Marangoni dissipation

Taking viscous and Marangoni dissipation together, and making the dependence of the source terms on the spectral energy level E explicit, the energy balance can be written as ... 

Surface Waves and Dissipative Solitons Sustained by the Marangoni Effect... 

From the thermodynamical point of view the formation of dissipative structures is entropy driven as intensively explained by Prigogine Glansdorf (1971). The criteria for surface instabilities due to mass transfer across a liquid interface were evaluated by Stemling Scriven (1959). The typical Marangoni instability starts on surfactant concentration or temperature differences between two phases. Surface tension differences along the surface are... 

The field of Marangoni instabilities shows a large variety of dissipative structures, including the principle of stationary structures, hierarchical structures with limited self-similarity, relaxation oscillations and regular behavior of travelling autowaves with chaotic turbulence-like behaviour. There is also the oscillatory regime with trains of waves with soliton-like behaviour of each wave. Anormal as well as normal dispersion of these waves have recently... 

Many surfactant solutions show dynamic surface tension behavior. That is, some time is required to establish the equilibrium surface tension. If the surface area of the solution is suddenly increased or decreased (locally), then the adsorbed surfactant layer at the interface would require some time to restore its equilibrium surface concentration by diffusion of surfactant from or to the bulk liquid. In the meantime, the original adsorbed surfactant layer is either expanded or contracted because surface tension gradients are now in effect, Gibbs—Marangoni forces arise and act in opposition to the initial disturbance. The dissipation of surface tension gradients to achieve equilibrium embodies the interface with a finite elasticity. This fact explains why some substances that lower surface tension do not stabilize foams (6) They do not have the required rate of approach to equilibrium after a surface expansion or contraction. In other words, they do not have the requisite surface elasticity. 

Buzza et al. (105) have presented a qualitative discussion of the various dissipative mechanisms that may be involved in the small-strain linear response to oscillatory shear. These include viscous flow in the films. Plateau borders, and dispersed-phase droplets (in the case of emulsions) the intrinsic viscosity of the surfactant monolayers, and diffusion resistance. Marangoni-type and marginal regeneration mechanisms were considered for surfactant transport. They predict that the zero-shear viscosity is usually dominated by the intrinsic dilatational viscosity of the surfactant mono-layers. As in most other studies, the discussion is limited to small-strain oscillations, and the rapid events associated with T1 processes in steady shear are not considered, even though these may be extremely important. 

Linde, H., Schwartz, R, and Wilke, H., Dissipative structures and nonlinear kinetics of the Marangoni instability, in Dynamics and Instability of Fluid Interfaces, Sorensen, T.S. (ed.). Springer-Verlag, Berlin, 1979, p. 75. 

We write = to define e in terms of Ga). Then the effects of energy output (due to heat and viscous dissipation) and input (due to the Marangoni effect) will be of the same order as nonlinearity and dispersion. The latter two are in appropriate (local) balance for the Bounssinesq-Korteweg-de Vries (BKdV) equation for long waves in shallow inviscid liquid layers. 

Garazo A. N., and Velarde, M. G. (1991) Dissipative Korteweg-de Vries description of Marangoni-Benard convection. Phys. Fluids A 3 2295-2300. 

Velarde, M. G., and Chu, X.-L. (1989b) Dissipative hydrodynamic oscillators. I. Marangoni effect and sustained longitudinal waves at the interface of two liquids. II Nuovo Cimento Dll 707-716. 

Some classification of parameters in their connection with physical or mechanical processes is to be done. The main parameter connecting hydrodynamic and diffusion parts of the film flow problem with surfactant is Marangoni number Ma. The both variants of positive (Ma > 0) and negative (Ma < 0) solutal systems are considered. The main hydrodynamic parameters are Re, 7 or equivalently S. 7. This two values determine the mean film thickness i/, mean velocity and flow rate as well as parameter k. The diffusion parameters Pe,co determine the local thickness of diffusion boundary layer h and smallness parameter e. Two values T, Di characterize the masstransfer of surfactant by the adsorption-desorption and the intensity of dissipation by the surface diffusion. Besides the limiting case of fast desorption (T = 0) the more general case (T 1) are considered. Intensity of the surfactant evaporation by parameter Bi is determined. The remaining parameter G gives an indication to the typical value of surface excess concentration A in comparison with c. ... 

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