Effects of surfactants on an undeformable drop initially at rest


We study the effect of some gradients of surface tension acting on the surface of a liquid drop supposed undeformable and initially at rest. For the spreading of the surfactant on the drop surface we introduce a particular law. From mathematical point of view we solve by variable separation a Stokes-Ossen system. Then an asymptotic study is carried out in order to determine the normal and tangential components of the force acting on the drop. Ultimately the drop undergoes an upward translational motion.


C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis
Z. Kasa
I. Stan


liquid drop; Marangoni flow; gradient of surface tension; Stokes-Ossen system; variable separation; force on the drop surface;


See the expanding block below.

Paper coordinates

C.I. Gheorghiu, Z. Kasa, I. Stan, Effects of surfactants on an undeformable drop initially at restStudia Univ. Babeş-Bolyai Math.XXXVIII (1993) 113-126.


not yet

About this paper

Publisher Name

Babes-Bolyai University

Paper on journal website

not yet

Print ISSN


Online ISSN






Google Scholar



[1] G. K. Batchelot,  An Introduction to Fluid Mechanics,  Cambridge Univ. Press. Cambridge, 1967.

[2] E. Chifu, I. Stan, Z. Finta and E. Gavrila,
 Marangoni-type surface flow on an undeformable drop.  J. Colloid Interface Sci., 93(1), 140-150, 1983.

[3] T. M. Fischer, G. C. Hsiao and W. L. Wendland,
 singular perturbation for the exterior three-dimensional slow viscous flow problem,  J. Math. Anal. Appl., 110, 583-603, 1985.

[4] D. D. Joseph, K. Nguyen and G. S. Beavers,
 Nonumiqueness and stability of the configuration of flow of immiscible fluids with different viscosities,  J. Fluid Mech., 143, 319, 1984.

[5] S. Kaylun and P. A. Lagerstrom,
 Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers,  J. Math. and Mechanics, 6, 585-603, 1957.

[6] L. Landau and E. I. Lifschitz,
 Mechanique de fluides,  Mir. Morcow, 1971.

[7] M. E. O’Neill and F. Chorlton,
 Viscous and Compressible Fluid Dynamics,  Ellis Horwood, Chicester, West Sussex, 1989.

[8] I. Stan, E. Chifu, Z. Finta and E. Gavrila,
 Marangoni translational motion of a free drop initially at rest, I Rev. Roumaine Chim. 34(2), 603-615, 1989.

[9] T. D. Taylor and A. Acrivos,
 On the deformations and of a folling viscous drop at low reynolds number,  J. Fluid Mech., 18, 466-476, 1964.

[10] M. Van Dyke,
 Perturbation Methods in Fluid Mechanics,  Academic Press, 1964.

Related Posts