Solutal Marangoni

In the 1990s, this problem of surface structuration was revisited in the light of recent theoretical hndings obtained on nonlinear surface waves. It could be established that the waves sustained by a Marangoni effect, as observed by Linde and Schwarz and Orell and Westwater, are relevant to a nonhnear theory. They have solitonic properties and the patterns that structure the surface are produced by their colhsion. The description and analysis of these nonlinear waves sustained by a solutal Marangoni effect are the subject of this chapter. 

Nakache E., and Raharimalala S. (1988). Interfacial Convection Driven by Surfactant Compounds at Liquid Interfaces Characterisation by a Solutal Marangoni Number. In Velarde M G, editor. Physicochemical Hydrodynamics Interfacial Phenomena. Plenum Press, New York and London,... 

The Marangoni effect refers to the variation of surface tension of a liquid with temperature (thermocapUlarity) or with the concentration of a surfactant (solutal Marangoni effect). The variation of surface tension in turn leads to convective motion of the fluid Marangoni convection. This motion along the surface of the liquid layer then leads to flow in the bulk and may be used to transport fluids in microfluidic devices. 

Solutal Marangoni convection is caused by variations in the concentration of a surfactant at the interface between two liquids or a liquid and a gas. The surface tension being a function of... 

The first term on the right part of last equation (33) is the desorption or evaporation of the surfactant from the liquid phase into the gas phase, kg — gas phase masstransfer coefficient of surface active solute, m — the ratio of the concentration in the liquid phase to the concentration in the gas phase at equilibrium. These equations have been employed by Palmer and Berg (1972), Hennenberg et al. (1992) for the stability of a horizontal liquid layer with solutal Marangoni effect. In Ji and Setterwall (1994) the instability of falling film for the partial case of T = const is investigated. The coefficient... 

Solutal Marangoni convection is caused by variations in the concentration of a surfactant at the interface between two liquids or a liquid and a gas. The surface tension being a function of the local surface concentration of surfactant, a variation in the latter will affect the value of surface tension locally and therefore give rise to stresses along the interface. The relation between the surface concentration of surfactant and the surface tension is a complex one which will be addressed first. Furthermore, three irr5)ortant dynamical phenomena need to be accounted for in order to compute the Marangoni flow for a moving interface ... 

The hydrodynamic instability leading to convective flow in the biochemical systems is driven by unbalanced forces (surface tension) at the liquid/gas interface, mainly caused by temperature gradients due to evaporative cooling [1,4]. Our experiments show that the chemical composition of the solution has to be accounted for as well. The significant parameters for the onset of pattern formation are the thermal and the solutal Marangoni numbers. Both are also important for spatial patterning in biochemically reactive liquid layers. 

E, Nakache, S. Raharimalala, Interfacial convection driven by surfactant compounds at liquid interfaces. Characterization by a solutal Marangoni number , in Proc. on Physicochemical Hydrodynamics Interfacial, Spain, July 1986. M.G. Verlade and B. Nichols, eds., Plenum Press, New York, 1987... 

Rapid solvent evaporation can cause temperamre fluctuations leading to convective motion in the solution (Marangoni/Benard flows). This motion can result in uneven evaporation and thickness variations in the membrane. The solvent is allowed to evaporate until the membrane is fully vitrified, which is determined by a change in the appearance of the membrane. The resulting polymeric film is removed by lifting the edge of the film with a razor blade to ease the film off of the surface. If... 

With an open interface several other parameters enter the problem. Surface tension tractions must be considered if there is variation of surface tension with either temperature or solute (an impurity). This is accounted with the inclusion of the thermal and solutal Marangoni numbers (the latter is usually called the Elasticity),... 

For a given value of the temperature gradient the role of the impurity is rather clear. In accordance with the sign of E (solutal Marangoni or elasticity number) there is a dramatic lowering of the threshold for thermoconvective instability or the possibility of overstable modes (oscillations). When all buoyancy phenomena in the bulk are negligible (Ra = Rs = 0) transition to steady convection is expected above the line... 

Solutal Marangoni number, Ma, is the ratio between the surface tension force due to concentration difference and the viscous force of fluid. 

Annibale, G., Canovese, L., Cattalini, L., Marangoni, G., Michelon, G. and Tobe, M.L. (1984) Displacement by chloride of pyridine-2-carboxylate from dichloro (pyridine-2-carboxylato) gold(111) in acidic solution the position of ring opening. Journal of the Chemical Society, Dalton Transactions, (8), 1641. 

All of these disturbances cause a many-fold increase in the rate of transfer of solute across the interface. If a chemical or thermal difference along an interface causes an interfacial tension gradient, violent flow in the direction of low a will result. This action is usually termed the Marangoni effect. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

In equation 13, C1 and Cs are the total concentrations in the liquid and solid phases, respectively. This statement of the problem assumes that the convective flux due to the moving boundary (growing surface) is small, the diffusion coefficients are mutual and independent of concentration, the area of the substrate is equal to the area of the solution, the liquid density is constant, and no transport occurs in the solid phase. Further, the conservation equations are uncoupled from the equations for the conservation of energy and momentum. Mass flows resulting from other forces (e.g., thermal diffusion and Marangoni or slider-motion-induced convective flow) are neglected. 

An absence of the Gibbs-Marangoni effect is the main reason why pure liquids do not foam. It is also interesting, in this respect, to observe that foams from moderately concentrated solutions of soaps, detergents, etc., tend to be less stable than those formed from more dilute solutions. With the more concentrated solutions, the increase in surface tension which results from local thinning is more rapidly nullified by diffusion of surfactant from the bulk solution. The opposition to fluctuations in film thickness by corresponding fluctuations in surface tension is, therefore, less effective. 

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