Thermokinetic Oscillator

α

0.05

β

5

γ

500

For a thermokinetic oscillator, the reaction scheme is

A⟶X

,

X⟶R

. The second reaction is exothermic with a reaction enthalpy

H

; it has a substantial activation energy

E

. The concentration of component

A

is constant, the temperature of the surroundings is

T

0

, the density and specific heat of the reaction mixture are

ρ

and

c

ρ

, the area for heat transfer is

A

, the volume of the system is

V

,

α=

2

(E/(RT))

,

β=Ah(Vρ

c

ρ

)

, and

γ=H

k

2

T

0

(ρ

c

ρ

)

. The relevant rate equations are solved and plotted for

ΔT(t)

and

C

X

, the latter scaled up by 1000 for convenience.

Details

The reaction produces heat, accelerating the reaction and reducing the concentration of

C

X

. As you vary the parameters, the interplay of these opposing tendencies can produce oscillations and bifurcation behavior.

References

[1] P. Gray and S. K. Scott, Chapter 4, Chemical Oscillations and Instabilities, New York: Oxford University Press, 1990.

[2] D. A. Frank-Kamenetskii and I. E. Salnikov. Zhur. Fiz. Khim., 17, 1943 p. 79.

[3] xmds.org. thermkin.xmds. (Dec 28 2012)

Permanent Citation

Benson R. Sundheim

"Thermokinetic Oscillator"
http://demonstrations.wolfram.com/ThermokineticOscillator/
Wolfram Demonstrations Project
Published: January 11, 2012