Faxen effect

Saltation of solids occurs in the turbulent boundary layer where the wall effects on the particle motion must be accounted for. Such effects include the lift due to the imposed mean shear (Saffman lift, see 3.2.3) and particle rotation (Magnus effect, see 3.2.4), as well as an increase in drag force (Faxen effect). In pneumatic conveying, the motion of a particle in the boundary layer is primarily affected by the shear-induced lift. In addition, the added mass effect and Basset force can be neglected for most cases where the particle... 

The case of transport through microporous membranes is different from that of macroporous membranes in that the pore size approaches the size of the diffusing solute. Various theories have been proposed to account for this effect. As reviewed by Peppas and Meadows [141], the earliest treatment of transport in microporous membranes was given by Faxen in 1923. In this analysis, Faxen related a normalized diffusion coefficient to a parameter, X, which was the ratio of the solute radius to the pore radius... 

Now, if the Reynolds number of the flow is sufficiently small for the creeping-motion approximation to apply, it can be shown by the arguments of Subsection B.3 in Chap. 7 that no lateral motion of the drop is possible unless the drop deforms. In other words, Us = Useiin this case, though, of course, Us is not generally equal to the undisturbed velocity of the fluid evaluated at the X3 position of the drop center. The drop may either lag or lead (in principle) because of a combination of interaction with the walls and the hydrodynamic effect of the quadratic form of the undisturbed velocity profile - see Faxen s law. Because the drop deforms, however, lateral migration can occur even in the complete absence of inertia (or non-Newtonian) effects. In this problem, our goal is to formulate two... 

While the effect of Faxen (1922) is caused by viscous interaction of particles with the spatially... 

Faxen-Irving, G., and Cederhohn, T. (2011). Energy dense oleic acid rich formula to newly admitted geriatric patients—feasibility and effects on energy intake. Clin. Nutr., 30(2), 202-208. 

In the above equationis the correction factor for die wall effect. The correction factor has been studied flieoreti-cally and experimentally (Faxen, 1923 Barr, 1931 Fidleris and Whitemore, 1961 Sutterby, 1973 and Kawata et al, 1991). Faxen (1923) expressed the factor as a function of the Reynolds number, Re, and the ratio r/R)... 

Extensive reviews of turbulent diffusion were provided by Levich andHinze. Tchen ° was the first investigator who modified the Basset-Boussinesq-Oseen (BBO) equation and applied it to study motions of small particles in a turbulent flow. Corrsin and Lumley pointed out some inconsistencies of Tchen s modifications. Csanady showed that the inertia effect on particle dispersion in the atmosphere is negligible, but the crossing trajectory effect is appreciable. Ahmadi and Ahmadi and Goldschmidt smdied the effect of the Basset term on the particle diffusivity. Maxey and Riley obtained a corrected version of the BBO equation, which includes the Faxen correction for unsteady spatially varying Stokes flows. 

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... 

When the solute dimension is no longer orders of magnitude smaller than the pore dimensions, the solute molecules experience an additional transport resistance due to the proximity of the pore wall. The effective diffusion coefficient is reduced further by a hindrance factor/ drag factor Gm i i,rp). If the solute molecules are assumed spherical of radius r, and diffusing through the centerline of the pore of radius, tp, Faxen s expression may be used to estimate Gor for (r,rp) < 0.5 (Lane, 1950 Renkin, 1954) ... 

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