7R9. Breakup of Liquid Sheets and Jets.– Edited by SP Lin (Dept Mech and Aeronaut Eng, Clarkson Univ). Cambridge Univ Press, Cambridge, UK. 2003. 269 pp. ISBN 0-521-80694-1. $75.00.
Reviewed by KJ Ruschak (Global Manufacturing Tech Org, Eastman Kodak Co, Kodak Park Bldg 10, Flr 5, Rochester NY 14652-3703).
Breakup of Liquid Sheets and Jets is a monograph on the mathematical analysis of the hydrodynamic stability of laminar sheets and jets. Linear stability, the initial evolution of small disturbances, is the primary focus, and so the word stability would be more accurate than breakup in the title. Consideration is limited to Newtonian liquids with constant and uniform surface tension. The book is theoretical and mathematical but reviews relevant experimental measurements and observations. A solid background in capillary hydrodynamics, hydrodynamic stability, and applied mathematics, notably analytic surface geometry and complex variables and analysis, are requisites for the reader. A paucity of background material and the typically concise mathematical development at a high level makes the book unsuitable as a textbook or as an introduction to the subject matter.
The book primarily analyzes the Navier-Stokes equation linearized about simple exact solutions, the Orr-Sommerfeld equation or counterpart. Stability is determined from a normal mode or eigenfunction analysis. An energy budget computation may follow as an aid to interpreting results and elucidating mechanisms. The importance of considering disturbances that evolve both temporally and spatially is emphasized. The book first treats the problem of a uniform sheet or jet of inviscid liquid moving through an inviscid gas at rest. Complications are then added, such as a gradual variation of sheet or jet thickness due to gravity, and viscous effects. Because the approach is analytical, the inclusion of viscosity requires the sheet or jet to be surrounded by a conduit. Nonlinear stability analysis and computational fluid dynamics are briefly treated. An epilogue introduces related phenomena, including the breakup of liquid filaments; drop formation from a nozzle, and excited atomization at a nozzle tip.
The many photographs of flow instabilities are effective at stimulating interest. The book has a detailed table of contents, a four-page author index, and a three-page subject index. The graphics are generally clear and effective, although some plots are busy and definition sketches are sometimes spare or omitted. Some descriptions are confused; for example, the simple vertical sheet thinning by gravity in Figure 4.1 is inexplicably described as being “extruded vertically downward by the viscous drag exerted by the horizontal moving plate.” Indeed, the book is careless for one purporting mathematical rigor. As examples, there are mistakes right from the beginning, the first occurring in equation (1.5), and the Heaviside step function is referred to as the “heavy side” step function. Although there is a listing of notation, it is not exhaustive, and symbols are not always defined in the text when first used.
The author has produced a detailed review of existing results from analytic approaches to the linear stability of jets and sheets of Newtonian liquids of constant and uniform properties. Breakup is not the focus of the book despite its title. Readers interested in applications will find the material limited. For example, little consideration is given to the excitation of instabilities to promote and control breakup, although this is common in practice. Breakup of Liquid Sheets and Jets will be valuable to those conducting research in this specialized area of hydrodynamics and useful as a reference to those possessing the required background and having broader interests in capillary hydrodynamics.