Aspect ratios definitions

The above definition is more examples of fibers than a definition of a fiber. It supports the fact that not only is asbestos difficult to define, but fibers themselves are also difficult to define, for other reasons. Hopefully, a better definition can be based upon aspect ratio. Aspect ratio is defined as a ratio of the length of an object to its diameter. A fiber can be defined arbitrarily as an object with an aspect ratio of 10 or greater. (Some choose to define a fiber as any object with an aspect ratio of three or greater." By this definition most crystalline substances are fibers.) One deficiency of a definition based upon an aspect ratio of 10 or more is that no maximum diameter is specified. Therefore, a fence post, a utility pole, a railroad rail, a longboat, are all fibers by an aspect ratio definition. This does not serve our needs for a definition. Few readers will agree that a railroad rail is a fiber or that an elephant s rib is a phosphate fiber. In fact, an elephant s rib is a calcium phosphate fiber, albeit a large one. 

Electrochemistry provides routes to directly prepare nanostructures both delocalized in a random or organized way and localized at predefined surface sites with adjustable aspect ratios. Purity, monodispersity, ligation, and other chemical properties and treatments are definitely important in most cases. By delocalized electrodeposition it is possible to decorate large areas of metal or semiconductor surfaces with structures of a narrow size distribution stable nuclei-clusters can be... 

CNTs may consist of just one layer (i.e. single-walled carbon nanotubes, SWCNTs), two layers (DWCNTs) or many layers (MWCNTs) and per definition exhibit diameters in the range of 0.7 < d < 2 nm, 1 < d < 3 nm, and 1. 4 < d < 150 nm, respectively. The length of CNTs depends on the synthesis technique used (Section 1.1.4) and can vary from a few microns to a current world record of a few cm [16]. This amounts to aspect ratios (i.e. length/diameter) of up to 107, which are considerably larger than those of high-performance polyethylene (PE, Dyneema). The aspect ratio is a crucial parameter, since it affects, for example, the electrical and mechanical properties of CNT-containing nanocomposites. 

This review focuses on nanoparticles, namely objects that are roughly spherical. We use the commonly accepted definition for nanoscale objects of having a dimension below 100 nm, and so identify nanoparticles as objects with a diameter of 100 nm or smaller. The review does not focus on larger aspect ratio nanoscale materials such as nanotubes and nanorods, though they are mentioned in some cases. 

M 14] [P 14] Splitting of droplets can only occur at aspect ratios <0.2 (for definition see Effect of aspect ratio) [29]. Since this is an important microfluidic action, it was worth finding suitable novel mixing strategies to overcome this limitation. 

Show that Eqs. 5.20 and 5.21 can be derived from Eq. 5.17 and the definition of aerodynamic diameter. In this derivation, assume that the aspect ratio is sufficiently large that... 

We first define some terms commonly used in the field of fibrous materials. We should add that some of these definitions are expanded upon later in this chapter. However, before one can define the term fiber, one needs to define the most important attribute of the fiber that serves to define a fiber, namely the fiber aspect ratio. The aspect ratio of a fiber is the ratio of its length to diameter (or thickness). A fiber can be defined as an elongated material having a more or less uniform diameter or thickness less than 250 p,m and an aspect ratio greater than 100. This is an operational definition of fiber. It is also a purely geometrical one in that it applies to any material. Having defined the basic unit, the fiber, we are now in a position to define some other commonly used terms related to fibers. These are given below in alphabetical order ... 

Should the U.S. regulatory definition of an asbestos fiber (length 5 m with aspect ratio 3 1), establishedfor purposes of quantifying exposure levels, be changed ... 

This definition is suitable for axisymmetric droplet shapes or for small deformations. The aspect ratio of the droplet is then L/B = (1- -D)/(1 — D). 

To estimate which occurs in the definition of Eod an empirical correlation of the aspect ratio E for spheroidal bubbles in a contaminated system was used ... 

There is some doubt about the relevance of aspect ratio considered in isolation and as applied just to the empirically identified rigid mesogen. It can only really be applied to in-chain (or nematic unidirectional phases) but this is not applicable to discotic phases [61]. The examples quoted above also make it clear that flexible elements can be included in the mesogen. Strict definition of the mesogen is therefore difficult. 

Between the definite regimes of laminar and turbulent flow there is a transitional Re range. The exact values of this number range are a function of many parameters, such as channel shape, surface roughness, and aspect ratio. The transition Re is generally expected to be in the range of 1,500 and 2,500 for most situations [39]. For microfluidic systems. Re are typically smaller than 100 and the flow is considered essentially laminar. This characteristic has a direct consequence on mixing within microfluidic devices. 

These nanomaterials are also characterized by their extremely high aspect ratio. The aspect ratio is defined as the length of the major axis divided by the width or diameter of the minor axis. According to this definition, spheres have an aspect ratio of 1, while carbon nanotubes or nanofibers have an aspect raho ranging from... 

Before discussing the flow behavior of polymeric nanocomposites (PNCs), the nature of these materials should be outlined. As the name indicates, PNCs must contain at least two components, a polymeric matrix with dispersed nanoparticles [Utracki, 2004]. PNCs with thermoplastics, thermosets, and elastomers have been produced. The nanoparticles, by lUPAC s definition, must have at least one dimension that is not larger than 2 nm. They can be of any shape, but the most common for structural PNCs are sheets about 1 nm thick with the aspect ratio p=D/t= 20 to 6000, where D is the inscribed (or equivalent) diameter and t is the thickness of the sheet. These inorganic lamellar solids might be either natural or synthetic [Utracki et al., 2007]. 

For ellipsoids of rotation, the aspect ratio is frequently defined as a ratio of the major to minor axes p = ai/a2 (i.e., for prolate ellipsoids, p > 1, and for oblate ellipsoids, p oblate ellipsoids provided that their aspect ratio is, respectively, p and Up [Goldsmith and Mason, 1967], Such symmetry is not observed for [ ], as the flow is affected differently by rods than by platelets. Thus, a customary definition of the aspect ratio is used in this chapter, p being defined as the ratio of the largest to the smallest dimension that is, for rods, p = length/diameter, and for disks, p = diameter/thickness, so for both geometries, p>. ... 

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