The mechanisms building the overall concentration distribution in a scalar mixture, and the drops in a spray, are examined successively. In both cases, the distributions belong to a unique family of distributions stable by self-convolution, the signature of the aggregation process from which they originate.
REFERENCES
1.
H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).
2.
3.
4.
5.
6.
P. E. Dimotakis and H. J. Catrakis, in Mixing: Chaos and Turbulence, edited by H. Chat, E. Villermaux, and J. M. Chomaz (Kluwer, Dordrecht/Plenum, New York, 1999).
7.
8.
F. E. Marble, in Chemical Reactivity in Liquids: Fundamental Aspects, edited by M. Moreau and P. Turq (Plenum, New York, 1988).
9.
10.
J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, 1989).
11.
12.
13.
14.
This apparent power law is a transient effect reflecting the fact that the temporal window of the mixture’s evolution covers, at most, a few large scale turnover time Indeed, material lines increase like where is the distance from the injection point of the scalar blob in the medium advected at a velocity In the channel flow, the turbulence intensity is such that (Ref. 1) and the downstream distances of observation in the present experiments are such that so that realizing in practice an elongation linear in time, inducing, in this three dimensional flow, This behavior has thus to be understood as the birth of the ultimate exponential regime, but this slight difference, if any, has strictly no consequence on the mechanism building-up the concentration distribution which solely relies on random additions of concentration levels, independently of the rate at which these additions are made.
15.
W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970).
16.
S. K. Friedlander, Smoken Dust, and Haze (Oxford University Press, New York, 2000).
17.
18.
19.
A.
Pumir
, B. I.
Shraiman
, and E. D.
Siggia
, Phys. Rev. Lett.
66
, 2984
(1991
).20.
21.
B.
Castaing
, G.
Gunaratne
, F.
Heslot
, L.
Kadanoff
, A.
Libchaber
, S.
Thomae
, X. Z.
Wu
, S.
Zaleski
, and G.
Zanetti
, J. Fluid Mech.
204
, 1
(1989
).22.
23.
S. T.
Thoroddsen
and C. W.
Van Atta
, J. Fluid Mech.
244
, 547
(1992
).24.
B. S.
Williams
, D.
Marteau
, and J. P.
Gollub
, Phys. Fluids
9
, 2061
(1997
).25.
M. C.
Jullien
, P.
Castiglione
, and P.
Tabeling
, Phys. Rev. Lett.
85
, 3636
(2000
).26.
27.
E.
Villermaux
, C.
Innocenti
, and J.
Duplat
, Phys. Fluids
13
, 284
(2001
).28.
29.
30.
G.
Falkovich
, K.
Gawedzki
, and M.
Vergassola
, Rev. Mod. Phys.
73
, 913
(2001
).31.
32.
L. Bayvel and Z. Orzechowski, Liquid Atomization (Taylor & Francis, London, 1993).
33.
A. H. Lefebvre, Atom and Sprays (Hemisphere, New York, 1989).
34.
E. L.
Andreas
, M.
Pattison
, and S. E.
Belcher
, J. Phys. Res.
106
, 7157
(2001
).35.
36.
S. Twomey, Atmospheric Aerosols (Elsevier, New York, 1977).
37.
B. J. Mason, The Physics of Clouds (Clarendon, Oxford, 1971).
38.
39.
40.
41.
42.
43.
44.
J. Mayer and M. Mayer, Statistical Mechanics (Wiley, New York, 1966).
45.
46.
P. Marmottant and E. Villermaux (in preparation).
47.
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961).
48.
49.
50.
51.
J. Plateau, Statique Exprimentale et Thorique des Liquides Soumis Aux Seules Forces Molculaires (Gauthier Villars, Paris, 1873).
52.
53.
54.
55.
56.
57.
58.
S. K. Friedlander, Smoke, Dust, and Haze (Oxford University Press, Oxford, 2000).
59.
60.
W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1971).
61.
62.
This content is only available via PDF.
© 2004 American Institute of Physics.
2004
American Institute of Physics
You do not currently have access to this content.
