Diffusocapillary Flow

Spatial gradients in surface tension may arise from a variety of causes, including spatial variations at the interface in temperature (Eq. 10.1.3), in surface concentrations of an impurity or additive (Eq. 10.1.4), or in electric charge or surface potential. The resulting flows are termed, respectively, thermocapillary flows, diffusocapillary flows, and electrocapillary flows. We shall limit our discussion of electrocapillary phenomena because of space restrictions but instead refer the reader to Levich (1962) and Newman (1991). 

In the preceding section, we have examined a variety of steady thermocapillary and diffusocapillary flows. Not all such flows are stable and in fact surface tension variations at an interface can be sufficient to cause an instability. We consider here the cellular patterns that arise with liquid layers where one boundary is a free surface along which there is a variation in surface tension. It is well known that an unstable buoyancy driven cellular convective motion can result when a density gradient is parallel to but opposite in direction to a body force, such as gravity. An example of this type of instability was discussed in Section 5.5 in connection with density gradient centrifugation. 

When surface active species are present at an interface, they can suppress the flow of fluid perpendicular to the interface. For an interface rich in surfactants (see Figure 8) the flow of liquid will transport the surfactant away from the interface and this decrease in surfactant concentration cannot be instantaneously replaced from the bulk of the liquid. This results in a high surface tension at point of emergence (A) and a diffusocapillary flow will be established in the direction B —> A i.e. counter to that of the original flow. 

In distillation columns, a substance with a vapour pressure will transfer preferentially into the vapour phase. If the vaporising species is a surfactant, it will result in a local increase in surface tension, thus, it will produce diffusocapillary flows and pull liquid toward it. This, in turn will create better spreading and higher transfer coefficients and frequent replenishment of liquid (see Figure 40a). If, however, the vaporising species results in a decrease in the surface tension, the diffusocapillary flow will be away from the point of vaporisation and this could produce a dry spot (Figure 40b). 

Spatial variation in surface concentration of an impurity or additive. The resulting flow is termed as diffusocapillary flow. 

During the movement of gas bubbles, the oil film is collected at the production well located outside the reservoir. As the bubble travels down the capillary, the flow in the surrounding fluid causes a nonuniform distribution of surfactant on the bubble surface. This nonuniform surfactant distribution determines the surface forces, since the surface tension gradient depends on the local surface concentration of the adsorbed material. The film thickness and the total pressure drop to drive the bubble are dependent on the surfactant distribution. This kind of flow is known as diffusocapillary flow. The surfactant is swept toward the rear of the bubble where it accumulates. 

These are, for the most part, thermocapillary forces but diffusocapillary forces can arise when welding steels with different sulphur contents (see Section 4.1.7). The direction of the thermocapillary flow is determined by the concentration of O or S in the alloy. 

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. 

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