Radial surface

To explain this spreading rate behavior, Nikolov et al. [35] postulated that the excess driving force (assuming that capillary and hydrostatic forces balance each other) is a radial surface tension gradient, which can be approximated as... 

Figure 3. Softwood block showing three complete and part of two other growth rings in the cross-sectional plane lX). Individual springwood cells can be detected, whereas the smaller summer-wood cells cannot be seen as individual cells. Also note the absence of vessels and the uniformity of the wood. Two longitudinal surfaces (R—radial T— tangential) are illustrated. Food-storing cells can be easily detected on the radial surface (arrow). 47 X (Courtesy of N. C. Brown Center for Ultrastructural Studies, S.U.N.Y. College of Environmental Science and Forestry)...

Figure 2.10 The flat-fielded Chandra image in the energy band 0.5-2.5 keV with a King model subtracted to remove the large scale radial surface brightness gradient. Many faint features are seen including 1) the prominent eastern and southwestern arms and their bifurcation (El, E2 and SI, S2 identify the extensions of the eastern and southwestern arms), 2) the 14 kpc (3 ) ring, 3) the 17 kpc (3.75 ) arc, and 4) the faint southern 37 kpc (8 ) arc.

Electronic transition between stationary states consists in the transfer of a photon by the Wheeler-Feynmann handshake mechanism which implies the photon to exist between the radial surfaces of the two vibrating states before emission or absorption, exactly as envisaged in Schrodinger s beat model for electron transition. 

Figure 7. Representation of a tree cross section cut to reveal the three major structural planes of wood. This particular stem was cut in the spring of its 10th growing season. Key X, cross-sectional or transverse plane surface R, radial surface T, tangential surface. (Reproduced with permission from Ref 40. Copyright 1982, Technical Association of the Pulp ana Paper Industry Press.)...

Figure 12. SEM of calcium oxalate crystals in the ray parenchyma of the wood radial surface of a tropical hardwood. (Reproduced from Ref. 39. Copyri t 1982, American Chemical Society.)...

Copyright 1982, American Chemical Society.) (A) SEM of interfiber pits in earluwood as seen on the wood radial face. Note the donut-shaped borders. (B and C) SEM of pit pairs between adjacent fibers cross-sectional suiface. (D) SEM ofbordered-pit membranes (PM) in face view of a split wood radial surface. (E) Light micrograph of pit pairs as seen in cross section with a light microscope. Key PM, pit membranes PB, pit border and PA, pit aperture. 

Figure 21. Softwood bordered-pit membranes of western hemlock. (Reproduced from Ref 39. Copyright 1982, American Chemical Society.) (A) SEM of unaspirated pit in earlywood. Note porous periphery of the membrane. Rodlike bacteria are also present here, apparently filtered out onto the membrane during sample preparation split wood radial surface. (B) Light micrograph of aspirated pits (AP) in latewood cross section. (C) Light micrograph y aspirated pit and unaspirated pit (UP) in earlywood cross section. (D) Fully aspirated pit in earlywood. Note the reduction in porosity upon aspiration. (Compare to A above.)...

Figure 23. SEM of spiral thickenings in the fibers of Douglas-fir wood radial surfaces. Key A, spirals in the vicinity of ray cross-field pits in early wood and B, nigh magnification of spirals in the last latewood fiber of one year and the first earlywood fiber of the next year. Pits shown in B are interfiber-bordered pits.

Protective effects of chromic acid and ferric chloride treatments on surface degradation also were observed on radial surfaces. The preservation of both simple and bordered pits in woods treated by these inorganic salts was observed. At a 10% chromic acid treatment concentration, the structure of the pits retained most of the original shape after 1000 h of UV irradiation. The diagonal microchecks passing through the bordered pits in radial walls of tracheids, however, can still be observed (Figure 30). 

Little is known about the mechanism of lateral permeability other than that transverse flow is very small by comparison to longitudinal flow. It is generally less than in softwoods. Surprisingly there is little difference in radial and tangential permeability (Comstoek, unpub., see Sian, 1984). Ray tissue, despite the generally higher volume fraetion in hardwoods, is not particularly efficient in radial flow. Neither are the pits on the radial surfaces of fibres efficient in tangential flow. 

Tiller, F.M. Yeh, C.S. The role of porosity in filtration. Part 10. Deposition of compressible cakes on external radial surfaces. AIChE J. 

Eqs. (7) and (8) allow for a characteristic radial surface shear rate to be calculated as... 

Figure 3 Terahertz imaging of tablet coadng thickness. These 3D images Ulustrate ttie variabUity in coating thickness around a film-coated tablet and show how flie coating was thinner on the upper and lower axial surfaces than on the radial surface of the tablet The original illustration was color coded to highlight the variations in eveimess of coating, and some of these can also be seen in tins grayscale interpretation. The scales in the x, y, and z directions are in millimeter. Source From Ref. 55.

Half-bordered and bordered pits on exposed radial surfaces are severely degraded by UV light. 

Tiller FM, Hsyung NB (1991) Theory of filtration of ceramics, 2. Slip casting on radial surfaces. J Am Ceram Soc 74 210-218... 

The images shown in Figure 6 were obtained by surface wave (Rayleigh wave) inspection of 4 silicon nitride modulus of rupture test bars with laser-machined simulated voids. The technique utilized a focused 50 MHz transducer designed to produce a radial surface wave. Centrally positioned surface voids of 100,50, and 20 micrometers were readily detected. One bar (shown on bottom) had a 10 micrometer surface void, indicated by a marker pen, which would probably not have been detected. Longitudinal grinding marks were also apparent. 

The next series of tests involved the introduction of radial elements onto the rotor. Two rotors were used, with radii of 116mm and 121mm, to give radial surface elements at the cylinder ends. It was assumed that the relationship between local skin friction coefficient and local Reynolds number for both disc and cylinder elements was the same as that between the skin friction coefficient and rotor Reynolds number for the cylindrical surfaces. This... 

Predicted and measured torque for a rotor with radial surface elements... 

The proportion of the total torque due to the radial surfaces is small, typically around 15%, but the estimate of the total torque is still sensitive to large errors in the estimate of the radial surface torque. Figure 7 shows a recalculated prediction assuming that the local skin friction coefficient for the radial surfaces was double the value for the cylindrical surfaces. It can be seen that the prediction differs significantly from the experimental data. 

It can be concluded that, for this type of geometry where the proportion of total torque due to the radial surfaces is small, taking the local radial surface skin friction coefficient to be equal to the cylinder surface skin friction coefficient is a valid approach to predicting the total torque. 

It is clear that all the end effects are not caused by the seal friction and cylinder end surfaces alone. A 40mm long rotor with a 5mm annular gap has an end effect equivalent length of 58mm. Approximately half of this can be explained as due to the radial surfaces at the sides of the rotor and the likely losses in the thick fluid films on the seal faces. The remaining end effects are probably due to three dimensional flow effects which may be unique to the test rig or may be generally applicable. 

A mean value of skin friction coefficient should be applied to both the radial and the cylindrical surfaces. The value suggested is = 3.16. 10" Re where Re is either a function of R for the cylindrical surface, or a variable function of r for the radial surface. These numerical values are mean values of those determined for the different gap ratios and have been tested and found to give good correlation. 

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