Flame extinguishment properties of dry chemicals: Extinction concentrations for small diffusion pan fires

1989 ◽  
Vol 25 (2) ◽  
pp. 134-149 ◽  
Author(s):  
Curtis T. Ewing ◽  
Francis R. Faith ◽  
J. Thomas Hughes ◽  
Homer W. Carhart
Keyword(s):  
Small Diffusion ◽  
Flame Extinguishment ◽  
Dry Chemicals

Formation of High Resistivity Phases of Nickel Silicide at Small Diffusion Region

2007 ◽  
Author(s):  
Ryuji Tomita ◽  
Hiroshi Kimura ◽  
Makoto Yasuda ◽  
Tomowo Nakayama ◽  
Kazutaka Maeda ◽  
...  
Keyword(s):  
Nickel Silicide ◽  
High Resistivity ◽  
Diffusion Region ◽  
Small Diffusion

Metastability for a generalized Burgers equation with applications to propagating flame fronts

1999 ◽  
Vol 10 (1) ◽  
pp. 27-53 ◽  
Author(s):  
X. SUN ◽  
M. J. WARD
Keyword(s):  
Flame Front ◽  
Principal Eigenvalue ◽  
Vertical Channel ◽  
Front Propagation ◽  
Slow Motion ◽  
Diffusion Limit ◽  
Asymptotic Results ◽  
Small Diffusion ◽  
Generalized Burgers Equation ◽  
Exponentially Small

In the small diffusion limit ε→0, metastable dynamics is studied for the generalized Burgers problemformula hereHere u=u(x, t) and f(u) is smooth, convex, and satisfies f(0)=f′(0)=0. The choice f(u)=u2/2 has been shown previously to arise in connection with the physical problem of upward flame-front propagation in a vertical channel in a particular parameter regime. In this context, the shape y=y(x, t) of the flame-front interface satisfies u=−yx. For this problem, it is shown that the principal eigenvalue associated with the linearization around an equilibrium solution corresponding to a parabolic-shaped flame-front interface is exponentially small. This exponentially small eigenvalue then leads to a metastable behaviour for the time- dependent problem. This behaviour is studied quantitatively by deriving an asymptotic ordinary differential equation characterizing the slow motion of the tip location of a parabolic-shaped interface. Similar metastability results are obtained for more general f(u). These asymptotic results are shown to compare very favourably with full numerical computations.

scholarly journals Arbitrary nonlinearities in convective population dynamics with small diffusion

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
I. D. Peixoto ◽  
L. Giuggioli ◽  
V. M. Kenkre
Keyword(s):  
Population Dynamics ◽  
Small Diffusion

scholarly journals Advection of a passive scalar by a vortex couple in the small-diffusion limit

1994 ◽  
Vol 270 ◽  
pp. 219-250 ◽  
Author(s):  
Joseph F. Lingevitch ◽  
Andrew J. Bernoff
Keyword(s):  
Boundary Layer ◽  
Diffusion Equation ◽  
Particle Method ◽  
Passive Scalar ◽  
Outer Edge ◽  
Diffusion Limit ◽  
Asymptotic Results ◽  
Small Diffusion ◽  
Diffusive Boundary ◽  
Large Peclet Number

We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe−½) forms; asymptotic matching to the interior of the dipole yields effective boundary conditions for the averaged diffusion equation. The analysis predicts that first the scalar is homogenized along the streamlines on a timescale O(Pe−$\frac{1}{3}$). The scalar then diffuses across the streamlines on the diffusive timescale, O(Pe). Scalar that diffuses into the boundary layer is swept to the rear stagnation point, and a finite proportion is expelled into the exterior flow. Expulsion occurs on the diffusive timescale at a rate governed by the lowest eigenvalue of the averaged diffusion equation for large times. A split-step particle method is developed and used to verify the asymptotic results. Finally, some speculations are made on the viscous decay of the dipole in which the vorticity plays a role analogous to the passive scalar.

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