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In Fig. 1, two plates of a given material are placed in a solution. The geometry is given by the lenght L of the liquid column between the plates and the cross sectional area A of the liquid column. If an AC voltage E is connected across the two plates (called electrodes), ions will move between the electrodes, and an electric current I will start to flow.
Fig. 1: Setup to measure conductivity of a solution
Conductivity is denoted by the symbol κ (kappa) and bears the unit Siemens per centimeter S / cm.
Fig. 2: Conductivity versus Resistivity
For ultrapure water applications the reciprocal value of conductivity, called resistivity is common. Resistivity is expressed as Ohm cm (Ω cm). Some corresponding values are shown in Fig. 2.
In a cell using 1 cm squares of platinum, 1 cm apart, the cell constant is 1.0 cm-1 and the conductance reading in µS is numerically equal to the conductivity reading in µS / cm. For low conductivity solutions, the electrodes can be placed closer together (reducing L) to give cell constants of 0.1 cm-1 or 0.01 cm-1. This raises the conductance between the plates and makes it easier for the electronic circuitry to obtain a result. Similarly, for high conductivity solutions, L can be increased to give a cell constant of 10.0 or more.
Alternative sensors have been developed to overcome the problems associated with traditional cells : 4-electrode conductivity sensors consist of two current and two voltage electrodes. Polarization occurs only at the current electrodes while a voltage drop is measured between the voltage electrodes where polarization has no effect. The advantage of such a sensor are as follows:
- No polarization
- Wide measuring range with a single cell constant
- Suitable sensor dimensions.
The sensor is designed in a way that part of the liquid media forms a closed conductive current path passing trough the toroids.
The primary coil is activated with a sinusoidal alternating voltage creating a magnetic field. In liquids which conduct electricity, this causes a current flow proportional to the conductivity of the sample solution. The liquid loop acts at the same time as the primary winding of the secondary coil where the magnetic field induces a voltage. This current is rectified to the correct phase and amplified. An inductive sensor has the following advantages:
- No polarization
- Insensitive to contamination, fouling or film formation on the sensor surface
- Total galvanic separation of the measuring components from the process media.
κ†: Conductivity at T†
κ0: Conductivity at T0
α0: Temperature coefficient at T0
T†: Measured temperature
T0: Reference temperature
In ultrapure water, the change in conductivity by increasing the temperature is much greater than in high-conductivity solutions. Fig. 3 shows this dependency over a temperature range from 0ºC to 100ºC. The temperature coefficient changes from 7.3%/ºC at 0ºC to 2.3%/ºC at 100ºC. It is obvious that the function is not linear.
Fig. 3: Resistivity of ultrapure water at various temperatures
The temperature-dependency, which also depends on the concentration, is different for each component. Usually the temperature coefficient varies between 1% and 6% per ºC.
For natural water and most salt solutions, the temperature coefficient is approx. 2 %/ºC. For strong acids, the temperature coefficient is approx. 1.9%/ºC. For strong bases, the temperature coefficient is approx. 1.6%/ºC.
κ25: Conductivity at 25 ºC
κ†: Conductivity at temperature T
α: Temperature coefficient
Unfortunately, some solutions do not have a linear relation between conductivity and temperature. These relations require polynomial equations in order to arrive at accurate results. Today’s microprocessor-driven analyzers easily manage customers’ requirements.
Fig. 4: Maximum conductivity limits for online conductivity measurements
Specific demands for the measurement equipment (sensor and transmitter) are described in the guideline and in Fig. 5.
Sensors must show a cell constant accuracy of less than 2%, while several specifications needs to be fulfilled by the transmitter.
Fig. 5: Specific demands for measurement equipment