Function Of Reaction Rate Research Articles

Kinetics of Diffusion-Controlled Reactions in Polymer Melts

It is shown that in the limit of continuously flexible, Gaussian polymer chains, the first-order rate for end-to-end reactions, ${k}_{\mathrm{cyc}}(t)$, scales as the fundamental reptation time, ${\ensuremath{\tau}}_{\mathrm{rep}}$. At short times $t<{\ensuremath{\tau}}_{\mathrm{rep}}$, ${k}_{\mathrm{cyc}}(t)\ensuremath{\rightarrow}(\frac{0.333}{{\ensuremath{\tau}}_{\mathrm{rep}}}){(\frac{t}{{\ensuremath{\tau}}_{\mathrm{rep}}})}^{\ensuremath{-}\frac{1}{4}}$, while at long times, ${k}_{\mathrm{cyc}}(\ensuremath{\infty})=\frac{0.363}{{\ensuremath{\tau}}_{\mathrm{rep}}}$. The analysis also gives the exact chain-length-dependent memory and reaction-rate functions in the discrete case of bead-rod chains obeying the earthworm equations of Doi and Edwards.

SIMILARITY SOLUTIONS FOR REACTIVE SHOCK WAVES

Possibilities for similarity solutions of the flow following the impact of a piston on a reactive γ-law gas are delineated for the cases where the transmitted shock is strong or of constant strength. Reaction-rate functions that can be used with power-law, exponential and logarithmic shock paths are obtained. A particular case is worked out, namely, plane reactive flow with the reaction rate proportional to the internal energy and the shock velocity varying exponentially with time. For certain values of the parameters, the solution is shown to contain an envelope of characteristics which corresponds to a singular point of the ordinary differential equation which determines the flow. Results are obtained regarding the behaviour of the flow variables, a special case where Whitham's rule holds exactly, and the possibility of accelerating a strong shock indefinitely, without introducing secondary shocks into the flow.

Contribution to the theory of the structure of gaseous detonation waves

The paper presents exact solutions to the equations governing the distributions of temperature, velocity and pressure in a gaseous detonation wave, for the cases in which the dimensionless volumetric-reaction-rate w: (a) has a concentrated peak near the hot boundary but negligible values elsewhere; (b) obeys the law w=n(τ−τC){(τ−τCτH−τC)n−1−(τ−τCτH−τC)2n−2}, where n is a constant, τ is the dimensionless stagnation temperature, and subscript C denotes upstream conditions. Other exact solutions are also discussed. The methods used are analytical and graphical, requiring no high-speed computing facility. The gas is supposed to have a Lewis Number of unity and a Prandtl Number of 3/4; for convenience its thermodynamic properties are supposed to be those of a perfect gas. It is argued that, although the reaction-rate functions considered do not correspond to the chemical-kinetic properties of any particular detonating gas, studies of the kind presented permit clear perception of most of the important properties of real gaseous detonations.