Shear stress induced bubbles

Figure 10.12 Effect of standard deviation of shear stress induced by bubbles on the rate of fouling, dTMP/dt, of submerged fiber (Yeo et at., 2007).

Since the present study aims at carrying out the investigation of the break-down phenomenon and searching for the possible mechanism of the phenomenon, we have chosen the similar condition as in [1] for the wall shear stress to induce break-down The reference temperature in the degradation studies was 60 °C. This value may be lower than the value used in a typical DHS. In a low-pressure system, however, it was necessary to use lower the temperature to avoid the formation of bubbles. For parametric studies, one of the variables was varied while the other variables were fixed at the reference condition (Tanperature 60 °C Re 8,000 Surfactant concentration 200ppm Volume of solution charged 0.010 m ). 

Erosion corrosion is associated with a flow-induced mechanical removal of the protective surface film that results in subsequent corrosion rate increases via either electrochemical or chemical processes. It is often accepted that a critical fluid velocity must be exceeded for a given material. The mechanical damage by the impacting fluid imposes disruptive shear stresses or pressure variations on the material surface and/or the protective surface film. Erosion corrosion may be enhanced by particles (solids or gas bubbles) and impacted by multi-phase flows [29]. Increased flow stream velocities and increases of particle size, sharpness, density, and concentration increase the erosion corrosion rate. Increases in fluid viscosity, density, target material hardness, and/or pipe diameter tend to decrease the corrosion rate. The morphology of surfaces affected by erosion corrosion may be in the form of shallow pits or horseshoes or other local phenomena related to the flow direction. 

Hinze (1955) proposed that bubble breakup is caused by the dynamic pressure and the shear stresses on the bubble surface induced by different liquid flow patterns, e.g., shear flow and turbulence. When the maximum hydrodynamic force in the liquid is larger than the surfaee tension foree, the bubble disintegrates into smaller bubbles. This mechanism can be quantified by the liquid Weber number. When the Weber number is larger than a eritical value, the bubble is not stable and disintegrates. This theory was adopted to prediet the breakup of bubbles in gas liquid systems (Walter and Blaneh, 1986). Calculations by Lin et al. (1998) showed that the theory underprediets the maximum bubble size and cannot predict the effeet of pressure on the maximum bubble size. 

In a recent study Jakobsen et al. [71] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise equivalent simulations were performed. Additional simulations were run with three different turbulence closures for the liquid phase, and no shear stress terms for the gas phase. A standard k — e model [95] was used to examine the effect of shear induced turbulence, case (a). In an alternative case (b), both shear- and bubble induced turbulence were accounted for by linearly superposing the turbulent viscosities obtained from the A — e model and the model of Sato and Sekoguchi [138]. A third approach, case (c), is similar to case (b) in that both shear and bubble induce turbulence contributions are considered. However, in this model formulation, case (c), the bubble induced turbulence contribution was included through an extra source term in the turbulence model equations [64, 67, 71]. The relevant theory is summarized in Sect. 8.4.4. 

There have been few experimental measurements of Ul in submerged systems, but the reported values are in the range 0.1-0.5 m/s (Liu et ah, 2003 Madec, 2004). A decrease in fouling rate (dTMP/df) as Ul increased was reported by Liu et al. (2003). However, this is probably only part of the story, as decreased fouling rate appears to be linked to bubble-induced instabilities as well as average shear stress effects. 

Figure 8.5 Illustration of the forces connected to bubble deformation. Arrows indicate deformation-induced pressure. Upon shearing a hemispherical bubble, a Laplace pressure of magnitude y x A[l/r] develops at the deformed surfaces. Here 1/r is the curvature and A[l/r] is the shear-induced change in curvature. For a given shear deformation, the change in curvature is proportionai to the curvature in the undeformed state. The Lapiace stress wiii significantiy deviate the flow whenever y/r is comparabie the shear stiffness of the liquid, which is o r]. With r] 10 Pa.s, (o 2jt S MHz, and y 72 x 10 N/m, one finds that shear-induced Lapiace pressure matters when the radius is less than about a micron.

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