Transversal drag

Figure 2.8 illustrates the relative values of the transversal drag against a similar shape factor. The dashed line shows exact results for spheroids. One can calculate the relative coefficients of transversal drag by the formula [94]... 

Transverse drag force (F,) or (TDH) aeting on hair is given by ... 

Transverse drag force parameters on hair Longitudinal drag force parameters on hair ... 

Transverse drag forces aeting on hair constituted by fibers of different deniers is shown in Figure 4.8. The ealculated diameters of 1.0, 1.2, and 1.4 denier fibers are 10, 11, and 12 pm. The transverse drag force acting on 1.4 denier hairs is higher in comparison to that on 1.2 and 1.4 denier hairs. Most of the bending of hairs is likely to take place at planes in between 0 to... 

Figure 4.8. Comparison of transverse drag forces (TDH) acting on hairs constituted by fibers of different deniers (Nozzle 45°, 2.2 mm diameter at 0.5 bar, gauge) [Source Reference 1].

Rao et al. (R5) and Raju et al. (R2) also investigated mass transfer at vibrating electrodes for low vibration frequencies (higher frequencies would cause cavitation). Mass transfer follows a laminar-type correlation both for a transverse vibration of a vertical cylinder and for a vertical plate vibrating parallel to the face. In the case of the plate, the Reynolds number is based on width, indicating the predominance of form drag. When vibrations take place perpendicular to the thickness, skin friction predominates and the Reynolds number is then preferably based on the equivalent diameter (total surface area divided by transverse perimeter). 

Flow FFF is the most versatile FFF subtechnique (and one of the most versatile of all separation techniques) because it requires nothing more than the interaction of the transverse stream with a suspended or dissolved component. This interaction is made up of the drag forces which induce... 

In a cross-flow classifier, the feed material enters the flow medium at one point in the classification chamber, at an angle to the direction of fluid flow with a component of velocity transverse to the flow and is fanned out under the action of field, inertia and drag forces. Particles of different sizes describe different trajectories and so can be separated according to size. 

The MRS closures will attract most interest for use wherever MTE methods fail. For example, in flows with rotation the Coriolis terms enter the Rij equations, but drop out in the equation for Ru — q Therefore, an MRS method probably will be essential for including rotation effects, which are of considerable importance in many practical engineering and geophysical problems. Other effects that have not yet been adequately modeled and for which MRS methods may offer some hope include additive drag reduction, ultrahigh Reynolds numbers, separation, roughness, lateral and transverse curvature, and strong thermal processes that affect the hydrodynamic motions. 

The importance of the ionomer in the electrode for the performance of the PEMFC has been well known since the pioneering work of Raistrick et al. [37]. In the PEMFC, the electroosmotic drag of water due to the proton transport from the anode to the cathode leads to the membrane drying out from the anode side (back diffusion of water from cathode to anode compensates partly for the water loss from the anode side of the membrane). Therefore, the loss of conductivity of the ionomer at the anode is also an additional important issue related to the membrane topic, since the ionomer in the electrode needs to connect ionically and chemically to the membrane. In an investigation of the transverse water profile in Nafion in PEMFCs with a... 

The terms on the right-hand side of Eq. (11.4) correspond to interphase drag force, virtual mass force. Basset force and lift force, respectively, /l is a transversal lift... 

In another attempt to account for turbulence effects Jakobsen [65] performed turbulence modelling of the drag force, and showed that this procedure gave rise to a transversal force acting in the opposite direction compared to the classical lift force [7, 8, 152]. 

Deen et al [30] used the lift force in addition to the steady drag- and added mass forces in their dynamic 3D-model to obtain the transversal spreading of the bubble plume which is observed in experiments. A prescribed zero void wall boundary was used forcing the gas to migrate away from the wall. The continuous phase turbulence was incorporated in two different ways, using... 

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). 

By applying turbulence modeling to the drag force, negative transversal forces arise. The resulting transversal force was written as [12] ... 

The surface circulation of the western basin apparently remains anticyclonic, and the deep circulation cyclonic, under the predominant winds. As far as the relatively fast surface currents are concerned, the transversal spatial scale of today s sea is too small for the Coriollis force to be significant, so that the direct wind drag matters rather than the Ekman transport. On the other hand, the bottom layer circulation seems to immediately follow the sea surface slopes in the classic barotropic manner, so the Coriollis force is still effective for the slower, near-bottom currents. 

Here Cf is the drag coefficient of the body, d is the center section diameter, and b(X) is the local half-width of the wake. The coordinate X is measured from the rear point of the body and Y is the transverse coordinate. The definition of the local half-width b(X) of the wake is a matter of convention it can be estimated as... 

It follows from (2.6.14) and (2.6.15) that to calculate the drag force of a body of revolution of any shape with arbitrary orientation in a Stokes flow, it suffices to know the value of this force only for two special positions of the body in space. The axial (Fy) and transversal (Fl) drags can be obtained both theoretically... 

The axial and transverse motion of two drops close to each other was considered in [525], Some leading terms were obtained in the asymptotic expansion of the drag force with respect to the small dimensionless distance between the drop boundaries. The case of interaction between a solid particle and a drop was also investigated. 

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