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Archive for Rational Mechanics and Analysis

, Volume 19, Issue 2, pp 81–99 | Cite as

Prolegomena to the rational analysis of systems of chemical reactions

  • Rutherford Aris
Article

Keywords

Neural Network Complex System Nonlinear Dynamics Electromagnetism Rational Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

partitioned, augmented stoicheiometric matrix

at

atomic weight

cs

concentration, ns/V

fr

kinetic expression for rate of change of ξr

gs

kinetic expression for rate of change of cs

J

Jacobian of transformation to equivalent reactions

Ki

equilibrium constants (sec. 6)

Rs∽r

rate constants

M

total mass

Ms

mass of A s present

ms

molecular weight

ns

number of moles of A s present

T

temperature

V

volume

Z

thermodynamic variables

α

matrix of stoicheiometric coefficients

β

atomic matrix

γ, γr

arbitrary scalar multipliers

Δ, γ

arbitrary nonsingular transformation and inverse

ζ

extent in number of moles

ηe

invariant

x, xr, \(\bar x_{\bar r}\)

logarithms of equilibrium constants

\(\mu ^{\bar r}\)

stoicheiometric numbers

ξ

extent in moles per unit volume

σ

rate of entropy production

\(\varphi ^r ,x\), x

factors of fr in a kinetic expression

As

molecular species

t

atomic species

r

reaction

\(\mathfrak{a}_\mathfrak{r}\)

affinity of reaction

\(\mathfrak{A}_\mathfrak{r}\)

vector space of species

\(\mathfrak{B}_\mathfrak{s}\)

vector space of reactions

Suffixes and their Ranges

γ, ϱ

denotes a reaction; ranges: γ, (1, r); γ′, (1, r′); γ′', (r′+1, r); \(\bar r, (1, \bar R)\); ϱ, (R+1, s)

s, σ

denotes a molecular species; ranges: s, (1,s); s′, (1,s′); s″, (s′+1,s); \(\bar s\) (1, \(\bar s\)); σ, (s+1,)

t

denotes an atomic species; ranges: t, (1, t); t′, (1, t′); t′', (T′+1, t)

o

denotes an initial value.

Small Capitals

\(R,\bar R\)

number of reactions

r′

rank of α

s, \(\bar s\)

number of molecular species

t

number of atomic species

t′

rank of β

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References

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Copyright information

© Springer-Verlag 1965

Authors and Affiliations

  • Rutherford Aris
    • 1
  1. 1.Department of Chemical EngineeringUniversity of MinnesotaMinneapolis

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