Density discontinuity

The point of intersection of I, R M is known as the triple point, TP. The resulting existence of the above three waves, causes a density discontinuity. The surface of this discontinuity, known as slipstream, S, represents a stream line for the flow relative to the intersection. Between this and the reflecting surface is the region of high pressure, known as Mach region here the pressure is approx twice that behind the incident wave. The top of this pressure region, the triple point, travels away from the reflected surface. As pressure and impulse appear to have their maximum values just above and below the triple point, respectively, the region of maximum blast effect is approximately that of the triple point... 

The problem that remains is the study of the interaction of a shock with a matrix of holes in three-dimensional geometry. The basic two-dimensional processes involved in the failure of detonation, the failure diameter of explosives, and the sputtering initiation observed for density discontinuities near the critical size have been described. The three-dimensional study of the interaction of numerous failures and reignited detonations which is necessary for a complete numerical description of these problems must await new computing hardware ... 

McIntyre, S., A. L. Alldredge, and C. C. Gottschalk. 1995. Accumulation of marine snow at density discontinuities in the water column. Limnology and Oceanography 40 449-468. 

Glazner A. F. and Ussier W. (1988) Trapping of magma at midcrustal density discontinuities. Geophys. Res. Lett. 15, 673-675. 

A formula which connects the surface energy with the distribution function and the intermolecular potential was derived by Fowler.11 He assumed that there is a mathematical surface of density discontinuity where the density changes discontinuously from the value of the liquid in bulk to the value of the vapor, which can be taken to be zero at lower temperatures. This assumption will be criticized later in this paper. If, following the assumption, the molecular distribution of the liquid is uniform up to the surface of discontinuity as in the interior of the liquid, the surface energy is given by... 

We now proceed to the problem of surface tension. Fowler11 assumed, as explained in Section II, that there is a mathematical surface of density discontinuity, one side of which is occupied by the liquid and the other side by the vapor. Assuming that the density of the vapor can be neglected and calculating the work done when the liquid is brought into two semi-infinite halves by an isothermal procedure, he obtained the following expression for the surface tension ... 

VII. CRITIQUE OF THE ASSUMPTION OF A MATHEMATICAL PLANE OF DENSITY DISCONTINUITY... 

Markstein s experiments were done with a flame ignited in a shock tube. Picone s calculations were done for a density discontinuity modeled on that expected for a flame. 

Medium- to large-scale oscillations and density discontinuities within upper few hundred meters of water column, can suspend sediment by fluid turbulence... 

Reverberation/clutter Inhomogeneities, such as dust, sea organisms, schools of fish, and sea mounds on the bottom of the sea, which form mass density discontinuities in the ocean medium. When an acoustic wave strikes these inhomogeneities, some of the acoustic energy is reflected and reradiated. The sum total of aU such reradiations is called reverberation. Reverberation is present only in active sonar, and in the case where the object echoes are completely masked by reverberation, the sonar system is said to be reverberation limited. 

It is well known that the liquid-gas coexistence line does not extend to arbitrarily large T, but terminates at the critical point, where second derivatives of the free energy are singular (e.g., the heat capacity and the isothermal compressibility). Density along isotherms versus pressure are continuous at temperatures above the critical temperature, whereas they display a density discontinuity at lower temperatures, at the coexistence pressure. The same kind of behavior is expected for the liquid-liquid transition, and hence, Vasisht et al. computed the equation of state (pressure vs density for varying temperature) in order to study... 

A large range of home-made equipment is used to sample at interfaces to the sediment and the atmosphere or across internal density discontinuity layers or redox (chemo-)clines e.g.. Bale and Barrett, 1995 Eversberg, 1990 Hallberg et al, 1977 Schwedhelm et al, 1988 ... 

While / and N ai-e fixed for a certain material, the interaction parameter can be varied due to its dependency on temperature, which may be assumed as x = aT +p, with a and p as constants. Systems like ours with a positive a exhibit a transition from order to disorder during the raise of temperature. Experiments on polymer blends exhibit a dependence of % also on pressure [10]. Kasten and Stilhn [11] found a small density discontinuity at Tmst for a comparable material and presumed a linear shift of Tmst with applied pressure derived from the latent heat of the transition (see also [12]) and the Clausius-Clapeyron equation. 

Experimental measurements of the reaction zone of heterogeneous explosives need to be made with high resolution in space and time. The space scale required must be less than the size of the smaller density discontinuities, and the time scale must be small enough to follow the variable flow associated with the density discontinuities. 

The voids or density discontinuities in a heterogeneous explosive cause irregularities of the mass flow when shocked. The heterogeneous explosive is initiated by local hot spots formed in it by shock interactions with density discontinuities. The hot spot mechanism is important in the propagation and failure of the detonation wave. As shown in Chapter 1, the density discontinuities are also a dominant feature of the heterogeneous explosive reaction zone. 

Since the interaction of shocks with density discontinuities as simple as corners produces a very complicated fluid flow, it appears that detailed numerical studies are essential for an understanding of the experimental results of more complicated systems such as heterogeneous explosives. 

To increase the understanding of the basic processes involved in shock initiation of inhomogeneous explosives, numerical two and three-dimensional hydrodynamics have been used to study the formation of hot spots from shocks interacting with single and multiple voids, air holes, and other density discontinuities. 

The process of heterogeneous shock initiation is described by the Hydrodynamie Hot Spot Modelf which models the hot spot formation from the shock interactions that occur at density discontinuities and describes the decomposition using the Arrhenius rate law and the temperature from the HOM equation of state described in Appendix A. 

Another result of the Hydrodynamic Hot Spot Model is that explosives with faster Arrhenius kinetics form hot spots that decompose faster and are less affected by side rarefactions before appreciable decomposition occurs. Explosives with faster Arrhenius kinetics exhibit increasing shock sensitivity with decreasing particle size for smaller particle sizes than explosives with slower kinetics. The effect of increasing the initial temperature of an explosive in the hydrodynamic hot spot model is to increase the temperature of the hot spots resulting from shock interactions with voids. The hotter hot spots decompose more and result in faster build up to detonation. Thus increasing the initial temperature of an explosive without significantly changing the density or density discontinuities results in a more shock-sensitive explosive. 

The three-dimensional modeling study demonstrated that the desensitization occurs because the preshock interacts with the holes and eliminates the density discontinuities. The subsequent higher pressure shock waves interact with a more homogeneous explosive. The multiple shock temperature is lower than the single shock temperature at the same pressure, which is the cause of the observed failure of a detonation wave to propagate in preshocked explosive for some ranges of preshock pressure. 

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