Particles prolate

Uniaxial deformations give prolate (needle-shaped) ellipsoids, and biaxial deformations give oblate (disc-shaped) ellipsoids [220,221], Prolate particles can be thought of as a conceptual bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently used for this purpose in thermoplastics and thermosets. Similarly, oblate particles can be considered as analogues of the much-studied clay platelets used to reinforce a variety of materials [70-73], but with dimensions that are controllable. In the case of non-spherical particles, their orientations are also of considerable importance. One interest here is the anisotropic reinforcements such particles provide, and there have been simulations to better understand the mechanical properties of such composites [86,222],... 

As a general guide, is usually less than C2 for a prolate particle, so that 6 < cj) and the direction of motion is between the axis and the vertical. On the other hand, an oblate body usually has > C2 so that the direction of fall is between the vertical and the equator. The settling velocity follows from Eq. (4-9) ... 

In a well-known paper Kuhn and Kuhn (759) have shown that the intrinsic viscosity of rigid prolate particles always consists of two parts ... 

It is important to note that the form effect is proportional to the square of the dielectric contrast, Ae, and will always be positive for prolate particles (Ll > L2), and negative for oblate shapes (L2 > Lx). The intrinsic contribution can change sign depending on the relative magnitudes of the principal values of the polarizability tensor of the particle. 

Figure 20. Calculated X-ray scattering patterns for various types and sizes of Pt nanocrystallites. Top left 3.5 nm (a) sphalerite (b) wurtzite (c) wurtzite with one stacking fault (d) experimental powder spectmm with ca. 3.5.nm avg. crystallites. Top right Experimental powder diffraction pattern of ca. 8.0 nm crystallites (dotted line) compared to (a) spherical and (b) prolate particles (solid line) Center (a) progression of habits of cuboctahedral shapes of nanocrystals, (b) change in shape as 111 faces increase and 100 decrease, (c) decahedron and icosahedron multiply twiimed forms. Bottom left to right three successive sizes of cuboctahedral nanociystallites three successive sizes of decahedral nanociystallites three successive sizes of icosahedral nanocrystallites. From Zanchet et al. (2000), used with permission of Wiley-VCH.

Let us consider diffusion to the surface of a circular cylinder of radius a in a flow with velocity Ui directed along the normal to the cylinder axis. This is a model problem used in chemical engineering for calculating mass transfer to prolate particles it is used even more widely in mechanics of aerosols for analyzing diffusion sedimentation of aerosols on fibrous filters [139,461]. 

To test the effectiveness of applying this procednre in practice, experiments were again performed with hematite prolate particles with major/minor axes 220nm and 60nm respectively, giving an aspect ratio of r ... 

A rodlike (highly prolate) particle is assumed to reorient in the same way. For disklike particles, the reorientation of a plane is considered... 

Simulations have also been carried out on ellipsoidal particles such as the polystyrene prolate and oblate ellipsoids. For example, oriented prolate particles showed that the anisotropy causes the modulus in the longitudinal direction to be significantly higher in the transverse direction. 

Sharaf, M. A. Kloczkowski, A. Mark, J. E., Monte Carlo Simulations on Reinforcement of an Elastomer by Oriented Prolate Particles. Comput. Jheor. Polym. Sci. 2001,11, 251-262. 

The streaming birefringence exhibits saturation effects when the extinction angle x approaches zero as the particles are as much as possible oriented in the flow direction. But the orientation is dynamic as the prolate particles possess the slowest rotational velocity in the flow direction. Hence they remain for a much... 

Particle shape is another important parameter affecting heat transfer. Recently, the effect of particle shape on ETC has been examined (Gan, 2015). Here, ellipsoids are used as they can represent a wide range ofparticle shapes from platy to elongate. Interestingly, the shape can be described by one parameter called as aspect ratio. Aspect ratio is less than 1.0 for oblate, equal to 1.0 for spherical, and larger than 1.0 for prolate particles. 

Wen et al. reviewed the two common approaches to bipolar charging of spherical particles the Boltzmann charge distribution and the steady-state ion diffusion flux toward a sphere [30-33]. Using these approaches, an equivalent charge diameter was introduced to extend the use of these approaches to include prolate particles. The equivalent charge diameter is defined as... 

For the prolate particles considered in our simulations, the sources are distributed on the axis of symmetry as in Fig. 3.12, while for the oblate particles, the sources are distributed in the complex plane as in Fig. 3.13. The wavelength of the incident radiation is A = 0.6328 pm, the relative refractive index... 

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