Barrer

Physical unit
Unit name	Barrer
Physical quantity (s)	Permeability (solid)
dimension	${\displaystyle {\mathsf {L^{3}\;T\;M^{-1}}}}$
system	Technical measurement system
In SI units	${\displaystyle 1\ {\text{Barrer}}\approx 7{,}5006\cdot 10^{-18}\,{\frac {{{\text{m}}^{3}}\cdot {\text{s}}}{\text{kg}}}}$
In CGS units	${\displaystyle 1\ {\text{Barrer}}=10^{-10}\,{\frac {{\text{cm}}^{3}}{{\text{s}}\cdot {\text{cm}}\cdot {\text{cmHg}}}}}$
Named after	Richard Barrer
Derived from	Torr , centimeter , second

Barrer (after Richard Maling Barrer ) is a unit in the technical measurement system ( no SI unit ) for the gas permeability of substances. The unit will u. a. used in describing the properties of membranes and sealing materials.

A comparable unit that describes the permeability of porous substances for liquids is the Darcy .

definition

Deviating from the permeability (SI unit m²), the permeability is defined in the Barrer's sense as: ${\displaystyle K}$

${\displaystyle {\frac {K}{\eta }}={\frac {Q\,x}{A\,\Delta p}}}$

With

• the dynamic viscosity (SI unit ) ${\displaystyle \eta }$ ${\displaystyle {\tfrac {\mathrm {N} \cdot \mathrm {s} }{\mathrm {m} ^{2}}}={\tfrac {\mathrm {kg} }{\mathrm {m} \cdot \mathrm {s} }}}$
• the flow rate (permeation rate) through the material, based on the volume under standard conditions and therefore given in cm ³ / s ${\displaystyle Q}$
• the thickness of the material in cm ${\displaystyle x}$
• the flowed through area in cm ² ${\displaystyle A}$
• the pressure difference in cmHg . ${\displaystyle \Delta p}$

The Barrer is defined as:

${\displaystyle {\begin{aligned}1\ {\text{Barrer}}&=10^{-10}\,{\frac {\mathrm {cm} ^{3}}{\mathrm {s} }}\cdot {\frac {\mathrm {cm} }{\mathrm {cm} ^{2}\cdot \mathrm {cmHg} }}\\&=10^{-10}\,{\frac {\mathrm {cm} ^{3}}{\mathrm {s} \cdot \mathrm {cm} \cdot \mathrm {cmHg} }}\end{aligned}}}$

Conversion in SI units:

${\displaystyle {\begin{aligned}1\ {\text{Barrer}}&\approx 10^{-10}\,{\frac {10^{-6}\,{\mathrm {m} ^{3}}}{s\cdot 10^{-2}\,\mathrm {m} \cdot 1{,}33322\cdot 10^{3}\,\mathrm {Pa} }}\\&\approx 7{,}5006\cdot 10^{-18}\,{\frac {\mathrm {m} ^{3}}{\mathrm {s} \cdot \mathrm {m} \cdot \mathrm {Pa} }}\\&\approx 7{,}5006\cdot 10^{-18}\,{\frac {{\mathrm {m} ^{3}}\cdot \mathrm {s} }{\mathrm {kg} }}\end{aligned}}}$

Additional calculation: the flow rate can also be represented in mol / s using the ideal gas law (see molar volume ):

${\displaystyle {\begin{aligned}p\cdot V&=n\cdot R_{\mathrm {m} }\cdot T\\\Leftrightarrow Q={\frac {V}{t}}&={\frac {n}{t}}\,{\frac {R_{\mathrm {m} }\cdot T}{p}}\\\Leftrightarrow {\dot {n}}&={\frac {Q\cdot p}{R_{\mathrm {m} }\cdot T}}\\\Rightarrow 1\,{\frac {\mathrm {m} ^{3}}{\mathrm {s} }}\cdot {\frac {101325\,\mathrm {Pa} }{8{,}314\,{\tfrac {\mathrm {J} }{\mathrm {mol} \,\mathrm {K} }}\cdot 273{,}15\,\mathrm {K} }}&\approx 44{,}6\,{\frac {\mathrm {mol} }{\mathrm {s} }}\end{aligned}}}$

With

• p - pressure
• V - volume
• n - amount of substance
• R _m - universal or molar gas constant
• T - absolute temperature
• t - time .

This results in:

${\displaystyle {\begin{aligned}\dots \Rightarrow 1\ {\text{Barrer}}&\approx 7{,}5006\cdot 10^{-18}\cdot 44{,}6\,\mathrm {mol} \cdot {\frac {\mathrm {s} }{\mathrm {kg} }}\\&\approx 3{,}346\cdot 10^{-16}\,{\frac {\mathrm {mol} \cdot \mathrm {s} }{\mathrm {kg} }}\end{aligned}}}$

Permeation rate

The rate of gas permeation follows the direction of the partial pressure difference:

${\displaystyle \dots \Leftrightarrow Q={\frac {K\,A\,\Delta p}{\eta \,x}}}$

It increases linearly with the pressure and with the penetration cross-section, it decreases linearly with the length of the permeation path and behaves like a molecular flow .

Permeation coefficient

In leak detection technology, instead of the permeation rate, you specify the product with the pressure difference , i.e. the power loss ${\displaystyle Q}$ ${\displaystyle \Delta p}$

${\displaystyle P=\Delta p\cdot Q}$

The permeation coefficient defines the permeation behavior of a gas-to-material combination: ${\displaystyle C}$

${\displaystyle {\begin{aligned}C&=10^{8}\cdot {\frac {P\cdot x}{A\cdot \Delta p}}\\&=10^{8}\cdot {\frac {Q\cdot x}{A}}\\&=10^{8}\cdot {\frac {K}{\eta }}\cdot \Delta p\end{aligned}}}$

With

• P - power loss in (W = watt ) ${\displaystyle \mathrm {mbar} \cdot {\frac {\mathrm {l} }{\mathrm {s} }}=10^{2}\,\mathrm {Pa} \cdot 10^{-3}\,{\frac {\mathrm {m} ^{3}}{\mathrm {s} }}=0{,}1\,\mathrm {W} }$
• x - length of the permeation path in cm
• A - permeation cross section in cm ²
• ${\displaystyle \Delta p}$ - partial pressure difference in bar.

The permeation coefficient is z. B. for ${\displaystyle C}$

• Helium through Teflon : ${\displaystyle C=523\cdot 10^{-4}\,{\frac {\mathrm {m} ^{2}}{\mathrm {s} }}=523\,{\frac {\mathrm {mbar} \cdot {\tfrac {\mathrm {l} }{\mathrm {s} }}\cdot \mathrm {cm} }{\mathrm {cm} ^{2}\cdot \mathrm {bar} }}}$
• Hydrogen through Teflon: ${\displaystyle C=17{,}8\cdot 10^{-4}\,{\frac {\mathrm {m} ^{2}}{\mathrm {s} }}}$
• Helium by Pyrex glass: . ${\displaystyle C=0{,}09\cdot 10^{-4}\,{\frac {\mathrm {m} ^{2}}{\mathrm {s} }}}$

The following results are resolved according to the power loss:

${\displaystyle \Leftrightarrow P=10^{-8}\cdot {\frac {C\cdot A\cdot \Delta p}{x}}.}$

So is z. B. the power loss of helium through a Teflon membrane with a thickness and an area at a pressure difference : ${\displaystyle x=1\,\mathrm {mm} }$ ${\displaystyle A=10\,\mathrm {cm} ^{2}}$ ${\displaystyle \Delta p=1\,\mathrm {bar} }$

${\displaystyle {\begin{aligned}P&=10^{-8}\cdot {\frac {523\,{\frac {\mathrm {mbar} \cdot {\tfrac {\mathrm {l} }{\mathrm {s} }}\cdot \mathrm {cm} }{\mathrm {cm} ^{2}\cdot \mathrm {bar} }}\cdot 10\,\mathrm {cm} ^{2}\cdot 1\,\mathrm {bar} }{1\,\mathrm {cm} }}\\&=5{,}23\cdot 10^{-5}\,\mathrm {mbar} \cdot {\frac {\mathrm {l} }{\mathrm {s} }}\\&=5{,}23\,\mu \mathrm {W} \end{aligned}}}$

literature

• Evaluation of gas diffusion through plastic materials used in experimental and sampling equipment. (Wat. Res. 27, No. 1, pp. 121-131, 1993)
• Marr, Dr J. William. Leakage Testing Handbook, prepared for Liquid Propulsion. Section. Jet Propulsion Laboratory. National Aeronautics and Space Administration, Pasadena, CA, Contract NAS 7-396, June 1968; LCCN 68061892

Web links

• A Dictionary of Units of Measurement (English)
• Lecksuchtechnik.de