Static Electricity 2000 Edition

Q
0
= initial charge density (coulombs per cubic meter)
e = 2.718, base of natural logarithms
t = time (seconds)
κ = liquid conductivity (picosiemens per meter)
ε = liquid dielectric constant
ε
0
= 8.854 
× 10
−12
, permittivity of free space (farads per 
meter)
According to W. M. Bustin (Bustin, W. M., et al, 1964), the
rate at which charge is lost depends on the conductivity of the
liquid. The lower the conductivity, the slower the relaxation.
Liquids with conductivity of less than 1 pS/m relax differently
when they are highly charged. The usual relationship
described by Ohm’s law does not apply. Instead, for nonvis-
cous liquids (i.e., less than 30 
× 10
−6
m
2
/sec), relaxation pre-
cedes hyperbolic decay. The Bustin theory of charge
relaxation has been experimentally confirmed for low-con-
ductivity hydrocarbon liquids, both in small-scale laboratory
experiments and in full-scale tests and is described by the fol-
lowing equation:
where:
Q
t
= charge density (coulombs per cubic meter)
Q
0
= initial charge density (coulombs per cubic meter)
µ = ion mobility, about 1 × 10
−8
m
2
/V-sec for charged 
distillate oil (square meters per volt-second)
t = time (seconds)
εε
0
= electrical permittivity (farads per meter)
The Bustin theory of charge relaxation depends only on
the initial charge density, Q
0
, and ion mobility, 
µ. The conduc-
tivity of the uncharged liquid is not a factor. In addition, Bus-
tin charge decay theory is not very sensitive to initial charge
density when the initial charge density is greater than about
100 microcoulombs per cubic meter.
A.7.3.3
The mechanism of charge generation is highly com-
plex. For flow of liquid in pipes, the charging current depends
on the liquid’s electrical conductivity and dielectric constant
and its viscosity and flow characteristics, which involve factors
such as flow velocity, pipe diameter, and surface roughness.
For equal flow characteristics, electrical conductivity is the
dominant factor. This is most pronounced for low conductiv-
ity liquids, due to trace contaminants. Trace contaminants
have negligible effect on the liquid’s dielectric constant and
viscosity, but have a dominant effect on conductivity. Conduc-
tive liquids are much less affected by trace contaminants. In
many systems, such as long pipes, the charge density reaches a
steady state at which the rate of charge generation is balanced
by the rate of charge relaxation back to ground.
Classification of Liquids Based on Conductivity. The conductiv-
ity of most flammable and combustible liquids varies from
about 10
−2
pS/m to 10
10
pS/m (i.e., by 12 orders of magni-
tude). Dielectric constants usually range from 2 to 40 — the
τ
εε
0
κ
-------
=
Q
t
Q
0
e
t
–
κ εε
0
⁄
=
Q
t
Q
0
1
(
µQ
0
t
εε
0
)
⁄
+
---------------------------------------
=

---

APPENDIX A
77
–39
2000 Edition
higher values being generally exhibited by polar liquids, which
also exhibit higher conductivity. Because relaxation behavior
is primarily governed by conductivity, conductivity can be used
to classify liquids relative to their potential for charge accumu-
lation as nonconductive, semiconductive, and conductive.
Because conductivity is so sensitive to purity and temperature,
class demarcations can be given only to within an order of
magnitude. It should be kept in mind that conductivity under
actual conditions could be less than what is measured in the
laboratory. (See Appendix B for conductivity values and relaxation