Stephen H. Davis

McCormick School (Institute) Professor
Walter P. Murphy Professor of Applied Mathematics
Ph.D., Rensselaer Polytechnic Institute

Editor-In-Chief, Journal Of Fluid Mechanics
General Editor, Cambridge Monographs in Mechanics
Editor, Annual Review of Fluid Mechanics
E-mail address:

Visiting Faculty
L.N. Brush
S.J. Watson

Postdoctoral Associates:
M.S. Park
S.M. Roper

Recent Graduate Students:
S. A. Norris, 2006
V. A. Ajaev, 1999
J. D. Kirill, 1999
P. - Q. Luo, 1999
R. P. Flemming, 1998
C. H. Panzarella, 1998
D. J. Diller, 1996
T. P. Schulze, 1995
B. S. Tilley, 1994
D. M. Anderson, 1993
D. A. Huntley, 1993
J. R. Braun, 1991

Present Graduate Students:
A.M. Anderson
J.C. Kao

Member, National Academy of Sciences
Member, National Academy Of Engineering
Member, American Academy Of Arts & Sciences
Fluid Dynamics Prize, American Physical Society 1994
G.I. Taylor Medal, Society Of Engineering Science 2001

Research Interests:
Fluid Dynamics and Materials Science

Professor Davis works in the area of interfacial dynamics and stability. The interfaces can be in small-scale hydrodynamics in which two immiscible fluids are separated by an interface having surface tension, e.g. thin films, spreading of liquid on solid, and thermocapillary effects. The interfaces can be in systems with phase transformations in which, say, a liquid and its frozen counterpart are separated by a front having surface energy.

The main questions to be answered involve the nonlinear dynamic states of the system, their stability, nonlinear evolution, and pattern selection. Interfacial waves in fluids propagate, steepen, and evolve into three-dimensional complex wave systems, perhaps chaotic. Interfaces in solidification become cellular or dendritic and can lead to oscillatory states. Thin, continuous solid films of semi-conductors formed by vapor deposition can break up into islands as a result of crystal-mismatch stresses.

The means of analyzing such systems involves modelling, asymptotic and numerical methods. The answers have both practical and intrinsic interest.

Recent Publications

1997 "Long-scale evolution of thin liquid films," Rev. Mod. Phys. 69, 931 (co-authors A. Oron and S. G. Bankoff).

1998 "A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth" Physica D 122, 202 (co-authors A. A. Golovin and A. Nepomnyashchy).

2000 "Flow-induced patterns in directional solidification: localized morphologies in three-dimensional flows," Journal of Fluid Mechanics 421, 369-380 (co-author Y.-J. Chen).

2001 "Theory of Solidification," Cambridge, University Press.

2003 "Boundary-integral simulations of containerless solidification," Journal of Computational Physics 187, 492 (co-author V.S. Ajaev).

2004 "Faceting instability in the presence of wetting interactions: A mechanism for the formation of quantum dots," Phys. Rev. B 70, 235342 (co-authors T.V. Savina and A.A. Golovin).

2005 "A new law for thinning in foam dynamics," J. Fluid Mech. 534, 227 (co-author L.N. Brush).

2006 "Rupture of thin films with resonant patterning," J. Coll. Interf. Sci. 303, 532 (co-authors J.C. Kao and A.A. Golovin).

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Last Modified: April 09, 2007