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## Continuous Analytical Measurement - Conductivity Measurement - Page 3

**Two-electrode conductivity probes**

Conductivity is measured by an electric current passed through the solution. The most primitive form of conductivity sensor (sometimes referred to as a conductivity cell ) consists of two metal electrodes inserted in the solution, connected to a circuit designed to measure conductance (G), the reciprocal of resistance (1/R):

The following photograph shows such direct-contact style of conductivity probe, consisting of stainless steel electrodes contacting the fluid flowing through a glass tube:

The conductance measured by a direct-contact conductivity instrument is a function of plate geometry (surface area and distance of separation) as well as the ionic activity of the solution. A simple increase in separation distance between the probe electrodes will result in a decreased conductance measurement (increased resistance R) even if the liquid solution’s ionic properties do not change. Therefore, conductance (G) is not particularly useful as an expression of liquid conductivity.

The mathematical relationship between conductance (G), plate area (A), plate distance (d), and the actual conductivity of the liquid (k) is expressed in the following equation_{4}:

Where,

G = Conductance, in Siemens (S)

k = Specific conductivity of liquid, in Siemens per centimeter (S/cm)

A = Electrode area (each), in square centimeters (cm^{2})

d = Electrode separation distance, in centimeters (cm)

The unit of Siemens per centimeter may seem odd at first, but it is necessary to account for all the units present in the variables of the equation. A simple dimensional analysis proves this:

For any particular conductivity cell, the geometry may be expressed as a ratio of separation distance to plate area, usually symbolized by the lower-case Greek letter Theta (θ), and always expressed in the unit of inverse centimeters (cm−1):

Re-writing the conductance equation using θ instead of A and d, we see that conductance is the quotient of conductivity k and the cell constant θ:

Where,

G = Conductance, in Siemens (S)

k = Specific conductivity of liquid, in Siemens per centimeter (S/cm)

θ = Cell constant, in inverse centimeters (cm^{-1})

Manipulating this equation to solve for conductivity (k) given electrical conductance (G) and cell constant (θ), we have the following result:

Two-electrode conductivity cells are not very practical in real applications, because mineral and metal ions attracted to the electrodes tend to “plate” the electrodes over time forming solid, insulating barriers on the electrodes. While this “electroplating” action may be substantially reduced by using AC instead of DC_{5} to excite the sensing circuit, it is usually not enough. Over time, the conductive barriers formed by ions bonded to the electrode surfaces will create calibration errors by making the instrument “think” the liquid is less conductive than it actually is.

4This equation bears a striking similarity to the equation for resistance of metal wire: , where l is the length of a wire sample, A is the cross-sectional area of the wire, and ρ is the specific resistance of the wire metal.

5The use of alternating current forces the ions to switch directions of travel many times per second, thus reducing the chance they have of bonding to the metal electrodes.