Drag force correction factor

Lyachshenko number, dimensionless left hand side, dimensionless particle mass, kg pressure, N/m or force, N mass feed rate, kg/s or volumetric flowrate in mVhr drag or resistance force, N physical properties correction factor for slurries Reynolds number, dimensionless right hand side hydraulic radius, m... 

Note that the lubrication effect due to particle collisions in liquid is significant. The liquid layer dynamics pertaining to the lubrication effect was examined by Zenit and Hunt (1999). Zhang et al. (1999) used a Lattice-Boltzmann (LB) simulation to account for a close-range particle collision effect and developed a correction factor for the drag force for close-range collisions, or the lubrication effect. Such a term has been incorporated in a 2-D simulation based on the VOF method (Li et al., 1999). Equation (36) does not consider the lubrication effect. Clearly, this is a crude assumption. However, in the three-phase flow simulation, this study is intended to simulate only the dilute solids suspension condition (ep = 0.42-3.4%) with the bubble flow time of less than 1 s starting when bubbles are introduced to the solids suspension at a prescribed ep. 

It was shown in [179] that the effective viscosity is related to the ratio of the velocity of free sedimentation of a single particle according to the Stokes law to the velocity of particles in the suspension, that is, the effective viscosity is related to the correction factor A in the drag force. The expression... 

Values of Cc as a function of the particle diameter Dp in air at 25°C are given in Table 9.3. The slip correction factor is generally neglected for particles exceeding 10 pm in diameter, as the correction is less than 2%. On the other hand, the drag force for a 0.1 pm in diameter particle is reduced by almost a factor of 3 as a result of this slip correction. 

Making use of the correlation proposed by Ishii and Zuber [24] for correction of the drag force in a bubble swarm, the drag coefficient q is multiplied with the correction factor/ which is given by ... 

It is clear that both the Couette model and the ID Stokes model fail to predict the quality factor correctly. They overestimated the value of the quality factor by a factor of two. On the other hand, results from the 3D analysis agree well with the experimental result, with an error of 10 %. This indicates that 3D effects are profound in this resonator. Figure 5 shows the detailed drag force distribution for the resonator. The drag force from the ambient air on the top of the resonator contributes 15.7 % to the total drag, and the drag... 

For droplets in air less than about 5 pm in diameter, the actual drag force is even lower, since the surrounding air is not a continuum at these scales. Millikan s resistance factor (or Cunningham s correction) multiplies the terms on the right-hand side of Eq. 9 to form the corrected drag force ... 

For.this hindered flow the settling velocity is less than would be calculated from Eq. (14.3-9) for Stokes law. The true drag force is greater in the suspension because of the interference of the other particles. This higher effective viscosity of the mixtureis equal to the actual viscosity of the liquid itself, fi, divided by an empirical correction factor,, which depends upon e, the volume fraction of the slurry mixture occupied by the liquid (SI). 

Particles moving relative to the surrounding air are subjected to a resisting force by collision with air molecules. This force is the same whether the particle moves through the air or the airflows past the particle. For small airborne aerosol particles the resisting force, or drag force (Fd), is described by Stokes law Fd = S.jr.q.U.D, to which several correction factors may be applied (as for the shape factor see definition). In this equation q is the dynamic viscosity of the air, U is the particle velocity (relative to the air) and D is the particle diameter. 

The mobilizing drag, lift, and inertia forces contributing to sliding. The correction factors of the drag force Fd and lift force Fl (KScd and KScl) are obtained as the ratios of the areas As and At with and without deformation effect. The correction factor KScm is assumed to be 1.0 since the container volume V remains constant. 

The mobilizing moment induced by the drag, lift, and inertia forces. The correction factor for the moments induced by the drag and lift forces (KOcd and KOcl ) area is obtained as the ratio of describing the changes of both surface areas (As and At) and lever arms (r and Vs) of the drag and lift forces Fd and Fl. The correction factor KOcm is obtained as the ratio of lever arms Vsn of the inertia force with and without deformation effect. 

If the solute shape is nonspherical, a relation other than Stokes law will apply. For the determination of the resistance of nonspherical macromolecules, the reader may consult pp. 356-364 of Tanford (1961). We will provide a very brief perspective on this effect here. Some cells, and especially many proteins, are ellipsoids of revolution. The drag force encountered by such an ellipsoid of revolution of species i is described in terms of the drag encountered by a sphere of equal volume whose radius is ro via an appropriate correction factor (ff/ffo) which is always greater than 1. This factor is called the Perrin factor. The magnitude of is enhanced by this factor, i.e. 

Inspecting the foregoing equations we see that, as pressure decreases and the gas density decreases, the mean free path of the gas phase increases. This, in turn, increases the correction factor, Cc and, hence, decreases the drag force acting on the particle. The practical effect of this is that particles are separated with greater efficiency imder vacuum conditions than under ambient or elevated pressures. 

When a particle moves within a containment, the development of a boundary layer and a wake and therefore its motion will be hindered— depending on the ratio of particle diameter to containment diameter. Happel and Brenner (1973) discussed this effect extensively for low particle Reynolds number flows. More recently, Chen and McLaughhn (1995) derived a set of correction factors for the drag force in the vicinity of just a waU. 

The dynamic shape factor %) is used to correct for the influence of shape on the resistance force or drag experienced by a particle moving through a fluid. For micron-sized particles this term can be expressed as ... 

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