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Bending surface

In order to estimate the extent of decrease in the particle velocity due to the pipe curvature, it is assumed that the drag force is negligible in comparison with the sliding force of the particle on the bend surface. With this consideration, Eq. (11.51) is reduced to... [Pg.482]

M. Green, Semiconductor Electrochemistry, in Modern Aspects of Electrochemistry, J. O M. Bockris and B. E. Conway, eds., Vol. 2, Ch. 2, Plenum, New York (1959). First formulation of semiconductor electrode kinetics in terms of equations band bending surface states limiting currents. [Pg.70]

Figure 6.1 Schematic cross-section through monolayer of amphiphilic molecules consisting of polar head (solid dot) and hydrocarbon chain. (PCs, PEs and DGDGs are two-chain molecules with zwitterionic polar heads.) The thickness of the monolayer h, as well as the positions of the neutral surface z , and the actual bending surface, Z, are indicated in the flat state for co < 0 (see text). The sign of curvature is defined by the lower diagram. Figure 6.1 Schematic cross-section through monolayer of amphiphilic molecules consisting of polar head (solid dot) and hydrocarbon chain. (PCs, PEs and DGDGs are two-chain molecules with zwitterionic polar heads.) The thickness of the monolayer h, as well as the positions of the neutral surface z , and the actual bending surface, Z, are indicated in the flat state for co < 0 (see text). The sign of curvature is defined by the lower diagram.
In general, it is sufficient to know that there is a surface in the monolayer for which stretching and bending deformations are in effect decoupled. This will be the classical neutral surface (for Cq = 0) or a new surface of equal molecular density at a slightly shifted position (for Cq 0). In the latter case, nonunifoim curvature c, + C2 is associated with an inherent lateral tension that is proportional to it Henceforth, the term bending surface is used in both cases. [Pg.58]

Th bending surface of the bilayer is its middle surface, the total... [Pg.58]

C2 vanishes for the bilayer because of C2 = —Cj. However, it does not vanish for the bending surfaces of the monolayers. For the outer monolayer,... [Pg.60]

This section concludes with a few words on bilayers that are asymmetric because their monolayers consist of different molecules. In such cases a reasonable choice of the bilayer bending surface may be the middle between the monolayer bending surfaces. It ensures that bilayer bending without stretching conserves the sum of the monolayer bending surface areas for arbitrary cylindrical curvature. The bending rigidity and the spontaneous curvature of the bilayer may be expected to obey... [Pg.61]

Any dilation of the bilayer bending surface due to Gaussian curvature is proportional to C C2 and therefore does not affect Hookean elasticity. Substituting (z - z ) +Zj, for z in eq. (30) leads to... [Pg.63]

Later studies by Mills and Mason (1977) considered the effect of particle concentration on erosion in bends. It was found by these investigators that the effect of particle concentration on erosion is slight, however, the depth of penetration of the particles into the bend surface material increases significantly with increase in particle concentration. The specific erosion measured as the mass of material eroded from the bend per unit mass of product conveyed is related to the solids loading as... [Pg.120]

A. N. Shalaginov, Influence of the liquid crystal splay-bend surface elastic constant on director fluctuations and light scattering, Phys. Rev. E1994, 2472-2475. [Pg.1179]

The effect of surface elastic constants on the nematic director configurations is of basic interest for the elastic theory of liquid crystals and plays a critical role in those device applications where the nematic is confined to a curved geometry. The saddle-splay surface elastic constant, K24, and the splay-bend surface elastic constant, K13, defied measurement for more than sixty years, since the pioneering work of Oseen, who made the first steps toward the elastic theory of liquid crystals. [Pg.179]

Measurements of the saddle-splay surface elastic constant, K24, and the splay-bend surface elastic constant, K13, were first introduced by Oseen [1] in 1933 from a phenomenological viewpoint, and later by Nehring and Saupe [2] from a molecular standpoint. These constants tend to be neglected in conventional elastic continuum treatments for fixed boundary conditions because they do not ent the Euler-Lagrange equation for bulk equilibrium. Experimental determination of tiie two surface elastic constants is undoubtedly a difficult task, since their effects are hard to discriminate from those of ordinary sur ce anchoring [3]. [Pg.179]

H e Ki, K2 and K3 correspond to the splay, twist, and bend bulk elastic constants, respectively. Further, the terms K24 and K13, known as the saddle-splay surface elastic constant and mixed splay-bend surface elastic c( istant, respectively, are called surface elastic constants because they enter EQN (3) as divergences of a volume integral, which are converted to surface integrals via Green s theorem. It should be noted that the second derivative of the K24 term in EQN (3) is apparent however, this is... [Pg.180]

If we put point forces to the plate by, for example, attaching lead weights at the prescribed nodes, the plate will be deformed into a bending surface. The corresponding physical model is described by the potential energy U of the deformed plate which is a quadratic homogeneous function of the reciprocal curvature [16]. If we approximate the reciprocal curvature by derivatives of second order, we arrive at the mathematical model... [Pg.390]


See other pages where Bending surface is mentioned: [Pg.1036]    [Pg.365]    [Pg.71]    [Pg.310]    [Pg.416]    [Pg.97]    [Pg.420]    [Pg.327]    [Pg.1065]    [Pg.6]    [Pg.471]    [Pg.60]    [Pg.63]    [Pg.468]   
See also in sourсe #XX -- [ Pg.58 , Pg.60 ]




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Band bending surface dipoles

Band bending surface states

Bending motions: potential surfaces

Bending surface tensions

Potential energy surface bending

Splay-bend surface elastic constant

Surface States and Band Bending

Surface Steps, Defects, Band Bending

Surface bending energy

Surface fluctuations bending

Surfaces band bending

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