Bubble base

Sandberg et al. conducted similar tests with a heated linear jet so that the buoyancy forces opposed the forces due to the lower pressure in the circulation zone (bubble). Based on the results of these tests, it was concluded that... 

Here v, the velocity of the center of the bubble, is made up of two parts, viz. the velocity of the bubble base due to movement and the velocity of the center due to expansion. Thus,... 

The equation of motion is more useful in the above form when expressed in terms of v, the velocity of the base, because the condition of detachment pertains to the bubble base and not to the bubble center. Equation (25) can be written as... 

The increase in 4> tends to reduce the first stage volume because of the smaller net downard force, whereas it increases the second stage volume because of the distance covered by the bubble base. The final volume is the result of both these conflicting factors. 

For Re < 110 the wake is closed and laminar as discussed above. Transfer over the front portion of the cap is again described by Eq. (8-20). Transfer from the base occurs by diffusion into the wake fluid as it moves along the bubble base, producing a concentration boundary layer. The solute in this... 

Figure 9.11 shows a comparison between the measured dynamic pressure and the calculated results based on Eq. (9.24). The profile indicates that there is a local high-pressure region near the bubble nose and a local low-pressure region around the bubble base, i.e., the wake region. The low pressure in the wake region promotes pressure-induced bubble coalescence in the bed. 

The mass balance for A in large bubbles based on these assumptions is... 

Every detached bubble enters the electrolyte and a Lagrangian tracking procedure is used to update the velocities and positions of all dispersed gas bubbles in the electrolyte at each time step of the Navier-Stokes solver. From Newton s second law, an equation of motion can be obtained for every bubble, based on the formulation stated in [24], Together with the relation between the particle s position and velocity, a set of two ordinary differential equations in three space dimensions can be formed in order to update the bubble trajectory... 

Fig. 7.7 Two-dimensional color Doppler ultrasound images show a dog lymph node treated with administered L-selectin ligand-specific USCA. (A) Four selected images from the first scan. (B) Image from the second scan of the same lymph node, which was performed immediately after the first scan. The images in (A) show typical micro-bubble-based SAE signals in the paracortex,...

Purge and trap (PAT), Chapter 33, involves bubbling a gas through a liquid which contains volatile or semivolatile compounds. These compounds transfer into the gas bubble based on the second law of thermodynamics systems tend to maximum disorder, or compounds go from high concentration to low concentration. In this case, the inside of the gas bubble is at zero concentration so volatile compounds in the liquid transfer into the bubble in the form of a vapor. The bubbles of gas rise to the surface, pass through an adsorption tube, and the contents trapped. This is not only a separation technique, but it is valuable in concentrating trace materials. The most common use of this technique is to separate EPA s priority pollutants from water supplies. 

Ahmed D, Mao X, Shi J, Juluri B, Huang T (2009) A millisecond micromixer via single-bubble-based acoustic streaming. Lab Chip 9(18) 2738-2741. http //dx.doi.org/10.1039/ B903687C... 

The preceding section has described a useful technique for characterizing blown film bubbles based on easfly calculated processing values. However, as indicated, the technique is generalized and only provides qualitative information about the degree of melt stretching imparted on the film. Many comprehensive studies have been performed to develop more sophisticated models that characterize bubble stresses and kinematics (shape and velocities). For more detailed reading on this subject, the reader is referred to additional resources [17—28]. 

From the above derivation, we can see that the SFM may revert to the cluster-based EMMS or bubble-based EMMS hydrodynamic models under different assumptions of structure parameters. Thus, SFM unifies these models. Indeed, the mesoscale structure has always been the critical part of the EMMS model. We may expect more variants of the EMMS model wiU be proposed because of different descriptions of the mesoscale structure (Hong et al, 2013). 

Lungu M, WangJ, Yang Y Numerical simulations of a bubbling fluidized bed reactor with an energy minimization multiscale bubble based model efiect of the mesoscale, Ind Eng Chem Res 53 16204-16221, 2014. 

Shi Z, Wang W, Li J A bubble-based EMMS model for gas-sohd bubbhng fluidization,... 

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