Marangoni force

ELECTRODE, ICE EILMS, MARANGONI FORCES AND DIFFUSION IRREVERSIBILITIES... 

The three-phase interface is a well-known concept, notably in connection with the invention by Bacon of bi-porous electrodes (Bacon, 1969). At equilibrium, in such electrodes, gas, liquid electrolyte and catalytic solid are in contact at a convoluted meniscus at the coarse-pore, liquid-containing region interface with the fine-pore, gas-containing region. The picture changes with departure from equilibrium. The meniscus becomes mobile under the influence of surface tension gradients or Marangoni forces - an invisible complex. 

The characteristic velocity is determined by the ratio of the characteristic tangential (Marangoni) stress, 0(PAT/L), which drives this motion to the viscous forces ()(p,uc/d) that derive from this motion. The definition (6 212) also allows us to return to the condition for neglect of buoyancy forces compared with Marangoni forces as a potential source of fluid motion in the thin cavity. To do this, we introduce the thermal expansion coefficient, which we denote as a, so that the characteristic density difference Ap = O(paAT). Then the condition (Apge2t2/puc) 1 can be expressed in the form... 

One can see from (5.9.15) that in the absence of thermogravitational forces and longitudinal pressure gradient (b = Gr=0), the velocity profile is linear. Then the rate of flow proves to be nonzero. At the same time, the expressions (5.9.15) and (5.9.16) show that a flow of zero rate can be produced by the Marangoni forces only if there is a nonzero longitudinal pressure gradient. 

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. 

Finally, microfluidics was mentioned in the earlier section. Fluid flows at the microscale can be much more strongly influenced by surface and capillary forces than is the case in macroscale systems. As a result, it is possible to passively drive fluid flows driven using only capillary or Marangoni forces. This is referred to as passive microfluidics. Conversely, active microfluidics refers to the use of active microcomponents to drive fluid flows. Active microfluidics devices use micropumps and/or microvalves to control the fluid flows and as such are an example ofMEMS. 

Fig. 7.6 Collisions of a water and an ethanol drop (a) head-on collision with coalescence and separation of one satellite (We =20,X = 0) (b) reflexive separation with formation of a small satellite due to Marangoni forces We = 38.5, X = 0.02) (c) stretching separation with formation of three satellite droplets (We = 82.3, X = 0.82). Droplets move from right to left the water droplet coming from above is marked with w [45] (With kind permission from Springer Science+Busi-ness Media Experiments in Fluids [45], Plates 3, 5 6, Copyright Springer-Verlag 2005)...

Tangential stress condition. The stress at any point on the interface in a direction tangential to the interface jumps as we cross from one phase to the other by an amount equal to the force exerted by surface tension gradients (Marangoni forces). 

In this case the exchange of surfactant between the bulk and the surface opens the possibility for reduction of the Marangoni force. When the rates of bulk diffusion and surfactant desorption are of the same order as surface convection (i.e. the present regime), the surfactant exchange mechanisms can be used to identify factors affecting the Marangoni force. The non-dimensional Marangoni force is... 

The opposite regime of bulk diffusion control oi the Marangoni force has Xo(l + A )/Pe = 0(1) and Bz >> 1, has received little attention. We can estimate from (116), therefore, that as Bi oo Tm = O( j ). Using this result we have the following paradigm for remobilization For large fc, Tm scales as Pe/(XoA ), so as the concentration increases. Be and xo held fixed, the Marangoni force should disappear. The numerical solutions described in what follows, lend support for this possibility for both zero and order one Reynolds numbers. 

The representative results that follow exhibit conclusively the possibility of removing the Marangoni force and completely remobilizing the surface. (For more details see [80], [81].)... 

Figure 16 (a) Thermocapillary (Marangoni) forces M(+) or M(-) (b) electromagnetic (Lorentz) forces E, resulting from interaction of current (c) buoyancy forces B, resulting from density differences caused by temperature... 

Tinkler et al [41] showed that when welding a 30 ppm sulphur (LS) plate to a 90 ppm sulphur (HS) plate, the resulting weld was off-centre and displaced towards the LS side. This can be accounted for if it is assumed that Marangoni forces dominate the fluid flow in the weld pool. It can be seen from Figure 21 that the thermocapillary forces in the LS and HS will be from left to right and the diffusocapillary forces will also operate from left to right. Thus these surface flows will cause hot metal to be carried to the LS side and melt back off the steel will result in an asymmetric weld. 

Figure 21 Schematic drawings showing the formation of a non-axisymmetric weld when welding steels have different sulphur contents (a) Marangoni force due to temperature gradients (b) Marangoni forces due to S content differences (c) combined Marangoni flow...

It is usually considered that Marangoni forces would be eliminated for a solid free surface. Thus, for the above mechanism to apply, it is necessary to have a bubble at the free surface. Although bubbles are generated near the solidification front the cause proposed is unlikely to be a major mechanism. 

This process is similar to GTA welding but a filler metal is used. Takasu and Toguri [47] have shown that there are four forces affecting the fluid motion (Figure 25) in the pool when the molten filler metal drop hits the molten pool, namely (i) a stirring force due to the momentum of the drop (ii) a buoyancy force related to the density difference between the drop and the pool (iii) a curvature force related to the surface tension normal to the surface and (iv) the Marangoni force related to the difference in surface tension of the drop and pool. Takasu and Toguri showed that when (a) ydrop > ypooi the droplet penetrated into the pool and (b) ydrop < ypooi the drop will spread out over the surface. 

For a negative potential, NaF will be depleted in the wall (low current density) region. Consequently, Yms will be low but will be high in the centre and thus the motion due to Marangoni forces will be in the direction of wall to centre. Thus the back reactions give rise to electrocapillarity forces causing movement of the liquid aluminium. 

One way of minimizing thermocapillary forces is to create a surface with a very high viscosity (a solid surface can be considered to have an infinite viscosity). Thus if the surface of the melt was allowed to oxidize to form an oxide skin on the surface, this would effectively eliminate the Marangoni forces and produce a very quiescent molten pool [65]. 

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