dispersions

The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter Dc defined as Dc = 1.26 ([sigma]/[rho])3/5[epsilon][minus sign]2/5, where [epsilon] is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to Dc, the breakup frequency is shown to increase as ([sigma]/[rho])[minus sign]2/5[epsilon][minus sign]3/5 [surd radical]D/Dc[minus sign]1, while for large bubbles whose sizes are greater than 1.63Dc, it decreases with the bubble size as [epsilon]1/3D[minus sign]2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities

/pdf/on-the-breakup-of-an-air-bubble-injected-into-a-fully-hopieur5xl.pdf

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

Providing a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems, this fully enhanced and updated edition covers all the topics essential for graduate courses on two-phase flow, boiling, and condensation. Beginning with a concise review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid two-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-phase choked flow. Numerous solved examples and end-of-chapter problems that include many common design problems likely to be encountered by students, make this an essential text for graduate students. With up-to-date detail on the most recent research trends and practical applications, it is also an ideal reference for professionals and researchers in mechanical, nuclear, and chemical engineering.

/pdf/two-phase-flow-boiling-and-condensation-in-conventional-and-5aink3qfmk.pdf

Two-phase flow, boiling and condensation in conventional and miniature systems

A number of approximate methods for modeling aggregation of particulate suspensions have been extended to simulate breakup as well and have been tested by comparison with rigorous solutions for conditions representative of most aggregation-fragmentation processes. The simplest methods, based on a geometric discretization with size ratio equal to two, can calculate satisfactorily the average values of the population for particularly well-conditioned situations only and, even in those cases, are not capable of predicting the shape of the particle size distribution. Therefore more complex methods are usually required, capable of using denser size discretization. The characteristics of these models and the guidelines for their choice are discussed in the paper, by considering their accuracy, ability to produce error estimates, ease of implementation and speed. Copyright 2000 Academic Press.

Approximate Population Balance Equations for Aggregation-Breakage Processes.

Photographic measurements of transient drop-size distributions from stirred liquid-liquid systems of low dispersed phase fraction in a batch vessel confirm consistency with a similarity behavior from population balance established earlier by Narsimhan et al. (1980). Moreover, breakage functions are presented in generalized dimensionless form accounting for dependence on physical properties of the system and power input through stirring. This information is essential for predicting drop-size distributions in stirred liquid-liquid systems. Experimental measurements of steady-state drip-size distributions obtained from stirred, continuous flow systems with known inlet drop sizes compare very favorably with theoretical predictions based on population balance analysis using the breakage functions obtained from batch experiments.

Gregory Nejfelt

Papers

Breakage functions for droplets in agitated liquid-liquid dispersions