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Boundary velocity

U = boundary velocity in the ic direction ip= squeeze number 12/raioL /po O wq = characteristic angular velocity ... [Pg.98]

Inserting Eq. (15) and using c,- = -ct gives pbub — 0. For nonstatic particles, the local fluid velocity must be set equal to the local boundary velocity b. This can be achieved by a simple modification of the bounce-back rule ... [Pg.82]

As in previous analyses, nondimensionalizing the equations leads to results that have general applicability. Here, however, it is not a simple task to identify a length scale and a velocity scale based on an inspection of the geometry and the boundary velocities. In fact, it was an insightful contribution of Hiemenz to identify the length and velocity scales that are required to develop a parameter-free system of nondimensional equations. They are... [Pg.259]

At the a/p phase boundary, an equivalent mass balance condition in terms of the boundary velocity is... [Pg.267]

Figure 11-5. Boundary velocity tib and the direction of fluxes (responsible for the boundary motion) in the contiguous phases a and 0. Figure 11-5 b corresponds to Figure ll-2a. Figure 11-5. Boundary velocity tib and the direction of fluxes (responsible for the boundary motion) in the contiguous phases a and 0. Figure 11-5 b corresponds to Figure ll-2a.
Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... [Pg.272]

Let us briefly outline the main concepts of a (linear) stability analysis and refer to the situation illustrated in Figure 11-7. If we artificially keep the moving boundary morphologically stable, we can immediately calculate the steady state vacancy flux, /v, across the crystal. The boundary velocity relative to the laboratory reference system (crystal lattice) is... [Pg.279]

The last condition we need concerns the coupling between the flux and the boundary velocity v. If e is the unit vector in the z direction and n is the vector normal to the boundary, this coupling condition yields... [Pg.279]

Let us assume that mb is independent of the non-stoichiometry da and 5p at the boundary, since Sa and 1. The rate of structure change rjb has to match the boundary velocity vb while the boundary velocity establishes the boundary condition for the diffusion. The driving forces A/ub (here A Ag) or rather (A/ib/A b) across the interface a/fi are thereby fully determined. These kinetic conditions may be written in a linearized version (see also Eqn. (10.31)) as... [Pg.307]

Mechanisms of Flame Stabilization. CRITICAL BOUNDARY VELOCITY GRADIENT. A flame stabilized at the port of a Bunsen burner does not actually touch the rim. There is a dark region, called the dead space, between the rim and the flame. Heat is removed and free radicals are destroyed by the solid surface the burning velocity is reduced to zero and the flame is quenched. Even beyond the dead space, where the flame is able to exist as a luminous reaction zone, the burning velocity only gradually rises to the value achieved at a distance from solid surfaces. [Pg.179]

There is a critical boundary velocity gradient for each flame, Qs (for flash-back) and... [Pg.179]

The boundary velocity gradients may be computed from the following expression ... [Pg.180]

Figure 16. Basis of critical boundary velocity gradients for flash-back and blow-off... Figure 16. Basis of critical boundary velocity gradients for flash-back and blow-off...
The stability of burner flames is well accounted for in terms of critical boundary velocity gradients. The way in which flameholdcrs stabilize supported flames in ducts... [Pg.183]

Segregated solute concentration profile c(x) across boundary as a function of increasing boundary velocity v (the x axis is perpendicular to the boundary). cXL is the solute concentration in the adjoining crystals, (b) Boundary velocity vs. pressure, P, on boundary as a function of increasing cXL. (c) In v vs. 1/T as a function of increasing cXL. (d) In v vs. In cXL as a function of increasing P. From Cahn [10],... [Pg.313]

Forced Convection. An additional complication arises from convection in the melt forced by the motion of the slider and only marginally assisted by the gas flow above the melt. Forced convection will transport solute across the substrate from the back edge. Moving a solid horizontal boundary across the bottom of an initially stagnant and semiinfinite liquid is a classical problem of unsteady viscous flow (91). The ratio of the velocity of the fluid in the direction of motion, v(y), to the solid-boundary velocity, V, is given by... [Pg.132]

During discontinuous grain growth, the grain boundaiy can move as is shown in Figure 16.14 [37]. Here we see that the grain boundary velocity is perpendicular to the grain boundary and in the direction... [Pg.805]

Schematic of abnormal grain growth showing the grain boundary veloc-... Schematic of abnormal grain growth showing the grain boundary veloc-...
In solution drag, the width of the grain bovmdaiy, w, is the zone over which impurities interact. The grain boimdary thickness is taken to be independent of grain size. The diffusion coefficients of the host, D , and the impvirity, D/, will depend on the structure in the grain boundary. Impurities can therefore have an effect on the grain boundary velocity, Vg, by either their effect on the Co term or an effect on the diffusion coefficients for host and impurity. [Pg.831]

When pores are the second phase, they are mobile and move at a velocity equal to the velocity of the grain boundary, thus Vgi, = Vp = MpFp, where the pore mobility, Mp, and the drag force on the pore, Fp, is given in Table 16.8. Separation of the pores from the grain boundaiy occurs when Vgi, > Vp [85]. Thus the pores exhibit a drag on the grain boundary velocity, giving [86]... [Pg.833]


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See also in sourсe #XX -- [ Pg.292 , Pg.293 , Pg.295 ]




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Boundary conditions velocity

Boundary layer from velocity decrease

Boundary layer thickness velocity

Boundary layer velocity profiles

Boundary velocity gradient

Deposition velocities boundary layer theory

Diffusive boundary exchange velocity

Entrance region velocity boundary layer

Grain boundary velocity

Laminar boundary layer velocity distribution

Tangential velocity within mass transfer boundary layer

The velocity boundary layer

Velocity boundary layer

Velocity grain boundary mobility

Velocity profile in laminar boundary layer

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