Penetration distances

In the breakup regime, spray characteristics include film angle, film velocity and thickness, breakup length, breakup rate, surface wave frequency, wavelength, growth rate, and penetration distance. These quantities, however, are extremely difficult to measure on account of the very small size and rapidly changing features of disintegrating Hquid jets or films. 

Two particular test methods have become very widely used. They are the Vicat softening point test (VSP test) and the heat deflection temperature under load test (HDT test) (which is also widely known by the earlier name of heat distortion temperature test). In the Vicat test a sample of the plastics material is heated at a specified rate of temperature increase and the temperature is noted at which a needle of specified dimensions indents into the material a specified distance under a specified load. In the most common method (method A) a load of ION is used, the needle indentor has a cross-sectional area of 1 mm, the specified penetration distance is 1 mm and the rate of temperature rise is 50°C per hour. For details see the relevant standards (ISO 306 BS 2782 method 120 ASTM D1525 and DIN 53460). (ISO 306 describes two methods, method A with a load of ION and method B with a load of SON, each with two possible rates of temperature rise, 50°C/h and 120°C/h. This results in ISO values quoted as A50, A120, B50 or B120. Many of the results quoted in this book predate the ISO standard and unless otherwise stated may be assumed to correspond to A50.)... 

This discussion of geometric effects ignored the attenuation of radiation by material through which the radiation must travel to reach the receptor. The number of particles, dN, penetrating material, equals the number of particles incident N times a small penetration distance, dx, divided by the mean free path length of the type of particle in the type of material (equation 8.3-8). Integrating gives the transmission coefficient for the radiation (equation 8.3-9). 

In long rooms, i.e., where the room is slightly longer than the penetrating distance of the supply jet, the best location of the exhaust is opposite to the air supply opening. See Fig. 8.41. 

Penetrant activity 191 Penetration distance of indenter 120 Phase transformation 126... 

Depth of EB penetration The depth of penetration of energetic electrons into a material at normal angle of incidence is directly proportional to the energy of the electrons and inversely proportional to the density of the material [49,50]. The depth is expressed as a product of penetration distance and the density of the material (i.e., 1 g/cm = 1 cm X 1 g/cm ). The radiation energy and thus the type of electron accelerator to be used are dependent on the required penetration depth, the density of the irradiated material, and the chosen irradiation system. If one measures the density (d) in gram per cubic centimeter (g/cm ) and the layer thickness (T) in millimeter (mm), one can determine the radiation energy ( ) necessary for optimal homogeneity from [40] ... 

Diffusion and reaction takes place within a bead of volume 7t Rp- and area 4 71 Rp2. It is of interest to find the penetration distance of oxygen for given specific activities and aggregate diameters. The system is modelled by taking small spherical shell increments of volumes 4/3 (rn -rn 3). The outside area... 

Parameter estimation 112 Partial differential equation 578 Partial differentials 154 Peclet number 243, 579 Penetration distance 654 Perfect mixing 159 Perfectly mixed 142... 

Consider Fig. 4.32, a graph of flame velocity 5L as a function of distance, for a wave inside a tube. In this case, the flame has entered the tube. The distance from the burner wall is called the penetration distance dv (half the quenching diameter dT). If iij is the mean velocity of the gas flow in the tube and the line labeled (7, is the graph of the velocity profile near the tube wall, the local flame velocity is not greater than the local gas velocity at any point therefore, any flame that finds itself inside the tube will then blow out of the tube. At a lower velocity u2, which is just tangent to the SL curve, a stable point is reached. Then u2 is the minimum mean velocity before flashback occurs. The line for the mean velocity % indicates a region where the flame speed is greater than the velocity in the tube represented by in this case,... 

Most experimental data on flashback are plotted as a function of the average flashback velocity, navF, as shown in Fig. 4.34. It is possible to estimate penetration distance (quenching thickness) from the burner wall in graphs such as Fig. 4.34 by observing the cut-off radius for each mixture. 

Bouguer-Lambert-Beer law analy chem The intensity of a beam of monochromatic radiation in an absorbing medium decreases exponentially with penetration distance. Also known as Beer-Lambert-Bouguer law Lambert-Beer law. bCi ger lam bert ber, 16 ... 

The physical meaning of Equation (17) is simply this if the specific rate constant goes up, say nine times, because of an increase of temperature, the concentration profile must be steeper in order to diffuse in the extra amount of reactant gas. Consequently, the penetration into the carbon decreases. Obviously, equilibrium is reached when the concentration gradient increa.scs threefold, the penetration distance decreases threefold, and the over-all reaction rate (proportional to fc times penetration distance) increases threefold, where 3, in this example, is the square root of the factor of specific-rate-constant increase. For these conditions, the over-all reaction rate has increased threefold, but so has the diffusion gradient that is, equilibrium has been reached. 

As in Eq. 18-23 we can define a penetration distance. Now there is a loss penetration on one side of the boundary which is compensated for by the corresponding gain penetration on the other side of the boundary. Again, the penetration proceeds with a speed which is proportional to (Dt)1/2. We can also ask how much of the compound has crossed the interface at time t. In Fig. 18.5e this quantity is represented for time 6 by the hatched areas on either side of the boundary. The loss from system B corresponds to the gain of system A. By analogy to Eq. 18-25 the exchanged mass is given by ... 

The time scale xB determines the penetration distance in system A beyond which the influence of the variation of C can be disregarded. For instance, we can use the concept of half-concentration depth (Eq. 18-23) as a measure to assess the penetration distance of the time-dependent variation into system A. Thus ... 

A rough estimate of the diffusion penetration distance from a point source is the location where the concentration has fallen off by as 1/e of the concentration at x = 0. This occurs when... 

To estimate the time at which steady-state conditions are expected, the required penetration distance is set equal to the largest characteristic length over which diffusion can take place in the system. If L is the characteristic linear dimension of a body, steady state may be expected to apply at times r L2/Dmm, where Dmin is the smallest value of the diffusivity in the body. Of course, there are many physical situations where steady-state conditions will never arise, such as when the boundary conditions are time dependent or the system is infinite or semi-infinite. 

Figure 9.8 Isolated-boundary (Type-B) self-diffusion associated with a stationary grain boundary, (a) Grain boundary of width 6 extending downward from the free surface at y = 0. The surface feeds tracer atoms into the grain boundary and maintains the diffusant concentration at the grain boundary s intersection with the surface at the value cB(y = 0, t) = 1. Diffusant penetrates the boundary along y and simultaneously diffuses transversely into the grain interiors along x. (b) Diffusant distribution as a function of scaled transverse distance, xi, from the boundary at scaled depth, yx, from the surface. Penetration distance in grains is assumed large relative to 5.

TABLE 22.4 1 Some Properties of Ionizing Radiation Energy Range Penetrating Distance in Water... 

Where is the penetration distance and n is evaluated from equation 6. 

E2) is the average of the squared amplitude of the electric vector at distance x inside the solution, (E0) is the vector s value when x = 0, i.e. at the interface, and 8 the penetration distance. This is the evanescent wave, which exists in solution and interacts with species that adsorb in that region of small thickness. Absorbance measurements can give the concentration of an electroactive species, and if the process is transient, determine the development of the concentration profile at the electrode surface. The radiation can be visible or, for adsorbed species, in the IR region. 

In other words, the recombination width constitutes the double penetration distance of the electron current into the overlap region. Inserting appropriate expressions for the shallow-trap SCL current density, j = (9/8)s0E(pe +Pid /d (cf. Sec. 4.3.1), and yeh (4), we arrive at... 

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