Interfacial Phenomena and Convection

by Nepomnyashchy; Alexander A.

• ISBN13: 9781584882565
• ISBN10: 1584882565
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-11-13
• Publisher: Chapman & Hall/

Summary

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 Biography

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.

Table of Contents

Introduction	1	(18)
The interface as a physical system	1	(5)
Interfacial tension	1	(3)
Hydrodynamic properties of the interface	4	(2)
Mathematical formulation	6	(13)
Heat transfer in a system with an interface	7	(7)
Mass transfer in a system with an interface	14	(5)
Interfacial flows	19	(20)
Flows generated by a longitudinal surface tension gradient	19	(11)
Return flow	21	(4)
Unidirectional flow	25	(1)
Multilayer flows	25	(5)
Nonisothermal flows in thin liquid layers	30	(3)
Nonparallel flows	33	(6)
Two-dimensional flows	33	(3)
Azisymmetric flows	36	(3)
Thermocapillary and solutocapillary migration of drops (and bubbles) and their spreading due to the Marangoni effect	39	(52)
Hydrodynamic drag on a solid sphere, a drop, or a bubble	39	(6)
Passive drops and the Marangoni effect	45	(4)
Active drops and instability; from drag to self-propulsion	49	(21)
Active versus passive drops and the Marangoni effect	49	(1)
Nonlinear equations and linear stability results	50	(11)
A few striking features of the nonlinear stability of spontaneous drop self-propulsion with the Marangoni effect	61	(9)
Spreading of surfactant drops and films and the Marangoni effect	70	(21)
Static phenomena. Spreading of drops	70	(8)
Liquid-liquid spreading of partially miscible liquids and the Marangoni effect	78	(4)
Spreading of a drop of practically insoluble surfactant due to Marangoni stresses	82	(9)
Stationary interfacial patterns in liquid layers	91	(68)
Stability of a thin horizontal layer heated from below (Benard-Marangoni convection)	91	(14)
Heuristic arguments	91	(4)
Linear stability analysis	95	(6)
Experiments	101	(4)
Nonlinear evolution equation for a horizontal layer heated from below	105	(5)
Selection of convective patterns near the instability threshold	110	(9)
Modulations and instabilities of hexagonal patterns	119	(24)
Instabilities of hexagonal patterns	121	(5)
Influence of lateral boundaries, fronts, and defects	126	(17)
Strongly nonlinear patterns	143	(4)
Extensions of Knobloch's equation and related model equations	147	(12)
Influence of the mean flow for low Prandtl number liquids	147	(2)
Influence of surface deformation	149	(10)
Interfacial oscillations and waves	159	(90)
Classification of oscillatory instabilities	159	(8)
Transverse and longitudinal oscillatory instabilities	167	(21)
Two interfacial wave modes in the absence and in the presence of the Marangoni effect	167	(3)
Transverse (capillary-gravity) waves in the presence of the Marangoni effect	170	(12)
Mixing of transverse and longitudinal waves	182	(6)
Oscillatory instabilities in the mixed Rayleigh-Benard-Marangoni convection	188	(11)
Mode mixing of interfacial and internal waves	188	(2)
Competition between Marangoni and Rayleigh instability mechanisms	190	(9)
Longitudinal instability in two-layer systems	199	(4)
Oscillatory instability in the presence of both thermal gradient and surfactant transport	203	(6)
Nondeformable interface	203	(3)
Deformable interface	206	(3)
Oscillations and waves in multilayer systems	209	(8)
The case of undeformable interfaces	213	(3)
Deformable interfaces	216	(1)
Experiments on surface tension gradient-driven waves	217	(28)
Typical mass-transfer experimental set-up and experimental runs	220	(4)
Surface deformation, surface and internal waves	224	(5)
Solitary waves and wave trains	229	(3)
Collisions and reflections at walls	232	(12)
Heat transfer results	244	(1)
Hydrochemical surface waves due to the Marangoni effect	245	(4)
Instabilities of parallel flows and film flows	249	(46)
Flows generated by a longitudinal surface tension gradient	249	(9)
Purely thermocapillary flows	250	(3)
Combined action of thermocapillarity and buoyancy	253	(4)
Influence of lateral boundaries	257	(1)
Film flows	258	(21)
Formulation of the problem	260	(6)
Galerkin approach	266	(7)
Numerical results	273	(5)
Flows with a transverse thermal gradient	278	(1)
Flows in two-layer systems	279	(16)
Linear stability theory	280	(7)
Numerical exploration of nonlinear patterns	287	(8)
Outlook	295	(6)
Interfacial turbulence and dissipative waves	295	(2)
Control of instabilities	297	(1)
Interfacial phenomena in the presence of phase transitions and chemical reactions, multiphase flows, etc.	298	(1)
``Exotic'' patterns and defects	299	(2)
Bibliography	301	(62)
Index	363