Drop-Surface Interactions

317 Pages·2002·32.969 MB·English

by  Martin Rein (eds.)

CISM COURSESAND LECTURES
Series Editors:
The Rectors
Manuel Garcia Velarde -Madrid
Mahir Sayir - Zurich
Wilhelm Schneider -Wien
The Secretary General
Bernhard Schrefler -Padua
Former Secretary General
Giovanni Bianchi -Milan
Executive Editor
Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and
proceedings in the field of Mechanics, Engineering, Computer Science
and Applied Mathematics.
Purpose of the series is to make known in the international scientific
and technical community results obtained in some of the activities
organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES
COURSES AND LECTURES -No. 456
DROP-SURFACE INTERACTIONS
EDITEDBY
MARTINREIN
GERMAN AEROSPACE CENTER
Springer-Verlag Wien GmbH
This volume contains 157 illustrations
This work is subject to copyright.
All rights are reserved,
whether the whole or part of the material is concemed
specifically those of translation, reprinting, re-use of illustrations,
broadcasting, reproduction by photocopying machine
or similar means, and storage in data banks.
© 2002 by Springer-Verlag Wien
Originally published by CISM, Udine in 2002.
SPIN 10887789
In order to make this volume available as economically and as
rapidly as possible the authors' typescripts have been
reproduced in their original forms. This method unfortunately
has its typographicallimitations buti t is hoped that they in no
way distract the reader.
ISBN 978-3-211-83692-7 ISBN 978-3-7091-2594-6 (eBook)
DOI 10.1007/978-3-7091-2594-6
PREFACE
Drop-surface interactions comprise a manifold of physical processes. Re
lated aspects have been studied both on their own, and in the context of their im
portance to a wide variety of technical applications. The purpose of the present
book is to provide a comprehensive picture of the many interesting features of
drop-surface interactions and to give new insights into relevant physical mecha
msms.
This book is based on lectures presented during a course on drop-surface
interactions at the International Centre of Mechanical Seiences in Udine. The
content of the chapters is multidisciplinary, ranging from fluid mechanics and
thermal sciences to physico-chemical processes and numerical analysis.
Initially, a systematic survey of free-surface flow phenomena characteris
tic of drop impact on solid and liquid surfaces is given and fundamental physical
mechanisms are explained. Throughout the book the importance of scaling and
dimensionless quantities is emphasized.
Wave processes occurring in the liquid during high-velocity drop impact
are the subject of a chapter on the impact of compressible liquids. Analytical
tools are presented for calculating the formation and propagation of shock and
expansion waves within the drop. The role played by the liquid free surface is
especially illustrated.
Physico-chemical fundamentals relating to a forced spreading of complex
solutions are provided at some depth in another chapter. The importance of cap
illarity, surface active agents, dynamic surface properties and the contact line
hysteresis on spreading drops is discussed.
Heat transfer and phase change phenomena occurring during solidifica
tion and evaporation processes are considered separately. The effect of temper-·
ature gradients and mesoscopic phenomena (such asthermal contact resistance
and molten wetting lines) on solidification are addressed. Heat transfer away
from hot walls is described by a boiling curve of drops. Particular emphasis is
placed on dynamic interactions between drops and bot surfaces.
Numerical analysis provides powerful tools for simulating drop-surface
interactions. Numerical methods and algorithms particularly suited for this pur
pose are surveyed. First, boundary integral methods are introduced in som~ de
tail, then Navier-Stokes algorithms are reviewed. In particular, volume of fluid,
level set, and front tracking algorithms are concisely overviewed. Programming
details usually absent from the literature are also provided.
The course on drop-surface interactions was held in conjunction with a
workshop on the same topic. Participants presented and discussed their results
in an interdisciplinary environment. The topics addressed covered many of the
aspects treated in the lectures. Most of the presentations given at the workshop
have been peer-reviewed and are contained in this volume.
We are still far from a complete knowledge of all facets of drop-surface
interactions. Future studies of open questions will provide a deeper understand
ing not only ofp henomena of drop-surface interactions, but also of more general
problems of fluid mechanics as well. This has been well expressed in the form of
an after dinner poem given by Marty Lesser during the course in Udine:
Holding fast by tensile stress,
Toward a fate we would know.
A fiowing zone of interest,
With scales of time in tow.
Brimming with surfactants of calories and tension,
Even things we dare not mention.
But in the end my small petal,
Your destiny is cast.
A frozen ball of metal,
Or a puddle from the past.
