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Conductivity and electronic field

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2. Basics of air ions (2)

F. Conductivity and electronic field

F. Conductivity and electronic field

(1) Conductivity and Electronic field

An electrical current flows from an ion molecules in the air. There are 4 kinds of ions, large-positive, large-negative, small-positive and small-negative. Where the electric field strength is F, the total electrical current which flows from these 4 kinds of ions is it, and all ions have different mobility values (k/K/+/-) and ion counts (n/N/+/-).

[Mobility values]
k+: Positively charged small ion
k-: Negatively charged small ion
K+: Positively charged large ion
K-: Negatively charged large ion

[Ion counts]
n+: Positively charged small ion
n-: Negatively charged small ion
N+: Positively charged large ion
N-: Negatively charged large ion

Each current which flows from each ion:
[Current: Ion]
en+Fk+: small positive ion
en-Fk-: small negative ion
eN+FK+: large positive ion
eN-FK-: large negative ion

The total electrical current is the sum of each current and it is described by:

it = (en+Fk+) + (en-Fk-) + (eN+FK+) + (eN-FK-)

= F(en+k++en-k-+eN+K++eN-K-) ----- (A)
(e=4.77X1010C)

where

λ+ = (en+k++eN+K+) ----- (B)
λ- = (en-k-+eN-K-) ----- (C)
λ = λ+- ----- (D)

(A) can be descried by:

it = F(λ+-) = Fλ ----- (E)

Each term in λ+- is the ratio of the electronic field and the electrical current density, which shows the electrical conductivity.

λ+: Positive polar conductivity
λ-: Negative polar conductivity
λ: Whole conductivity

The SI unit of conductivity is: Sm-1



(2) Conductivity depending on environment

e.g. #1
where the air is well purified and n/N/k/K/+/- are:
n+ = 600
n- = 600
N+ = 2000
N- = 2000
k+ = 1.5(cm2/Vs)
k- = 1.5(cm2/Vs)
K+ = 0.0004(cm2/Vs)
K- = 0.0004(cm2/Vs)
ekn:eKN = 1125:1 (ref. to B/C)
This shows that the electronic conductivity in the purified air is largely determined by small ions.

e.g. #2 where the air is polluted and n/N/k/K/+/- are:
n+ = 100
n- = 100
N+ = 50000
N- = 50000
k+ = 1.5(cm2/Vs)
k- = 1.5(cm2/Vs)
K+ = 0.0004(cm2/Vs)
K- = 0.0004(cm2/Vs)
ekn:eKN = 7.5:1 (ref. to B/C)
This shows that large ions play a partial role to determine the electronic conductivity in the polluted air.
 
Author: Masaharu Nemoto
(Universal Plan Co., Ltd.)
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Measurement principles of air ions
Related pages of: Conductivity and electronic field
Contents of: Theory of Air Ion
1. Basics of air ions (1) 2. Basics of air ions (2) 3. Measurement Theory of Air Ion
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