Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces

Journal of Fluid Mechanics

Volumn 544, Issue , 2005, Pages 339-351

  Cermelli, Paolo ^a   Fried, Eliot ^b   Gurtin, Morton E ^c  

^a UNIVERSITY OF TURIN   (Italy)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; INTERFACES (MATERIALS); PARTIAL DIFFERENTIAL EQUATIONS; REYNOLDS NUMBER; SET THEORY; VECTORS;

FLUID INTERFACES; TANGENTIAL VECTOR FIELD; TRANSPORT RELATIONS;

FLUID DYNAMICS;

FLUID DYNAMICS;

EID: 28644444970     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005006695     Document Type: Article

References (24)

1. Anderson, D. M., Cermelli, P., Fried, E., Gurtin, M. E. & McFadden, G. B. 2005 General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids. J. Fluid Mech. submitted.
2. Angenent, S. & Gurtin, M. E. 1989 Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface. Arch. Rat. Mech. Anal. 108, 323-391.
3. Aris, R. 1962 Vectors, Tensors, and the Basic Equations of Fluid Dynamics. Prentice-Hall.
4. Borhan, A. & Mao, C.-F. 1992 Effect of surfactants on the motion of drops through circular tubes. Phys. Fluids A 4, 2628-2640.
5. Danov, K. D., Alleborn, N., Raszillier, H. & Durst, F. 1998 The stability of evaporating thin liquid films in the presence of surfactant. I. Lubrication approximation and linear analysis. Phys. Fluids 10, 131-143.
6. Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.
7. Estrada, R. & Kanwal, R. P. 1991 Non-classical derivation of the transport theorems for wave fronts. J. Math. Anal. Applic. 159, 290-297.
8. Gurtin, M. E. 1981 An Introduction to Continuum Mechanics. Academic.
9. Gurtin, M. E., Struthers, A. & Williams, W. O. 1989 A transport theorem for moving interfaces. Q. Appl. Maths 47, 773-777.
10. Hayes, W. D. 1957 The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595-600.
11. McConnell, A. J. 1957 Applications of Tensor Analysis. Dover.
12. Mavrovouniotis, G. M. 1989 Transport of interfaces involving surface-active substances. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
13. Mavrovouniotis, G. M. & Brenner, H. 1993 A micromechanical investigation of interfacial transport processes. I. Interfacial conservation equations. Phil. Trans. R. Soc. Lond. A 345, 165-207.
14. Milliken, W. J., Stone, H. A. & Leal, L. G. 1993 The effect of surfactant on the transient motion of Newtonian drops. Phys. Fluids A 5, 69-79.
15. Petryk, H. & Mroz, Z. 1986 Time derivatives of integrals and functionals defined on varying volume and surface domains. Arch. Mech. 38, 697-724.
16. Reynolds. O. 1903 Papers on Mechanical and Physical Subjects, Volume III, The Sub-Mechanics of the Universe. Cambridge University Press.
17. Scriven, L. E. 1960 Dynamics of a fluid interface. Chem. Engng Sci. 12, 98-108.
18. Slattery, J. C. 1972 Momentum, Energy, and Mass Transfer in Continua. McGraw-Hill.
19. Slattery, J. C. 1990 Interfacial Transport Phenomena. Springer.
20. Stone, H. A. 1989 A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface. Phys. Fluids A 2, 111-112.
21. Stone, H. A. & Leal, L. G. 1990 The effect of surfactants on drop deformation and breakup. J. Fluid Mech. 220, 161-186.
22. Thomas, T. Y. 1957 Extended compatibility conditions for the study of surfaces of discontinuity in continuum mechanics. J. Maths Mech. 6, 311-322.
23. Waxman, A. M. 1984 Dynamics of a couple-stress fluid membrane. Stud. Appl. Maths 70, 63-86.
24. Wong, H., Rumschitski, D. & Maldarelli, C. 1996 On the surfactant mass balance at a deforming fluid interface. Phys. Fluids 8, 3203-3204.