Andrea Prosperetti

Bio: Andrea Prosperetti is an academic researcher from University of Houston. The author has contributed to research in topics: Bubble & Two-phase flow. The author has an hindex of 68, co-authored 330 publications receiving 17313 citations. Previous affiliations of Andrea Prosperetti include University of Milan & MESA+ Institute for Nanotechnology.

Bubble Dynamics and Cavitation

Abstract: The first analysis of a problem in cavitation and bubble dynamics was made by Rayleigh (1917), who solved the problem of the collapse of an empty cavity in a large mass of liquid. Rayleigh also considered in this same paper the problem of a gas-filled cavity under the assumption that the gas undergoes isothermal com­ pression. His interest in these problems presumably arose from concern with cavitation and cavitation damage. With neglect of surface tension and liquid viscosity and with the assumption of liquid incompressibility, Rayleigh showed from the momentum equation that the bubble boundary R(t) obeyed the relation RR+W<)2 = p(R)oo, p (1.1)

Linear pressure waves in bubbly liquids: Comparison between theory and experiments

Abstract: Recent work has rendered possible the formulation of a rigorous model for the propagation of pressure waves in bubbly liquids. The derivation of this model is reviewed heuristically, and the predictions for the small‐amplitude case are compared with the data sets of several investigators. The data concern the phase speed, attenuation, and transmission coefficient through a layer of bubbly liquid. It is found that the model works very well up to volume fractions of 1%–2% provided that bubble resonances play a negligible role. Such is the case in a mixture of many bubble sizes or, when only one or a few sizes are present, away from the resonant frequency regions for these sizes. In the presence of resonance effects, the accuracy of the model is severely impaired. Possible reasons for the failure of the model in this case are discussed.

Computational Methods for Multiphase Flow

Abstract: Preface 1. Introduction: a computational approach to multiphase flow A. Prosperetti and G. Tryggvason 2. Direct numerical simulations of finite Reynolds number flows G. Tryggvason and S. Balachandar 3. Immersed boundary methods for fluid interfaces G. Tryggvason, M. Sussman and M. Y. Hussaini 4. Structured grid methods for solid particles S. Balachandar 5. Finite element methods for particulate flows H. Hu 6. Lattice Boltzmann methods for multiphase flows S. Chen, X. He and L. S. Luo 7. Boundary integral methods for Stokes flows J. Blawzdziewic 8. Averaged equations for multiphase flows A. Prosperetti 9. Point particle methods for disperse flows K. Squires 10. Segregated methods for two-fluid models A. Prosperetti, S. Sundaresan, S. Pannala and D. Z. Zhang 11. Coupled methods for multi-fluid models A. Prosperetti References Index.

Bubble dynamics in a compressible liquid. Part 1. First-order theory

Abstract: The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.

Dynamics of bubble growth and detachment from a needle

Abstract: Several aspects of the growth and departure of bubbles from a submerged needle are considered. A simple model shows the existence of two different growth regimes according to whether the gas flow rate into the bubble is smaller or greater than a critical value. These conclusions are refined by means of a boundary-integral potential-flow calculation that gives results in remarkable agreement with experiment. It is shown that bubbles growing in a liquid flowing parallel to the needle may detach with a considerably smaller radius than in a quiescent liquid. The study also demonstrates the critical role played by the gas flow resistance in the needle. A considerable control on the rate and size of bubble production can be achieved by a careful consideration of this parameter. The effect is particularly noticeable in the case of small bubbles, which are the most difficult ones to produce in practice.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Cavitation and Bubble Dynamics

Abstract: This book describes and explains the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation. It is intended as a combination of a reference book for those scientists and engineers who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multiphase flows. A basic knowledge of fluid flow and heat transfer is assumed but otherwise the analytical methods presented are developed from basic principles. The book begins with a chapter on nucleation and describes both the theory and observations of nucleation in flowing and non-flowing systems. The following three chapters provide a systematic treatment of the dynamics of the growth, collapse or oscillation of individual bubbles in otherwise quiescent liquids. Chapter 4 summarizes the state of knowledge of the motion of bubbles in liquids. Chapter 5 describes some of the phenomena which occur in homogeneous bubbly flows with particular emphasis on cloud cavitation and this is followed by a chapter summarizing some of the experiemntal observations of cavitating flows. The last chapter provides a review of the free streamline methods used to treat separated cavity flows with large attached cavities.

Long-scale evolution of thin liquid films

Abstract: Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.

Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ...

Abstract: The review deals with drop impacts on thin liquid layers and dry surfaces. The impacts resulting in crown formation are referred to as splashing. Crowns and their propagation are discussed in detail, as well as some additional kindred, albeit nonsplashing, phenomena like drop spreading and deposition, receding (recoil), jetting, fingering, and rebound. The review begins with an explanation of various practical motivations feeding the interest in the fascinating phenomena of drop impact, and the above-mentioned topics are then considered in their experimental, theoretical, and computational aspects.