Characteristic Size

A liquid is normally contained in a solid vessel with vertical walls. The surface of the liquid is horizontal because of gravity, except near the walls where Young s relation [equation (1.23)] induces a distortion. When the 

The shape of the meniscus is determined by the equilibrium between the capillary forces (responsible for the curvature) and gravity forces (which oppose it). One can invoke the following pressure argument Immediately underneath the surface, Laplace s pressure [equation (1.6)] is equal to the hydrostatic pressure. This can be written as 

As a general rule, the characteristic size of a meniscus is either the capillary length or the size I of the vessel itself, whichever is smaller. 

FIGURE 2.12. Meniscus in a glass of water in reduced gravity. 

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We consider the motion of a large particle in a fluid composed of lighter, smaller particles. We also suppose that the mean free path of the particles in the fluid, X, is much smaller than a characteristic size, R, of the large particle. The analysis of the motion of the large particle is based upon a method due to Langevin. Consider the equation of motion of the large particle. We write it in the fonn... 

The coefficient of variation (cp) of a distribution is a measure of the spread of the distribution about some characteristic size. It is often used in conjunction with dominant size to characterize crystal populations through the equation... 

The data used to generate the maps is taken from a simple statistical analysis of the manufacturing process and is based on an assumption that the result will follow a Normal distribution. A number of component characteristics (for example, a length or diameter) are measured and the achievable tolerance at different conformance levels is calculated. This is repeated at different characteristic sizes to build up a relationship between the characteristic dimension and achievable tolerance for the manufacture process. Both the material and geometry of the component to be manufactured are considered to be ideal, that is, the material properties are in specification, and there are no geometric features that create excessive variability or which are on the limit of processing feasibility. Standard practices should be used when manufacturing the test components and it is recommended that a number of different operators contribute to the results. 

The effect of exhaust performance on room air movement is limited compared to the effect produced by air jets. The distance from the opening to the point where air velocity drops to 10% of the initial velocity value (Fig. 7.14) is approximately equal to one characteristic si2e of the exhaust opening (D for the round duct) and 60 characteristic sizes for the supply outlet (60D for the round nozzle). 

An ideal particle moves relative to the fluid with velocity, v, dependent on just four quantities viz. fluid viscosity and density p and p respectively (i.e. fluid properties), and particle solid density and characteristic size ps and d respectively (i.e. particle characteristics), subject to the forces of buoyancy and friction, as illustrated in Figure 2.1. 

Generally, accidental emissions take place close to the earth s surface. The scale of the turbulence in the surface layer is limited by the distance to the earth s surface, so the characteristic size of the large-scale turbulence decreases towards the surface. Therefore, some degree of homogeneity in a vapor cloud is first to be expected in a thin layer adjacent to the ground (Wilson et al. 1982b). The thickness of this layer will increase as the vertical dimension of the cloud grows. 

In situations where the surrounding fluid behaves as a non-continuum fluid, for example at very high temperatures and/or at low pressures, it is possible for Nu to be less than 2. A gas begins to exhibit non-continuum behaviour when the mean free path between collisions of gas molecules or atoms with each other is greater than about 1/100 of the characteristic size of the surface considered. The molecules or atoms are then sufficiently far apart on average for the gas to begin to lose the character of a homogeneous or continuum fluid which is normally assumed in the majority of heat transfer or fluid... 

Since every atom extends to an unlimited distance, it is evident that no single characteristic size can be assigned to it. Instead, the apparent atomic radius will depend upon the physical property concerned, and will differ for different properties. In this paper we shall derive a set of ionic radii for use in crystals composed of ions which exert only a small deforming force on each other. The application of these radii in the interpretation of the observed crystal structures will be shown, and an at- Fig. 1.—The eigenfunction J mo, the electron den-tempt made to account for sity p = 100, and the electron distribution function the formation and stability D = for the lowest state of the hydr°sen of the various structures. 

AP is the pressure drop on a channel length L, d is the characteristic size. 

Shape of micro-channel Characteristic size Constant in Eqs. (3.2), (3.3)... 

Side of a equilateral triangle Ratio of Poexp/Poth eor specific heat Diameter Characteristic size Activation energy... 

Rdf The characteristic size of the TiCi s, dy, is reduced by 45%. The 3-hr. yield is thereby increased by 53%, a very significant benefit to the process. Methods to achieve this kind of change are well worth investigation. 

Minimum scale, L>7X, where L is a general characteristic size defined as i - where... 

The geometrical data and characteristic sizes of the HEX reactor studied in our lab are described in Table 12.2. 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

Neutron scattering has been used for studying the state of solvation of ions in aqueous solution (Enderby et al., 1987 Salmon, Neilson Enderby, 1988). These studies have shown that a distinct shell of water molecules of characteristic size surrounds each ion in solution. This immediate hydration shell was called zone A by Frank Wen (1957) they also postulated the existence of a zone B, an outer sphere of molecules, less firmly attached, but forming part of the hydration layer around a given ion. The evidence for the existence of zone B lies in the thermodynamics of... 

Departures of the electrokinetic behavior of real systems from that described by the equations reported occurs most often because of breakdown of two of the assumptions above because of marked surface conductivity (particularly in dilute solutions, where the bulk conductivity is low) and because of a small characteristic size of the disperse-phase elements (e.g., breakdown of the condition of bg <5 r in extremely fine-porous diaphragms). A number of more complicated equations allowing for these factors have been proposed. 

Physical properties of metal nanoparticles show characteristic size-dependent changes as their size increases from the limit of isolated atoms towards macroscopic dimensions. 

In order to verify the conditions of this averaging process, one has to relate the displacements during the encoding time - the interval A between two gradient pulses, set to typically 250 ms in these experiments - with the characteristic sizes of the system. Even in the bulk state with a diffusion coefficient D0, the root mean square (rms) displacement of n-heptane or, indeed, any liquid does not exceed several 10 5 m (given that = 2D0 A). This is much smaller than the smallest pellet diameter of 1.5 mm, so that intraparticle diffusion determines the measured diffusion coefficient (see Chapter 3.1). This intrapartide diffusion is hindered by the obstades of the pore structure and is thus reduced relative to D0 the ratio between the measured and the bulk diffusion coeffident is called the tortuosity x. More predsely, the tortuosity r is defined as the ratio of the mean-squared displacements in the bulk and inside the pore space over identical times ... 

S = characteristic size parameter, in the units given in Table 6.2,... 

Regime-IV flow patterns are of pragmatic interest when interphase heat and mass transfer are of key importance because the existence of the discrete phase generates a large interfacial area per unit tube volume. Evaluation of the interfacial area is made difficult because the bubbles or drops of the discrete phase are usually not of uniform size or shape. By assuming a characteristic size and shape for the drops or bubbles, the interfacial area and the other parameters can be estimated with reasonable accuracy for many situations. 

Spores may be spherical, ellipsoidal, or cylindrical in shape. The position of the spore in a cell may be central, subterminal, or terminal. A fully grown spore may have a diameter greater than that of the vegetative cell. This causes a bulging of the cell. The resulting forms are known as Clostridium if central, and plectridium if terminal. As a rule, each species has its own characteristic size, shape, and position of the spore, but this is subject to variation under different environmental conditions. 

Chromosome Individual chapter of the recipe book in humans there are 23 pairs of chromosomes (which are made of DNA) we can recognise which pair an individual chromosome belongs to by its characteristic size and shape. 

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