For impact of a little drop,
Can simply fill our days.
But when we hear that last plop,
There will still be much to say,
And as I shout Can I Say More?
Without doubt but please stop we implore!
Marty Lesser
These lines reflect the lively atmosphere that we all enjoyed during the
course at the International Centre of Mechanical Seiences in Udine. This would
not have been possible without the friendly help of the staff of CISM. The authors
would like to thank all members ofCISM andin particular Prof G. Bianchi, Prof
S. Kaliszky and Prof C. Tasso for their advice and support in preparing both the
course and this volume. The editor is especially grateful to Prof W Schneider
for his continuous advice and encouragement.
Martin Rein
CONTENTS
Introduction to Drop-Surface Interactions
by Martin Rein .................................................................................................... 1
Drop-Liquid Impact Phenomena
by Andrea Prosperetti ....................................................................................... 25
The Impact of a Compressible Liquid
by Martin Lesser. ............................................................................................... 39
Physico-Chemical Aspects of Forced Wetting
by Micheie Vignes-Adler. ................................................................................. 103
Heat Transfer and Solidification During the Impact of a Droplet
on a Surface
by D. Poulikakos, D. Attinger, S. Haferland Z. Zhao ..................................... 159
Interactions between Drops and Hot Surfaces
by Martin Rein ................................................................................................ 185
Boundary Integral Methods
by Andrea Prosperetti ..................................................................................... 219
Navier-Stokes Numerical Algorithms for Free-Surface Flow
Computatios: An Overview
by Andrea Prosperetti ..................................................................................... 237
Numerical Implementation of Free Surface Flow Algorithms
by Hasan N. Oguz and Jun Zeng .................................................................... 259
Workshop on Drop-Surface Interactions:
Low Speed Drop Impact Onto Dry Solid Surface
by Romain Rioboa and Cam Tropea ...................................................... 283
Asymptotic Theory of Droplet Spreading after Collision with a
Solid Surface
by Alexander F edorchenko .................................................................... 287
Bubble Formation on Porous Media Surfaces
by R. Teppner and U. Schaftinger .......................................................... 291
Theoretical and Experimental Study of Shock Wave Focusing
in a Confined Reflector
by Nicholas Apazidis, Ba Johansson and Martin Lesser ....................... 295
Splash Formation by Water Drops
by Jong-Leng Liow. ................................................................................ 299
On Some New Aspects of Splashing Impact of Drop-Liquid
Surface Interactions
by An-Bang Wang, Chi-Chang Chen and Wun-Chin Hwang ................. 303
Drop Impact on Liquid Layers: Some New Phenomena at the
Edges of Parameter Space
by S. T. Thoroddsen ................................................................................ 307
The Effect of Drop Viscoelasticity on the Drainage of
Newtonian Liquid Films
by A. N. Zdravkov, F. N. van de Vosse and H. E. H. Meijer ................... 311
Introduction to Drop-Surface lnteractions
MartinRein
Deutsches Zentrum für Luft-und Raumfahrt, Göttingen, Germany
1 Introduction
The interaction of drops with surfaces is an everyday occurrence that comprises a rieb variety
of fluid mechanical facets. Almost two and a half millenniums ago the phrase gutta cavat lapi
dem (dripping water hollows out a stone) was coined reflecting the erosive action of repetitively
impinging drops. The first scientific investigations into certain aspects of drop impact were then
conducted in the second half of the nineteenth century. Topics addressed at those times include
the formation of vortex rings by drops impinging on liquid surfaces, drops floating on or bounc
ing off pools, the spreading of a drop of one liquid on the surface of another liquid, splashing and
an instability of drops spreading on solid surfaces, the result of the instability being well-known
from the formation of ink blots. These and further phenomena of drop-surface interactions will
be discussed in the present and in the other chapters of this book. In this we willlimit ourselves
to the interaction of single drops with different surfaces. lt will become clear that processes oc
curring during drop-surface interactions are governed by a great number of different branches
not only of fluid mechanics but also ofthermal sciences. Often, a detailed understanding of the
processes of drop-surface interactions is not yet available.
1.1 Classification of Drop-Surface Interactions
Drop-surface interactions have been distinguished according to the various phenomena observed,
the physics involved or the applications considered. These classifications are not independent of
each other.
In a phenomenological classification the result of interaction processes occurring under par
ticular conditions is used to distinguish between different cases. An obvious difference is between
processes that cause a disintegration of the drop and those that do not. Typically, the former case
is called a splash. Drops impinging on both, solid and liquid surfaces can bounce off the surface.
