Shock, shockwave velocity

When the 2.5 N sodium chloride solution is fed to the column, the copper equivalent fraction, and concentration in the feed drop to zero. Since the column is at 2.5 N when the sodium wave reaches any part of the column, we use that equilibrium curve in Figure 18-19. This is an unfavorable isotherm for copper thus, with a drop in copper concentration in the feed a shock wave results. Then use Eq.( 18-461 to calculate the shockwave velocity. 

A detonation shock wave is an abrupt gas dynamic discontinuity across which properties such as gas pressure, density, temperature, and local flow velocities change discontinnonsly. Shockwaves are always characterized by the observation that the wave travels with a velocity that is faster than the local speed of sound in the undisturbed mixtnre ahead of the wave front. The ratio of the wave velocity to the speed of sound is called the Mach number. 

Explosive substances which on initiation decompose via the passage of a shockwave rather than a thermal mechanism are called detonating explosives. The velocity of the shockwave in solid or liquid explosives is between 1500 and 9000 m s-1, an order of magnitude higher than that for the deflagration process. The rate at which the material decomposes is governed by the speed at which the material will transmit the shock-wave, not by the rate of heat transfer. Detonation can be achieved either by burning to detonation or by an initial shock. 

Immediately ahead of the detonation firont the explosive rests quietly in its metastable state, while to the rear the shocked and reacted material flows at several kilometers per second with a pressure of several hundred thousand atmospheres and temperature of several thousand Kelvins. The rapid compression and heating of matter to these extreme conditions and the associated high velocity flow are properties of detonations that can be shared by strong shockwaves. However, with detonations the heated and compressed flow is selfsustaining. Typically, detonations are maintained by the exothermic chemistry they induce. Detonations driven by first order phase transitions have been envisioned, but have not yet been observed. 

In these latter studies, strong shockwaves were produced by driving the free edge of the molecular solid with a steadily moving piston as depicted in the lower part of Fig. 3. Two-dimensional simulations were initially carried out to determine the piston driven shock-to-detonation threshold in the perfect crystal. Once this threshold was determined, a crack such as that depicted at the top of Fig. 19 was introduced. Additional simulations were then performed for a series of piston velocities near, but below, the critical piston velocity, Vp, that is necessary to cause detonation in defect-free... 

The results demonstrate that nanometer wide cracks can have severe effects on the shock-to-detonation threshold. It might be tempting to conclude that the chemical reactions caused by these defects result from a velocity doubling as atoms are spalled into the crack. Indeed, we found that the velocities of the leading particles that are spalled into the crack by the shockwave had approximately twice the particle flow velocity in the shockwave, as predicted by the continuum theory. However, we also observed that when these high velocity molecules struck the opposite side of the crack, reactions were not induced immediately. Rather, the complex motions of the many atoms within the crack appears to seed the chemical reactions that ultimately cause detonation. These studies lay the foundation for additional studies with more complex models. 

In light of these observations from our MD simulations, we have proposed a simple model [41] describing the role of shockwave interactions with microscopic voids that leads to significant heating, sufficient to thermally initiate chemical reactions in solid explosives, or phase transitions in metals. The key ingredients to this dramatic overshoot in temperature are shown in Fig. 13. The dependencies on both shock strength (piston velocity Up) and onedimensional gap width /, which we observed in atomistic simulations of a two-dimensional unreactive Lennard-Jones solid, for the thermal overshoot AT was well predicted by our straightforward model ... 

The microchannel geometric characteristics are length (2L) and hydraulic diameter (Dh, equal to four times the area divided by the perimeter of a section), shown in Fig. la. The model relates the efficiency of the compression process to the velocity, pressure, and temperature of the gas at the entrance of the channel (station 1 Mj, pi, Ti) the pressure ratio across the shock 11s the friction coefficient fi and channel dimensicms. fri Fig. la, a shockwave is shown that moves in the opposite direction to the flow and is positioned in the middle of the channel. It can be shown that a snapshot evaluatimi at the mid position is a good representation of the overall results and does not affect the accuracy of the model. Friction is considered along the lengths L before and after the shock. The frictional effect is modeled as shear stress at the wall acting on a fluid with uniform properties over the cross section. 

Shock Tube as Vaccine Delivery System A unique form of powder delivery system, a biolistic system, has been developed [19]. This novel technology accelerates microparticles by a gas flow behind a traveling shockwave, so that they can attain sufficient momentum to penetrate the skin and thus achieve a pharmacological effect. One of the most recent developments is a mouse biolistic system, used in immunological studies. These studies require powdered vaccine to be delivered into the epidermis of the mouse with a narrow and highly controllable velocity distribution and a uniform spatial distribution. The preliminary results demonstrate the overall capability of a newly designed supersonic nozzle to deliver the particles to the skin targets with a more uniform velocity and spatial distribution. CTD has been utihzed to characterize the complete operation of a prototype mouse biolistic system. 

This relation describes the propagation of a finite discontinuity, or shock, separating two equilibrium states. The idealization implicit in its formulation is of particles in the bed making an instantaneous switch from one equilibrium condition to another as the shockwave passes over them. Only conservation of mass is involved in the analysis leading to eqn (5.8) inertial effects, which control the necessary deceleration of the moving particles to zero velocity, are not taken into account. The above analysis is thus in terms of a kinematic description of the fluidized state, and eqn (5.8) represents the velocity of a kinematic shock Mrs mrs = dLijdt. 

Consider the one-dimensional situation, depicted in Figure 14.2, of a shockwave propagating upwards, with velocity V, through a fluidized suspension. The void fractions immediately below and above the shock are e and 2 respectively. (The jump condition derivations that now follow are less restricted than appears from Figure 14.2, in that the void fractions directly across the shock, e and 2, need not in general correspond to equilibrium conditions.)... 

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