Stagnation rings

The expected surfactant distribution is also portrayed qualitatively in Figure 2. At low Ca, recirculation eddies in the liquid phase lead to two stagnation rings around the bubble, as shown by the two pairs of heavy black dots on the interface (18>19). Near the bubble front, surfactant molecules are swept along the interface and away from the stagnation perimeter. They are not instantaneously replenished from the bulk solution. Accordingly, a surface stress, rg, develops along the interface... 

Again, as expected, in Figure 5 there is an excess of surfactant near the rear stagnation ring due to surface convection towards that point. Forward from that location, however, there is also a depletion relative to equilibrium adsorption. This is caused by the traveling wave in the rear bubble profile as demonstrated in Figure 2 and in Figure 7 to follow. 

Any consideration of mass transfer to or from drops must eventually refer to conditions in the layers (usually thin) of each phase adjacent to the interface. These boundary layers are envisioned as extending away from the interface to a location such that the velocity gradient normal to the general flow direction is substantially zero. In the model shown in Fig. 8, the continuous-phase equatorial boundary layer extends to infinity, but the drop-phase layer stops at the stagnation ring. At drop velocities well above the creeping flow region there is a thin laminar sublayer adjacent to the interface and a thicker turbulent boundary layer between this and the main body of the continuous phase. 

In contrast to circular channels, there is less information available on Taylor flow in noncircular channels and most of the information that is available refers to square channels. In square channels at Ca < 0.1, the bubble is not axisym-metric and flattens out against the tube walls leaving liquid regions in the comers which are joined by thin flat films at the sides of the channels. As Ca increases, the bubble becomes axi-symmetric, and for high values of Ca, the bubble radius reaches an asymptotic minimum value, approximately equal to 0.68 times the square channel half-width [15]. A stagnation ring forms... 

The presence of bubbles affects the flow field within the liquid slugs and results in fluid recirculation [33]. At low Ca, there is a stagnation ring at each bubble cap (Figure 8.2). For 0.6 < Ca < 0.7 there is still recirculation in the liquid accompanied by two stagnation points on the bubble front and inside the liquid. At Ca > 0.7, complete bypass of the liquid occurs with a single stagnation point at the bubble front (34,35). Thulasidas et al. [34] found theoretically that complete bypass occurs at Ca> 0.5 in upward flow and at Ca > 0.6 in downward flow. In square channels, liquid bypass was found to occur at Ca > 0.54 for horizontal flow [36], whereas in upward and downward flows complete bypass occurred at Ca> 0.5 and Ca>0.57, respectively [34]. 

If Re increases beyond 20 the separation ring moves forward so that the attached re-circulating wake widens and lengthens. The separation angle measured in degrees from the front stagnation point is well approximated by 0 = 180-42.5 (ln(Re/20)) at 20 < Re < 400. The steady wake region appears at 20wake instability corresponds to 130 < Re < 400. 

Figliola has made steady flow velocity and shear stress measurements downstream from a 25 mm spherical disc aortic valve (47,89). At a flow rate of 25 1/min he measured a maximum wall shear stress of 722 dynes/cm and an occluder wall shear stress (resolved on the upper side of occluder) of 440 dynes/cm. He also monitored a maximum turbulent shear stress of 545 dynes/ cm2, a 25 mm downstream from the valve. His velocity measurements also showed a large region of stagnation across the outflow face of the disc. Tillman has measured the "wall" (i.e. surface) shear stresses along the orifice ring in the major and minor outflow regions of an aortic valve under pulsatile flow... 

The smaller region of stagnation, and the better distribution of flow between the major and minor orifices observed with the convexo-concave valve, may hopefully reduce the problems of thrombus formation on the outflow face of the disc, and excess tissue growth along the sewing ring of the minor orifice region. 

During bag breakup, separation of the flow around the deformed drop leads to a positive pressure difference between the leading stagnation point and the wake. This tends to blow the center of the drop downstream resulting in the formation of the bag [12]. The outer edge forms a toroidal ring to which the bag is attached. 

One of the main features of this cell is the double-gasket design. The cathode O-ring is located closer to the liquid than the anode O-ring, which is not in permanent contact with the chlorinated brine, thereby serving as a well-protected back-up seal. Rounded comers in the anode and cathode pans eliminate gas stagnation in the comers of the cell. 

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