Lift force importance

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

Other important considerations in process bioseparations are fluid management and membrane rejuvenation methods. Crossflow, or flow tangential to the membrane surface, induces shear at the membrane surface and helps reduce concentration polarization. This flow pattern also creates lift forces that counteract the deposition of particulate matter on the membrane resulting from permeation flow normal to the membrane surface. (See Section I.A.)... 

On the other hand, the mechanism of steric-FFF is complicated by a number of hydrodynamic phenomena [79]. The most important are the hydrodynamic lift forces that drive particles away from the wall and thus counteract the physical field [289-291]. This effect can even lead to an increase in the separation... 

Apart from the drag force, there are three other important forces acting on a dispersed phase particle, namely lift force, virtual mass force and Basset history force. When the dispersed phase particle is rising through the non-uniform flow field of the continuous phase, it will experience a lift force due to vorticity or shear in the continuous phase flow field. Auton (1983) showed that the lift force is proportional to the vector product of the slip velocity and the curl of the liquid velocity. This suggests that lift force acts in a direction perpendicular to both, the direction of slip velocity... 

Sommerfeld, M. (1990), Numerical simulation of the particle dispersion in turbulent flow the importance of particle lift forces and particle/wall collision models, in Numerical Methods for Multiphase Flows, Vol. 91, ASME, New York. 

In particular applications alternative relations for the slip velocity (3.428) can be derived introducing suitable simplifying assumptions about the dispersed phase momentum equations comparing the relative importance of the pressure gradient, the drag force, the added mass force, the Basset force, the Magnus force and the Saffman lift force [125, 119, 58]. For gas-liquid flows it is frequently assumed that the last four effects are negligible [201, 19[. 

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... 

In Eq. (29), Vd represents the dispersed phase velocity, Fq is the drag force, Fg denotes the force of gravity, Fl is the lift force, Fs represents effects of the fluid stress gradients, Fh is the Basset history term, and F-w represents interactions with the wall. The review paper by Loth (42) presents and discusses all the forces present in Eq. (29). Flere we limit ourselves to the most important effect of drag forces. In the case of spherical solid particles of diameter d, Fd can be expressed as... 

The change of momentum for a particle in the disperse phase is typically due to body forces and fluid-particle interaction forces. Among body forces, gravity is probably the most important. However, because body forces act on each phase individually, they do not result in momentum transfer between phases. In contrast, fluid-particle forces result in momentum transfer between the continuous phase and the disperse phase. The most important of these are the buoyancy and drag forces, which, for reasons that will become clearer below, must be defined in a consistent manner. However, as detailed in the work of Maxey Riley (1983), additional forces affect the motion of a particle in the disperse phase, such as the added-mass or virtual-mass force (Auton et al., 1988), the Saffman lift force (Saffman, 1965), the Basset history term, and the Brownian and thermophoretic forces. All these forces will be discussed in the following sections, and the equations for their quantification will be presented and discussed. 

Summarizing the forces introduced above, tests carried out in different multiphase systems have shown that the order of importance of the different forces involved typically ranks buoyancy and drag in the first positions and then lift and virtual-mass forces for fluid-solid systems and virtual-mass and lift forces for fluid-fluid systems (see, for example, the studies on non-drag forces by Diaz et al (2008) and Barton (1995)), whereas the most common values for the corresponding constants are Cl = 0.25 and Cv = 0.5 both for fluid-fluid and for fluid-solid systems. Naturally, since it is straightforward to implement all the forces in a computational code (Vikas et al, 201 lb), it is best to include them all for the sake of generality. 

The Kelvin-Helmholtz instability is thought to be a main driver in the early steps of atomization. This instability is driven by the lift forces on the interface because of the relative velocity between the two phases. When a numerical method smears velocities across the interface with insufficient resolution, the consequence may be a retardation of the predicted instability growth. Since the Kelvin-Helmholtz instability is so important, the numerical method should be capable of capturing this effect accurately. 

Micrometer particles As outlined above, micrometer size particles are separated in the steric/hyperlayer mode of FFF, and calibration using suitable standards is required (examples of typical fractograms are given in Figure 5). Shape will be a crucial factor as the lift force is highly shape dependent and can make a difference of two to three times in the elution time of particles with the same volume and mass. For SdFFF and GrFFF, the separation density will also be important, and standards with the same density as the samples must be used or careful adjustment of the field (rpm) applied for the standards, and the sample can be used to compensate for the difference in density. Fortunately, if FIFFF channels are operated with a vertical orientation, so the cross flow is horizontal and the channel flow is vertical, the particle density has no effect on the retention. 

In turbulent shear flows, the largest shear rates occur in the vicinity of rigid walls. Thus one might expect the lift force to be most important in the vicinity of walls. Saffman s analysis and the other work described above does not account for the presence of a wall. Let us consider the lift on a rigid sphere moving parallel to a flat wall as shown in Fig. 5. 

Maxey and Riley pointed out that the Magnus force is of order and, for that reason, it is less important than the Saffman lift force. 

A limitation of the above results is that they do not account for the presence of walls and it is not clear that this is permissible in situations where the lift force is likely to be important. 

Reviewing the work of Babock (1971). Geller and Gray (1986) indicated that for fine to intermediate sizes (80/100 quartz sand with o, = 0.16 mm) the value of mwas -0.25. In addition, they concluded that lift forces are at a maximum when the volumetric concentration C is less than 0,23, For intermediate sands at higher volumetric concentration, the lift forces seem to be minimal. This is an important factor to consider (for an understand ing of lift forces review Chapter 3. Section 3.1). 

Newitt et al. (1955) minimized the importance of lift forces when a bed cannot form because of lift forces on particles. However, the work of Bagnold (1954, 1955, 1957) indicated that the submerged weight of particles separated from the bed was transmitted to the bed or the pipe wall under the same conditions. Thus, mechanical friction can contribute to head loss. 

We have so far described drag and lift forces acting on a suspended particle. There are, however, additional hydrodynamic forces, such as Basset history, Faxen correction, and virtual mass effects that act on the particles. Some of these forces could become important especially for the particles suspended in a liquid. The general equation of motion of a small spherical particle suspended in fluid as obtained by Maxey and Riley is given as... 

It is important to analyze the forces exerted on the particle in terms of drag force and lift force. The drag force F)/ is the component of the hydrodynamic force exerted on the particle, projected onto the direction of the particle s relative velocity with respect to the fluid, while the lift force F is the component perpendicular to... 

The example discussed in the previous section using the BBOT equations shows that the trajectory of a solid particle tends to align with the direction of the fluid flow. The fluid flow does not exert a lift force on the particle, even if it possesses a velocity gradient in the direction perpendicular to that of the flow. This result contradicts some observations of fluid mechanics. The lack of a lift force, for example, does not allow fluid particles to migrate in the direction perpendicular to the direction of the flow, or the fluid to pick up a particle lying on a wall. The smdy of the lift force has given rise to a considerable amount of research, of which we summarize a few important results. The reader will find in the book by Michaehdes" ... 

The important values and characteristics of candidate materials for floating platforms are their price, lift force (in water), life time, strength, chemical stability in water, reliability, and so on. The water lift force of matter (L/) is difference between density of water dw) and density of platform matter dm). 

A l 50scalemodelofanairfoilistestedinawindtunnelwithstandard air flowing at a velocity (F) of 300 mph. If the lift force on the model LJ is 20 lbs, estimate the lift force on the protot5 e operating at 400 mph, assuming that a difference in Re5molds Number between model and prototype is not important. 

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