Cross-section radius

Cilia are thin cylindrical hair-like structures with a cross-sectional radius of 0.1 gm projecting from the apical epithelial surface of ciliated columnar cells. Ciliary length is thought to correspond to periciliary fluid depth and range from approximately 7 gm in proximal airways to roughly 5 gm in more distal airways.- Each ciliated epithelial cell supports approximately 200 cilia at a density of eight cilia/gm. Short microvilli, possibly associated with secretory functions, are interspersed among the cilia. 

If the collision cross-section of N2 is 0.43 x 10-18m2, what is the collision cross-sectional radius (d = 2r) ... 

If He has a collision cross-section radius of 2.18 x 10-10m, calculate the mean free path of He atoms at lO mbar and 293 K. 

Here x is a phenomenological parameter measuring the chirality and / is a size scale factor. Since here the Reynolds number is small ( 10 s), the Stokes equation can be used to get r = DS2. where D is the hydrodynamic drag coefficient and 2 is the rotational speed. The drag coefficient for a cylindrical object rotating about its axis with cross-sectional radius r and length L is D = 4ztT)r2L, where tj is the viscosity of the medium [19]. Therefore, D /3 and the rotational speed 2 of the rotor will scale as... 

Based on the studies of border and film shape in the dodecahedral model Kruglyakov et al. [18] and Kachalova et al. [19] have proposed an expression for foam expansion ratio, using a cylindrical border model with the same cross-sectional radius of curvature. The volume of excess vertex parts was considered in order to estimate the effect of the longitudinal radius of curvature on the border shape... 

Fig. 18. The anomalous dispersion of the cross section radius of gyration of Cs-DNA double helix. The depression of R is due to a decrease of the scattering factor of Cs at the Lj-absoption edge. ( ) absorption spectrum of Cs, (-(-) dispersion of R of Cs-DNA...

Further analysis of these preliminary SANS results is complex and can only be outlined here. The treatment takes as its basis, a model composed of an array of parallel cylindrical objects, length, 1 and cross-sectional radius, a [14]. 

Fig. 40 Cross-sectional radius of gyration RgjC as function of added salt for sample PM-PVP25-Me90 (squares, NaBr) and for sample F3-PS-PS41-S66 (triangles, NaCl)...

Table 7 Fraction of free counterions, fc (normalized to the number of chemically quater-nized monomers), the effective charge density, / (normalized to the total number of monomers), the effective charge density per main chain monomer fma the cross sectional radius of gyration RgjC) the mean concentration of counterions cc and the mean inverse Debye screening length Xb l within the volume of a cylindrical brush molecule due to condensed counterions...

Table 11 Cross-sectional radius of gyration for sample rions and for different amount of added salt F3-PS-PS41 S68 for different counte-...

Custom made release cell with a rectangular donor compartment (5x5x50 mm), to take up about 1 g of the VPG and an acceptor compartment of semicircular cross section (radius 2.5 mm) and 50mm length (For a layout of cell see ref 7). 

The plasma-oriented approach is also useful in estimating the interaction area between fast and slow charge carriers, by an appropriate adaptation of the concept of collision cross sections to electrolytes. As an illustration, the apparent cross-section radius of 181 nm in the case of a 0.005-mol dm solution subjected to a 1 mT magnetic field compares favorably with the 134 nm computed from the classical Rosenbluth formula applying to electron-ion collisions. 

FIG. 2.7 Relevant length scales for the colloidal structure of worm-like micelles contour length, Lc, entanglement length, /e, mesh size, m, persistence length, Zp and cross-sectional radius, rcs. Values shown are those measured for a solution with 1.5% total surfactant at a cetyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzenesulfonate (SDBS) ratio of 97/3 with 0.10% added sodium tosylate. (Reproduced from Schubert, B.A., Kaler, E.W., and Wagner, N.J., Langmuir, 19, 4079 -089, 2003. With permission.)... 

Infinite cylinder of half-circular cross section, Radius... 

From the plots shown in Fig. 1, it is evident that Eq. 3 is valid for the hydrophilic solutes examined in the present study. The dependence of Dm on cross sectional radius is evident from the linearity of the plots. The water contents of p-HEMA and p-HEMA crosslinked with 1 mole % EGDMA are 42° (w) and 37% (w) respectively. This effect of membrane hydration is contained in the slope of the plots given in Fig. 1. It is apparent that as the membrane hydration is increased, Dm is less sensitive to changes in the size of the permeating solute. 

Mass per unit length (2340 daltons/A) and the cross-sectional radius of gyration (30 A) of the polymers are independent of size, as expected for a linear mode of polymerization 106). 

Inductance is measured in henries per meter in the m.k.s. system of units Tq is the cross-section radius. 

In accord with eq. 4.207, the self-inductance Lq tends to infinity as Tq —> 0. Of course, under real conditions the cross-section radius, Tq, is not zero and correspondingly the self-inductance, Lq, has a finite value. 

For implantable reservoir devices, a cylindrical geometry is often more practical than a planar arrangement. Consider a cylindrical reservoir surrounded by a polymeric membrane (Figure 9.2c) the cylinder has a length L, cross-sectional radius b, and wall thickness b — a.ln practice, the rate of drug release from this cylinder can be modified by changing the geometry of the device (by... 

Figure 9.5 Drug release from a cylindrical-reservoir drug delivery system. The cumulative mass of drug released is plotted versus time for cylindrical-reservoir devices with a range of physical characteristics, which are determined principally by the diffusion coefficient for the drug in the polymer and the membrane thickness. In all cases, the overall length of the device, L, and the cross-sectional radius, b, were fixed at 2.7 and 0.5 cm, respectively. In each panel, one of the relevant design parameters was varied (a) hja was varied between 1.2 and 4 with Dj.p = 1x10" and Cl = 20mg/mL (b) Dj.p was varied (for curve A, Dj.p = 5 x 10 cm /s ...

Hexane, the least spherical molecule in the list, behaves as if its molar volume is much less, in fact more closely equivalent to the volume corresponding to the axial radius. For more general purposes, a more elaborate treatment might therefore recast Eq. (25) in terms of a solvent radius parameter rather than Vs, where a cross-sectional radius is more appropriate for elongated shapes. 

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