Interfacial phenomena and convection

Interfacial phenomena driven by heat or mass transfer are widespread in science and various branches of engineering. Research in this area has become quite active in recent years, attributable in part, at least, to the entry of physicists and their sophisticated experimental techniques into the field. Until now, however, the field has lacked a readable account of the recent developments.

Interfacial Phenomena and Convection remedies this problem by furnishing a self-contained monograph that examines a rich variety of phenomena in which interfaces pay a crucial role. From a unified perspective that embraces physical chemistry, fluid mechanics, and applied mathematics, the authors study recent developments related to the Marangoni effect, including patterned convection and instabilities, oscillatory/wavy phenomena, and turbulent phenomena. They examine Bénard layers subjected to transverse and longitudinal thermal gradients and phenomena involving surface tension gradients as the driving forces, including falling films, drops, and liquid bridges.

It is only in the past two or three decades that researchers have performed suitable, clear-cut experiments involving interfacial phenomena, and the stage is now set for a virtual explosion of the field. Interfacial Phenomena and Convection will bring you quickly up to date on the advances realized and prepare you to both use the results and to make further advances.

Author Notes

Alexander A. Nepomnyashchy is a Professor of Applied Mathematics at Technion, Haifa, Israel.
Manuel G. Velarde is a Professor of Physics at the Instituto Pluridisciplinar, Universidad Complutense, Madrid, Spain.
Pierre Colinet is an FNRS Research Associate at the Universite Libre de Bruxelles, Belgium.

1 Introduction	p. 1
1.1 The interface as a physical system	p. 1
1.1.1 Interfacial tension	p. 1
1.1.2 Hydrodynamic properties of the interface	p. 4
1.2 Mathematical formulation	p. 6
1.2.1 Heat transfer in a system with an interface	p. 7
1.2.2 Mass transfer in a system with an interface	p. 14
2 Interfacial flows	p. 19
2.1 Flows generated by a longitudinal surface tension gradient	p. 19
2.1.1 Return flow	p. 21
2.1.2 Unidirectional flow	p. 25
2.1.3 Multilayer flows	p. 25
2.2 Nonisothermal flows in thin liquid layers	p. 30
2.3 Nonparallel flows	p. 33
2.3.1 Two-dimensional flows	p. 33
2.3.2 Axisymmetric flows	p. 36
3 Thermocapillary and solutocapillary migration of drops (and bubbles) and their spreading due to the Marangoni effect	p. 39
3.1 Hydrodynamic drag on a solid sphere, a drop, or a bubble	p. 39
3.2 Passive drops and the Marangoni effect	p. 45
3.3 Active drops and instability; from drag to self-propulsion	p. 49
3.3.1 Active versus passive drops and the Marangoni effect	p. 49
3.3.2 Nonlinear equations and linear stability results	p. 50
3.3.3 A few striking features of the nonlinear stability of spontaneous drop self-propulsion with the Marangoni effect	p. 61
3.4 Spreading of surfactant drops and films and the Marangoni effect	p. 70
3.4.1 Static phenomena. Spreading of drops	p. 70
3.4.2 Liquid-liquid spreading of partially miscible liquids and the Marangoni effect	p. 78
3.4.3 Spreading of a drop of practically insoluble surfactant due to Marangoni stresses	p. 82
4 Stationary interfacial patterns in liquid layers	p. 91
4.1 Stability of a thin horizontal layer heated from below (Benard-Marangoni convection)	p. 91
4.1.1 Heuristic arguments	p. 91
4.1.2 Linear stability analysis	p. 95
4.1.3 Experiments	p. 101
4.2 Nonlinear evolution equation for a horizontal layer heated from below	p. 105
4.3 Selection of convective patterns near the instability threshold	p. 110
4.4 Modulations and instabilities of hexagonal patterns	p. 119
4.4.1 Instabilities of hexagonal patterns	p. 121
4.4.2 Influence of lateral boundaries, fronts, and defects	p. 126
4.5 Strongly nonlinear patterns	p. 143
4.6 Extensions of Knobloch's equation and related model equations	p. 147
4.6.1 Influence of the mean flow for low Prandtl number liquids	p. 147
4.6.2 Influence of surface deformation	p. 149
5 Interfacial oscillations and waves	p. 159
5.1 Classification of oscillatory instabilities	p. 159
5.2 Transverse and longitudinal oscillatory instabilities	p. 167
5.2.1 Two interfacial wave modes in the absence and in the presence of the Marangoni effect	p. 167
5.2.2 Transverse (capillary-gravity) waves in the presence of the Marangoni effect	p. 170
5.2.3 Mixing of transverse and longitudinal waves	p. 182
5.3 Oscillatory instabilities in the mixed Rayleigh-Benard-Marangoni convection	p. 188
5.3.1 Mode mixing of interfacial and internal waves	p. 188
5.3.2 Competition between Marangoni and Rayleigh instability mechanisms	p. 190
5.4 Longitudinal instability in two-layer systems	p. 199
5.5 Oscillatory instability in the presence of both thermal gradient and surfactant transport	p. 203
5.5.1 Nondeformable interface	p. 203
5.5.2 Deformable interface	p. 206
5.6 Oscillations and waves in multilayer systems	p. 209
5.6.1 The case of underformable interfaces	p. 213
5.6.2 Deformable interfaces	p. 216
5.7 Experiments on surface tension gradient-driven waves	p. 217
5.7.1 Typical mass-transfer experimental set-up and experimental runs	p. 220
5.7.2 Surface deformation, surface and internal waves	p. 224
5.7.3 Solitary waves and wave trains	p. 229
5.7.4 Collisions and reflections at walls	p. 232
5.7.5 Heat transfer results	p. 244
5.8 Hydrochemical surface waves due to the Marangoni effect	p. 245
6 Instabilities of parallel flows and film flows	p. 249
6.1 Flows generated by a longitudinal surface tension gradient	p. 249
6.1.1 Purely thermocapillary flows	p. 250
6.1.2 Combined action of thermocapillarity and buoyancy	p. 253
6.1.3 Influence of lateral boundaries	p. 257
6.2 Film flows	p. 258
6.2.1 Formulation of the problem	p. 260
6.2.2 Galerkin approach	p. 266
6.2.3 Numerical results	p. 273
6.2.4 Flows with a transverse thermal gradient	p. 278
6.3 Flows in two-layer systems	p. 279
6.3.1 Linear stability theory	p. 280
6.3.2 Numerical exploration of nonlinear patterns	p. 287
7 Outlook	p. 295
7.1 Interfacial turbulence and dissipative waves	p. 295
7.2 Control of instabilities	p. 297
7.3 Interfacial phenomena in the presence of phase transitions and chemical reactions, multiphase flows, etc.	p. 298
7.4 "Exotic" patterns and defects	p. 299
Bibliography	p. 301
Index	p. 363

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents