Andrade equation

The Andrade equation is used to correlate the dynamic viscosities of pure substances . It is named after Edward Andrade , but CV Raman published this model in Nature in 1923 .

formulation

The equation describes a linear relationship between the logarithm of the viscosity and the reciprocal of the temperature :

${\displaystyle {\begin{aligned}\eta &=A\cdot e^{\frac {b}{T}}\\\Leftrightarrow \mathrm {ln} \,(\eta )&=\mathrm {ln} \,(A)+{\frac {b}{T}}\end{aligned}}}$

With

• ${\displaystyle \eta }$: dynamic viscosity
• ${\displaystyle A,b}$: empirical constants
• ${\displaystyle T}$: absolute temperature in K
• ${\displaystyle e}$: Euler's number .

Goodness of fit

• Ethanol viscosity plots
• 

  Standard representation:
  viscosity / temperature

• 

  Logarithm of viscosity / reciprocal value of temperature

• 

  relative deviations

The deviation plot shows that the Andrade equation does not adequately reproduce the course of the viscosity over the entire temperature range. It should therefore only be used in a very limited temperature range.

Example parameters

	${\displaystyle a=\ln(A)}$	b [K]	T (min.) [K]	T (max.) [K]
water	−6.944	2036.8	274	373
benzene	−4.825	1289.2	273	483
acetone	−4.003	842.5	183	329
Ethanol	−5.878	1755.8	163	516

The table values ​​each provide the dynamic viscosity η in m Pa * s.

See also

• DIPPR equations : DIPPR equations 100 and 101 are alternatives to the Andrade equation
• Dortmund database : database for experimentally determined viscosities
• Arrhenius equation

Individual evidence

1. ^ EN da C. Andrade, "A Theory of the Viscosity of Liquids. - Part I.", London Edinb.Dub.Philos.Mag.J.Sci., 17 (112), 497-511, 1934
2. ↑ CV Raman, “A Theory of the viscosity of liquids”, Nature 111, pp. 532–533, London 1923 ( PDF ; 127 kB)
3. ↑ Horst Kuchling, Taschenbuch der Physik