Shock front, described

We assume that in (4.38) and (4.39), all velocities are measured with respect to the same coordinate system (at rest in the laboratory) and the particle velocity is normal to the shock front. When a plane shock wave propagates from one material into another the pressure (stress) and particle velocity across the interface are continuous. Therefore, the pressure-particle velocity plane representation proves a convenient framework from which to describe the plane Impact of a gun- or explosive-accelerated flyer plate with a sample target. Also of importance (and discussed below) is the interaction of plane shock waves with a free surface or higher- or lower-impedance media. 

Physically speaking, shock waves are compaction waves with a vertical shock front, which occur in supersonic fluxes or as described above the pressure reaches a maximum value and then falls rapidly towards zero. Shock waves can also occur in space, which is almost free of matter, via interactions of electrical and magnetic fields (Sagdejev and Kennel, 1991). 

Detonation, Predetonation Phase. This is an intermediate phase in the DDT (Deflagration to Detonation Transition) between deflagration (or combustion) and detonation Oppenheim (Ref 3, p 475) describes how during this phase a combustion front is accelerated by a shock process until the shock front is overtaken and a (CJ) Chapman-Jouguet detonation sets in. 

It follows that the reaction must be regarded as initiated at a shock front, in conformity with the picture of J. von Neumann (such as described briefly above and more fully in Ref 6 and in Ref 24a, p 6) 2) The front of the rarefaction wave, in a region of nonvanishing reaction velocity, moves with respect to the medium at a velocity equal to the local sound velocity computed under adiabatic - and frozen - reaction conditions... 

In essence, this model states that initiation occurs when a shocked region of LE becomes thermally superconductive (as a result of rising temp due to partial decompn of the shocked LE) and a heat pulse flashes across the shocked LE and catches up with the original shock front. As described in the article on Heatpulse (p H59-L), alternate explanations are possible for some of the observations that Cook considers to be the main experimental support for his heat pulse . Similarly, Dremin et al (Ref 17) have suggested an alternate ex-... 

Understanding of the basic factors of detonation, as of about 1970, has been reviewed by Johannson and Persson (Ref 99). Topics discussed include structure of the reaction zone and nature of the detonation process, with specific references to TNT. Conditions at the shock front, as described by Hugoniots, are reviewed in... 

The shock front created in the experimental gas is a physical and mathematical discontinuity that requires irreversible thermodynamics for description. For convenience the shock wave system is divided into three parts the parts before and after the shock front are considered to obey tile laws for reversible processes (dS = 0, etc.) so only what occurs at the discontinuity is described as an irreversible process (dS > 0). However, even at the front the laws of conservation (mass, momentum, and energy) still hold for the nonuniform, unidimensional flow of the shock wave when confined in a tube ... 

Cooling the shock gases is the most difficult process to describe, since the number of possible interactions is so large. Depending on length of driver and experimental sections of the tubes, initial pressure ratios, and types of gases used, the gases between the contact surface and the shock front could be cooled ... 

In a stationary detonation wave, the shock front is followed by a zone of chemical reaction which can be considered as an ordinary stationary-state combustion wave propagating through the denser and hotter gases behind the shock front (Fig. XIV.7). Such a combustion wave is characterized by a pressure decrease and a temperature increase across the flame front. Because of this and because, in the stationary state, the flame front must follow the shock front at a fixed distance, the model of the moving surface is not quite adequate to describe a stationary detonation/ A further difference between the two is that, whereas in the mechanical shock the surface velocity Vb was an independent parameter at the disposal of the experimenter, in the detonation the chemical composition of the reacting gases is the collective parameter which replaces vt and is the means by which the experimenter can control the detonation velocity. 

Here, and be taken as the displaced and displacing fluids, respectively, and k and k are their relative permeabilities, which are functions of the voffime fractions (i.e., saturations) of the fluids. As shown by Buckley and Leverett, the solution to Equation 4 gives a plot of saturation versus length along the flow direction that has a discontinuity (17). (The saturation of a fluid phase is its volume divided by the sum of the fluid volumes.) This discontinuity is often referred to as a shock front, and the flood is described as a piston-like displacement. 

Section 111 deals with nonreactive shock waves. The thread here is composed of three simple equations that describe the conservation of mass, momentum, and energy across the shock front. In this section we learn how to deal quantitatively with shock waves interacting with material interfaces and other shock waves. 

Using the techniques described above, we have performed systematic shock experiments on single-crystal calcite as well as on chemically pure calcite powder in the pressure range from 12.5 to 100 GPa. The shock front propagated parallel to the (1014) plane of single-crystal calcite. The calcite powder was compacted to pellets with a porosity on the order of 5 %, leading to higher shock and postshock temperatures than with the otherwise identical experimental setup. 

Equation 6.49 is strictly valid only for the disperse part of the peak (Chapter 2.2.3). Depending on the shape of the isotherm, this is the rear part ( Langmuir ) or the front part ( anti-Langmuir ) of the peak (Fig 2.6). The sharp fronts ( Langmuir ) or tails ( anti-Langmuir ) of the peaks are called concentration discontinuities or shocks. To describe the movement of these shocks, the differential in Eq. 6.49 has to be replaced by discrete differences A, the secant of the isotherm, which describe the amplitudes of the concentration shocks in the mobile and stationary phases ... 

These correlations can be transferred to continuous SMB or TMB chromatography where disperse as well as shock fronts are also present. The dimensionless flow rate ratios m,- can then be described as function of either the initial slope or the secant of the isotherm, depending on the situation in every zone. 

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