Particle Velocity Gauges

The P-t histories illustrated by Fig. 2.9 are not histories of a particle of material moving with the flow, because the coordinate that is fixed is x, and material is flowing past it. A more useful P-t history would use a coordinate system which is attached to the material itself, as a stress or particle velocity gauge would be. Such a coordinate system is defined in the next section. 

The objective in these gauges is to measure the time-resolved material (particle) velocity in a specimen subjected to shock loading. In many cases, especially at lower impact pressures, the impact shock is unstable and breaks up into two or more shocks, or partially or wholly degrades into a longer risetime stress wave as opposed to a single shock wave. Time-resolved particle velocity gauges are one means by which the actual profile of the propagating wave front can be accurately measured. 

Measurements from stress gauges, assuming equal accuracy and time resolution, are equivalent to measurements from particle velocity gauges in exploring a material s equation of state. Both piezoresistive and piezoelectric techniques have been used extensively in shock-compression science. 

The experimental methods for the determination of the detonation wave parameters can be classified into two groups. The first, the so-called internal methods group, includes the methods by which detonation parameters are directly determined. These are the determination of the mass velocity of the detonation products by the electromagnetic particle velocity gauge method, direct determination of the detonation pressure by a manganin pressure gauge, determination of the mass velocity of the detonation products by the flash X-ray technique, etc. The time resolution of these methods can be on a nanoseconds scale, which is still not sufficient for fully reliable study of a very narrow chemical reactions zone, and in particular, of a shock wave front. 

Determination of the Detonation Parameters Using the Electromagnetic Particle Velocity Gauge Technique... 

When the detonation wave reaches the particle velocity gauge, the gauge moves forward at a velocity equal to the velocity of detonation product particles behind the detonation wave front. It is consictered that, due to the small size of the gauge, its velocity becomes equal to the velocity of the detonation products in less than 0.1 ps. This means that the method enables registration of the state of the detonation wave in 0.1 ps behind the shock front. Therefore, it is to be expected that the method might be used in the study of detonation wave structure. 

Leiper, G.A., Kirby, I.J., and Hackett, A. Determination of Reaction Rates in Intermolecular Explosives Using the Electromagnetic Particle Velocity Gauge, Proc. 8th Symposium (International) on Detonation, NSWC MP 86-194, Albuquerque, NM, 1985, pp. 187-195. 

The development of devices that provide a direct measure of stress or particle velocity led to observations of new rate-dependent mechanical responses and showed the power of such time-resolved measurements. The quartz gauge was the first of these devices with nanosecond time resolution, but its upper operating limit of 4 GPa limited its application. The development of the VISAR has had the most substantial impact on capabilities. VISAR systems, with time-resolution approaching 1 ns and the ability to work to pressures of 100 GPa, provide capabilities that have substantially altered the scientific descriptions of shock-compressed matter. 

For detonation modeling, the first term again reacts a quantity of explosive less than or equal to the void volume after the explosive is compressed to the unreacted von Neumarm spike state. The second term in Eq. (2) models the fast decomposition of the solid into stable reaction product gases (CO2, H2O, N2, CO, etc.). The third term describes the relatively slow diffusion limited formation of solid carbon (amorphous, diamond, or graphite) as chemical and thermodynamic equilibrium at the C-J state is approached. These reaction zone stages have been observed experimentally using embedded particle velocity and pressure gauges and laser interferometry [57,61-63]. 

The equation is written in velocity gauge. Atomic units are used. The particle has charge unity and mass m in units of the free electron mass. V is the constant potential energy appropriate for the interval under consideration. The vector potential is supposed to be spatially constant at the length scale of the structure. With such a vector potential, the A2 term contributes an irrelevant phase factor which can be omitted. For a one-mode field A(t) is written as Ao cos(ut). The associated electric field is 0 sin(ut), with 0 = uAq. px is the linear momentum i ld/dx. For such a time-periodic Hamiltonian, a scattering approach can be developped, with a well-defined initial energy, and time-independent transition probabilities for reflection and transmission. 

When the detonation wave reaches the gauge, the gauge will be moved forward at the surrounding particles velocity, cutting the magnetic field. 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

The Reynolds number Re = vl/v, where v and l are the characteristic velocity and length for the problem, respectively, gauges the relative importance of inertial and viscous forces in the system. Insight into the nature of the Reynolds number for a spherical particle with radius l in a flow with velocity v may be obtained by expressing it in terms of the Stokes time, t5 = i/v, and the kinematic time, xv = l2/v. We have Re = xv/xs. The Stokes time measures the time it takes a particle to move a distance equal to its radius while the kinematic time measures the time it takes momentum to diffuse over... 

Mechanical vacuum gauges measure the pressure directly by recording the force which the particles (molecules and atoms) in a gas-filled space exert on a surface by virtue of their thermal velocity. 

In thermodynamics, the observer is outside the system and properties are measured in the surroundings. For example, pressure is measured by an external observer reading a pressure gauge on the system. Volume can be determined by measuring the dimensions of the system and calculating the volume or, in the case of complex shapes, by using the system to displace a liquid from a filled container. Important thermodynamic properties have low information content (i.e., they can be expressed by relatively few numbers). The details of the shape of a system are usually not important in thermodynamics, except, sometimes, a characteristic of the shape, such as the surface-to-volume ratio, or radii of particles, may also be considered. Information only accessible to an observer within the system, such as the positions and velocities of the molecules, is not considered in thermodynamics. However, in Chapter 5 on statistical mechanics, we will learn how suitable averages of such microscopic properties determine the variables we study in thermodynamics. 

Expressing w in lbs per sq ft, t in min, and v in ft per min, Williams et al determined the constant K for a number of dusts of different diameters. These are given in Table 84. The constant Kf may be termed the specific resistance and is expressed as in. water gauge per lb dust per sq ft filter area per lineal ft per min filtering velocity. The data contained in this table show that the resistance coefficient (1) increases with decreasing particle-size, and (2) does not vary greatly among several materials when compared at equivalent sizes. These facts are quite clear from Eq (21-5) since h varies inversely as d2. 

CSIRO Minerals has developed a particle size analyzer (UltraPS) based on ultrasonic attenuation and velocity spectrometry for particle size determination [269]. A gamma-ray transmission gauge corrects for variations in the density of the slurry. UltraPS is applicable to the measurement of particles in the size range 0.1 to 1000 pm in highly concentrated slurries without dilution. The method involves making measurements of the transit time (and hence velocity) and amplitude (attenuation) of pulsed multiple frequency ultrasonic waves that have passed through a concentrated slurry. From the measured ultrasonic velocity and attenuation particle size can be inferred either by using mathematical inversion techniques to provide a full size distribution or by correlation of the data with particle size cut points determined by laboratory analyses to provide a calibration equation. 

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