Lift force on bubbles

Experiments have shown that bubbles under certain conditions experience lift in the opposite direction to what would be predicted by rigid sphere analysis. Other mechanisms must therefore be important in determining the lift force on bubbles. Lift in turbulent flow is very complex, and few studies have been 

Interpreting their data it was concluded that when Eo is low, the bubble will migrate toward the pipe wall as explained with the classical shear-induced or Saffman type of lift force. On the other hand, when Eo is high, the vortex behind a deformed bubble becomes slanted and for this reason the bubble migrates toward the pipe center. This implies that there is a third transversal lift force contribution caused by the interaction between the wake and external shear field. 

Measurements performed under the experimental conditions of —5.5 log(Mo) —2.8 and 1.6 o 6 were used as basis making an empirical parameterization for the net transverse lift force coefficient. 

This parameterization gives 0 Cl 0.288 for small bubbles that migrate towards the pipe wall and negative values for large distorted bubbles. The sign of Cp changes at dp = 5.6 (mm) from positive to negative. 

In one of the latest studies reported by Tomiama et al [157] on the lift force the Cl value was found to be well correlated with Rep in accordance with the given parameterization for small bubbles, whereas for intermediate and large bubbles Cp was considered a function of a modified Eotvos number Eod (i.e., exchanging Eo with Eod in the above parameterization of Cp). The Eod is defined in terms of the maximum horizontal dimension of a bubble as a characteristic length  

To estimate dn which occurs in the definition of Eod, an empirical correlation of the aspect ratio E for spheroidal bubbles in a contaminated system was used  

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When a fluid is allowed to rise through a loose bed of particles, there will be a pressure drop across the bed that acts as a lifting force on the particles. At the point of incipient fluidisation this pressure drop has become large enough to balance the weight of the particles forming the bed. Further fluid flow then percolates through the bed in the form of bubbles. 

Kariyasaki [70] studied bubbles, drops, and solid particles in linear shear flow experimentally, and showed that the lift force on a deformable particle is opposite to that on a rigid sphere. For particle Reynolds numbers between 10 and 8 the drag coefficient could be estimated by Stokes law. The terminal velocity was determined to be equal to that of a particle moving in a quiescent... 

Larger bubbles increased the liquid circulation velocities and therefore are expected to be more efficient for air scouring of membrane surface due to the increase on the drag and lift forces on the particles... 

Fiat sheet Singie bubbie movement between membrane piates Distance between membrane piates (3-11 mm) Bubbie size equivaient sphericai diameter ranging from 3-24 mm 5 mm bubbles in 5 mm channels appear to be less clogged due to the increase in shear stress Drag and lift forces on single particle large particles can be removed by the lift force while smaller particles are transported to the membrane and form cake layer Drews et ai, (2010)... 

It must be noted here that even for Eulerian-Lagrangian simulations, although there is no complexity of averaging over trajectories, the accuracy of simulations of individual bubble trajectories depends on lumped interphase interaction parameters such as drag force, virtual mass force and lift force coefficients. All of these interphase interaction parameters will be functions of bubble size and shape, presence of other bubbles or walls, surrounding pressure field and so on. Unfortunately, adequate information is not available on these aspects. To enhance our understanding of basic... 

Esmaeeli et al [43] solved the full Navier-Stokes equations for a bubble rising in a quiescent liquid, or in a liquid with a linear velocity profile. The calculations were performed in 2-dimensional flow, but similar results have also been reported for 3-dimensional calculations. The surface tension forces were included, and the interface was allowed to deform. R was shown that deformation plays a major role in the lift on bubbles. Bubbles with a low surface tension have a larger Eotvos number, and are more prone to deform. 

The acceleration of the liquid in the wake of the bubbles can be taken into account through the added mass force given by (5.112), whereas the Eulerian lift force acting on the dispersed phase is normally expressed on the form (5.65). 

The interphase forces considered were steady drag, added (virtual) mass and lift. The steady drag force on a collection of dispersed bubbles with a given average diameter was described by (5.48) and (5.34). The transversal lift force was determined by the conventional model (5.65), whereas the added mass force was approximated by (5.112). 

The process of gas entrainment and circulation is complicated and not easily quantified. Problems arise from an abstract relationship between the liquid and gas phases. On the one hand, the gas flow rate affects the liquid flow rate through the gas holdup and hydraulic pressure differential relationship. As the gas flow rate increases, larger bubbles rise faster and increase the circulation velocity. A higher circulation velocity, in turn, would decrease the slip velocity and make entrainment easier. On the other hand, if the liquid velocity is higher than the bubble rise velocity, bubbles would experience a drag (lift) force, which would aid entrainment. 

Maxey and Riley [47] derived an equation of motion for a small rigid sphere of radius R in a nonuniform flow. If one considers small bubbles moving in a polar liquid, this equation might be appropriate because surfactants would tend to immobilize the surface of a bubble and make it behave like a rigid sphere. Maxey and Riley assumed that the Reynolds number based on the difference between the sphere velocity and the undisturbed fluid velocity was small compared to unity. In addition, they assumed that the spatial nonuni-formity of the undisturbed flow was sufficiently small that the modified drag due to particle rotation and the Saffman [48] lift force could be neglected. Finally, they ignored interactions between particles. 

The lift forces (Magnus forces) Fi, Fi y, and Flz, which represent the forces of generating a sidewise force on the spinning bubble in the liquid phase by the liquid velocity gradient, are given by Auton et al. [32] as... 

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