Further differences depend on the nature of the surface. On solid surfaces drops can spread the
fluid motion being governed either by inertial forces or by molecular interactions between the
liquid and the solid (see the chapter "Physico-Chemcial Aspects of Forced Wetting" by Vignes
Adler). When a drop approaches the surface of a liquid pool it can not only splash but also
coalesce with the pool liquid. These topics will be introduced in more detail in succeeding sec
tians (cf. also Rein, 1993). Heat transfer and phase change processes add additional phenomena
that are the subject of other chapters.
The phenomena mentioned in the last paragraph are closely connected with different physical
aspects. Often, the outcome of drop impacts is mainly determined by the kinetic energy of the
drop and by the surface tension. However, viscosity plays an important role in dissipation pro
cesses during spreading on solid surfaces and in the formation of vorticity during the coalescence
of drops with a pool. Compressibility effects that are characteristic of high velocity impacts are
2 M.Rein
the topic of a chapter by Lesser. Phase changes of the liquid to the solid or vapor state that can
occur during impacts on cold and bot surfaces, respectively, are also treated in separate chapters.
Drop-surface interactions are of importance in many industrial applications. These include
the deposition of single or multiple drops, spray cooling, fire extinguishing and the interaction
of drops with bot walls of combustion chambers in direct injection combustion engines. In many
of these applications phase change phenomena and thus heat transfer processes play a domi
nant role. The particular cases of spray deposition and droplet based material processes have
been reviewed by Poulikakos and Waldvogel (1996) and by Armster et al. (2002), respectively.
Sprays interacting with bot surfaces can remove large heat fluxes at low superheats (Yao, 1994,
and Chow et al., 1997). High-speed impacts can cause a severe erosion of the surface of steam
turbines or aerospace vehicles in flight through rain (Lesser and Field, 1983, Adler, 1999). In
forensie sciences splat patterns formed after the impact of blood droplets are analyzed in order
to use this information in reconstructing crimes (Pizzola et al., 1986a,b).
1.2 Scaling
In studying drop-surface interactions one deals with widely disparate scales. The size of imping
ing drops differs greatly from that of splash droplets or cavitation bubbles formed inside the
liquid. A small surface ro11ghness of solid surfaces is known to have a profound influence on the
limiting conditions of the onset of splashing. In the case of hot walls the surface roughness deter
mines the Leidenfrost point, i.e., that surface temperature above which impinging drops will no
Ionger form a contact with the surface but are reflected by a vapor cushion (cf. the chapter "In
teractions between Drops and Hot Surfaces"). A general feature of drop impact is the formation
of new contacts between drops and a solid or liquid surface, respectively. This process proceeds
on molecular scales. After the instant of contact liquids can spread not only on solid surfaces but
also on another liquid.
In order to obtain an idea of the significance of the different effects mentioned in the last
paragraph we will consider time scales characteristic of these effects. With the impact velocity u
and the diameterD of the drop, with the sound speed c, density p, thermal diffusivity a, viscosity
v and surface tension a of the liquid, and with the acceleration of gravity g, times scales can be
formed that are characteristic of convection, tconv = D Iu, compressibility effects, tcomp = D I c,
thermal effects, ttherm = D2 I a, surface tension effects, tu = (pD3 I a) 112, viscous effects,
tvis = D2 lv and gravitational effects, t rav = y'ff7'g. Ratios of thesetime scales yield char
9
acteristic nondimensional numbers. Here, we are dealing with eight parameters involving three
independent units (length, mass and time). Hence, a complete set of dimensionless numbers is
given by five numbers, e.g., by the Mach number, M = tcompltconv = ulc, the Weber number,
We = (tultconv)2 = pu2Dia, the Reynolds number, Re= tvisltconv = Dulv, the Peclet
nurober Pe = tthermltconv = Dula and the Froude nurober Fr= (t9ravltconv)2 = u2 l(gD).
Note, that these numbers have been formed with the properties of the drop liquid and not with
those of the surrounding gas.
Impact conditions resulting in different outcomes of incompressible drop impacts are often
classified according to the Weber number. The Weber nurober is not only a ratio of time scales
but also a measure of the energy of the drop. Prior to impact the kinetic energy Ekin of the drop
equals Ekin = p7r D3 l12u2 and the surface energy is given by Eu = a1r D2• The ratio of these
energies is proportional to the Weber number, W e = 12Ekin/Eu. Finally, the Weber nurober