Interface velocity

Due to the conservation law, the diffiision field 5 j/ relaxes in a time much shorter than tlie time taken by significant interface motion. If the domain size is R(x), the difhision field relaxes over a time scale R Flowever a typical interface velocity is shown below to be R. Thus in time Tq, interfaces move a distanc of about one, much smaller compared to R. This implies that the difhision field 6vj is essentially always in equilibrium with tlie interfaces and, thus, obeys Laplace s equation... 

Equation (A3.3.73) is referred to as the Gibbs-Thomson boundary condition, equation (A3.3.74) detemiines p on the interfaces in temis of the curvature, and between the interfaces p satisfies Laplace s equation, equation (A3.3.71). Now, since ] = -Vp, an mterface moves due to the imbalance between the current flowing into and out of it. The interface velocity is therefore given by... 

Rates of two-phase heat transfer depend on properties of the volatile fluid, dimensions of the interface, velocities of flow and the... 

The measured growth rates are illustrated by the circles in Fig. 7. The interface velocity is plotted versus the interface temperature T. The value of T is always greater than Tq because of the release of the latent heat at the interface. Dimensionless units for T and the velocity are used here. The maximum velocity corresponds to 80m /s for argon. The most surprising aspect is the rapid crystallization at low temperatures. Most materials exhibit sharply reduced rates at low temperatures, as expected for an activated growth process. That is, the kinetics can be represented as the product of an Arrhenius factor F(T) and a term that accounts for the net production of crystalline material as a result of the atoms ordering and disordering at the interface,... 

In the absence of a potential barrier, the rate at which liquid atoms in the interface could move to lattice sites is determined by the average thermal velocity, (3A T/m). If they travel a distance X, the interface velocity is... 

If eq. (l) were applicable to other materials, approximate values of the maximum growth rates could be obtained by scaling with (T / ). Accordingly, we estimate maximum rates of 400 m/s for nickel and 430 m/s for silicon. Interface velocities of 50 m/s have been measured for Ni... 

Far from a wellbore, the velocity of reservoir fluids is about one linear foot per day. Near a wellbore, the velocity can increase one-hundred fold. A static or quasi-static test such as the sessile drop (contact angle) test may not represent the dynamic behavior of the fluids in the field. The dynamic Wilhelmy device gives results which are comparable in interface velocity to the field displacement rate. The interface in the Wilhelmy test described here moved at a steady rate of 0.127 mm/sec or 36 ft/day. The wetting cycle for a hybrid-wetting crude oil system was not affected by moving at a rate less than 1 ft/day. 

The phase distribution observed in the alloys deposited from AlCb-NaCl is very similar to that of Mn-Al alloys electrodeposited from the same chloroaluminate melt [126 129], Such similarity may also be found between the phase structure of Cr-Al and Mn-Al alloys produced by rapid solidification from the liquid [7, 124], These observations are coincident with the resemblance of the phase diagrams for Cr-Al and Mn-Al, which contain several intermetallic compounds with narrow compositional ranges [20], inhibition of the nucleation and growth of ordered, often low symmetry, intermetallic structures is commonly observed in non-equilibrium processing. Phase evolution is the result of a balance between the interface velocity and... 

Contracting volume (CV) Three-dimensional growth diffusion controlled with decreasing interface velocity 168, 171... 

To summarize the structure of a moving interface on the atomic scale depends on the atomic mechanism which operates in the structure transformation. The mode selection depends on the driving force and thus on the interface velocity. The interface mobility itself is determined by its structure and depends therefore on the driving force. This means that interface controlled reactions are normally nonlinear functions of the driving force. 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The rate and characteristics of surface evolution depend on the particular transport mechanisms that accomplish the necessary surface motion. These can include surface diffusion, diffusion through the bulk, or vapor transport. Kinetic models of capillarity-induced interface evolution were developed primarily by W.W. Mullins [1-4]. The models involving surface diffusion, which relate interface velocity to fourth-order spatial derivatives of the interface, and vapor transport, which relate velocity to second-order spatial derivatives, derive from Mullins s pioneering theoretical work. 

Evolution by Surface Diffusion and by Vapor Transport. Although calculation of the morphological evolution for particular cases can become tedious, the kinetic equations are straightforward extensions of the isotropic case [11], For the movement of an anisotropic surface by surface diffusion, the normal interface velocity is an extension of Eq. 14.6 which holds for the isotropic case for the anisotropic case,... 

Growth Rate for Inclination-Dependent Interface Velocity. For a crystalline particle growing from a supersaturated solution, the surface velocity often depends on atomic attachment kinetics. Attachment kinetics depends on local surface structure, which in turn depends on the surface inclination, n, with respect to the crystal frame. In limiting cases, surface velocity is a function only of inclination the interfacial speed in the direction of n is given by v(h). The main aspects of a method for calculating the growth shapes for such cases when v(h) is known is described briefly in this section. 

Ilyukhin Pokhil (Ref 5) used plane wave shocks thru a brass barrier to initiate RDX. For RDX of MJ.lmm particle size at 1.74g/cc the threshold shock was found to be lSkbai A recent study by Dremin Shvedov (Ref 99) examined the effect of gas additives on the shock initiation of RDX and TNT lightly pressed charges of po M g/cc.The nature of the gas or its partial press had no effect. They did find an interesting effect in all their observations, namely a break in the plot of barrier/expl interface velocity (u) vs time. Their summary plot for RDX is shown in Fig 5... 

Dremin Shvedov (Ref 52 performed a series of expts with liq expls, granular expls (pressed and cast) and granular expls with inert liq and gas fillers, in which they monitored the barrier/exp interface velocity as a function of input pressure of rectangular shocks. According to the authors the shock-driven interface is decelerated by decompn products if there is reaction. Thus the data in F ° 2 fan4 in Pw 27 helnwt are interface deceleration curves. The data in Fig 26a are for liq TNT those in Fig 26b are for cast TNT ,numbers in the curves are input pressures in kbars... 

According to the authors, a decrease in interface velocity with time (negative dope) indicates reaction, whereas zero slope indicates no reaction. 

Within a narrow pressure range, P, the behavior of the interface velocity-time profiles changes from either a zero slope or continuous negative slope to a break in the slope (eg, at 155 kb in Fig 26a and 134 I40kb in Fig 26b)... 

The solid interface has a small velocity in the negative y direction that may slowly vary with x. Yet the solid is rigid enough to sustain the shear stresses in the him and to prohibit the development of an x-direction interface velocity. We are now in a position to state the... 

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