Surface Marangoni stress

A solvent dissolution, a vapor adsorption, any kind of surface-active substance exchange between the surface and the adjacent subphase, or heating makes the surface tension locally vary, thus generating Marangoni stresses and convection. Then, gravitocapillary waves (wavelength X and amplitude q) excited and sustained by the Marangoni effect in the shallow water waves approximation can be described by the equation ... 

Finally, we consider the problem of Marangoni instability, namely convection in a thin-fluid layer driven by gradients of interfacial tension at the upper free surface. This is another problem that was discussed qualitatively in Chap. 2, and is a good example of a flow driven by Marangoni stresses. 

Here p is the dimensionless pressure in the gas, i.e., p /(/j,uc/s2ic) and r is the dimensionless surface shear stress, r /(p,uc/e c)- In (6-21), we have also introduced the dimensionless surface-tension function b such that a = o b. We denote the value of a at the ambient temperature (and/or in the absence of surfactants) as a0. Hence, if there are no changes in a from its ambient value, the function Vsb = 0. Once again, it will be noted that we have retained terms that include the small parameter e. These are again terms that could be responsible for the motion of the film, and in this case, the appropriate choice for uc would be either eao//j or 3 er0//b depending on whether the dominant effect is Marangoni or capillary-driven motion, respectively. 

Figure 6-7. Three configurations for the shallow-cavity problem (a) Four isothermal solid walls with motion driven by tangential motion of the lower wall (b) the same problem as (a) except, in this case, the upper surface is an interface that may deform because of the flow (c) the configuration is the same as (b), except, in this case, the lower wall is stationary and the motion in the cavity is assumed to be driven by Marangoni stresses caused by nonuniform interface temperature that is due to the fact that the end walls are at different temperatures.

If we think about the physics of establishing the immobile cap at the rear of the bubble, it is necessary that the local Marangoni stress balance the net shear stress on the interface. In effect, this means that the condition (7-258) must be satisfied at all points on the surface where the cap exists,... 

Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Non-uniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. 

However, drop formation is not the only situation during which a new surface is created. Indeed, while the volume of fluid inside a drop must be ccmserved, its shape may vary and with it the surface area of its interface. For instance, a spherical drop (of minimal surface area) may be deformed by the external flow to form an oval or other shape. This creation of a new surface is coupled with the presenc e of Marangoni stresses as we shall see below, the surfac e variaticMi can create Marangoni stresses, but it can also be caused by uneven distribution of surfactant. 

When g = 0, eq.(149) provides an extension of the Kuramoto-Sivashinsky equation to the case presented here. There is a new term, Z (C ) due to the surface tension gradient-driven Marangoni stress. 

Other effects can also be observed in compatibilized blends. Due to the flow of the matrix surrounding the dispersed droplets, the compatibilizer can be conveyed towards the tips of the droplets, which makes the behavior of the droplets more complex [119]. An inhomogeneous distribution of the compatibilizer leads to the concentration gradient at the interface which causes so-called Marangoni stress that tries to equalize the compatibilizer concentration on the droplet surface (Figure 3.15). It is supposed that the formation of the concentration gradient is easier in the systems vrith a p-value below unity [120]. As the Marangoni stress... 

For two-phase flow, the conservation of mass and momentum requires corresponding transmission conditions at the interface, the so-called jump condi-ti(Mis. At this point, we assume a non-contaminated and fully mobile interface. The former corresponds to negligible surface mass densities, i.e., no occurrence of adsorbed species, while the latter means constant surface tension, i.e., no Marangoni stresses due to surface gradient of the surface tension, as well as zero surface viscosities. In this case, the surface stress tensor reduces to with constant a. Since no phase change is considered, the additional jump condi-ticHis read... 

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