High Reynolds number bubbly flows

Surfaetant effects are discussed in the review paper by Magnaudet and Fames, The motion of high-Reynolds number bubbles in homogeneous flows , Rev. Fluid Meek, Vol. 32, pp. 659-708 2000. 

Magnaudet JJM, Eames I (2000) The motion of high-reynolds-number bubbles in inhomogeneous flows. Annu Rev Fluid Mech 32 659-708... 

In this regard, it is of interest to contrast the two problems of the streaming motion of a fluid at large Reynolds number past a solid sphere and a spherical bubble. In the case of a solid sphere, the potential-flow solution (10 155)—(10—156) does not satisfy the no-slip condition at the sphere surface, and the necessity for a boundary layer in which viscous forces are important is transparent. For the spherical bubble, on the other hand, the noslip condition is replaced with the condition of zero tangential stress, Tr = 0, and it may not be immediately obvious that a boundary layer is needed. However, in this case, the potential-flow solution does not satisfy the zero-tangential-stress condition (as we shall see shortly), and a boundary-layer in which viscous forces are important still must exist. We shall see that the detailed features of the boundary layer are different from those of a no-shp, sohd body. However, in both cases, the surface of the body acts as a source of vorticity, and this vorticity is confined at high Reynolds number to a thin 0(Re x/2) region near the surface. 

The drag coefficient monotonically decreases as the Reynolds number increases. For high Reynolds numbers, one can use the approximation of ideal fluid for solving the problem on the flow past a bubble. In this case, the leading term of the asymptotic expansion of the drag coefficient has the form [291]... 

Let us consider the motion of a gas bubble at high Reynolds numbers. For small We, the bubble shape is nearly spherical. The Weber numbers of the order of 1 constitute an intermediate range of We, very important in practice, when the bubble, though essentially deformed, conserves its symmetry with respect to the midsection. For such We, the bubble shape is well approximated by an ellipsoid with semiaxes a and b = xa oblate in the flow direction the semiaxis b is directed across the flow, and x 1 ... 

Spherical bubble at any Peclet numbers for Re > 35. For a spherical bubble in a translational flow at moderate and high Reynolds numbers and high Peclet numbers, the mean Sherwood number can be calculated by the formula [94]... 

Bubble Laminar translational flow at high Reynolds numbers rr U = U is the fluid velocity at infinity... 

Bubble Axisymmetric shear flow at high Reynolds numbers Analytical, DBLA 0 [359]... 

For high Reynolds numbers Re = aU jv > 500, the Sherwood number in the constrained flow of gas bubbles can be evaluated by the formula [263]... 

Bubble Translational flow at high Reynolds numbers 2.6 1.6... 

If tmbulent transport mechanisms are neglected, then high-Reynolds-number flow around a gas bubble (i.e., in the laminar regime) can be approximated by potential flow, where viscous forces vanishes. Now, the tangential velocity component for... 

Provided that one may approximate the bubble by a sphere, one might use an equation of the following form to track a bubble in a high Reynolds number flow ... 

Apart from the aforementioned creeping flow treatments, Astarita and Marrucci (1964) extended the Levich analysis (Levich 1962 Moore, 1959) to estimate the drag on spherical bubbles (with clean interface) at high Reynolds number to obtain... 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

The disadvantages are that (1) they are not suitable for services that are dirty, abrasive, viscous, or mixed-flow (gas with liquid droplets, liquid with vapor bubbles), or that have low Reynolds numbers (below 20,000) (2) the available choices in materials of construction are limited (3) the pulse resolution (number of pulses per gallon or liter) drops off in larger sizes (4) the pressure drop is high (two velocity heads) and (5) substantial straight runs are required, both upstream and downstream. 

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