Some characteristics of membrane DO probes are:

The pH of the solution does not affect the performance of membrane probes.

Chlorine and hydrogen sulfide(H₂S) cause erroneous readings in DO probes.

Atmospheric pressure (altitude above sea level) affects the saturation of oxygen. DO probes must be calibrated for the barometric pressure when reading in mg/l.

Membrane thickness determines the output level of the probe.

Membrane thickness also determines the speed of response to change in DO levels.

As the temperature increases, the permeability of the membrane increases, permitting more oxygen to enter the probe. An internal thermistor automatically compensates for the error due to the permeability of the membrane.

 

At constant temperature, the current, I, given by a membrane covered solid electrode system for oxygen is given by:

I ~ k a P /b

where: a is the indicating electrode area

P is the membrane permeability coefficient

b is the membrane thickness.

At constant oxygen concentration, the current I_T at temperature T ^oK is given by:

I_T = K e ^-J/T

where J and K are constants for a particular cell geometry and membrane. Temperature coefficient of about 5% per ^oC is common for most membranes at 25^oC.

Compensation for the high temperature coefficient of the membrane is possible with the proper selection of a thermistor since the relation between their resistance and temperature is given by:

R_T = A e ^+B/T

where A and B are constants for a given thermistor.

Combining the two equations, the output voltage (IR) of the DO probe will be independent of temperature if the membrane and thermistor are selected so that K=A and J=B.

Since all the oxygen that passes through the membrane reacts with the cathode and since the amount of oxygen that passes through the membrane is a function of the partial pressure of the oxygen in solution, the measurement is actually the partial pressure of the oxygen in solution.

The Clark-type cell consist of a pair of electrodes separated from the sample by a semi-permeable membrane. This membrane permits the oxygen dissolved in the sample to pass through it to the electrodes while preventing liquids and ionic salts from entering.

The cathode is a hydrogen electrode and carries a negative potential with respect to the anode. Electrolyte surrounds the electrode pair and is contained by the membrane. With no oxygen, the cathode becomes polarized with hydrogen and resist the flow of current. When oxygen passes through the membrane, the cathode is depolarized and electrons are consumed. The cathode electrochemically reduce the oxygen to hydroxyl ions:

O₂ + 2 H₂O + 4 e^- = 4 OH^-

The anode reacts with the product of the depolarization with a corresponding release of electrons.

Zn + 4 OH^- = Zn(OH)₄^2- + 2e-

The electrode pair permits current to flow in direct proportion to the amount of oxygen entering the system. The magnitude of the current gives us a direct measure of the amount of oxygen entering the probe.

Because all of the oxygen entering the probe is chemically consumed, the partial pressure of oxygen in the electrolyte is zero. Therefore, a partial pressure gradient exists across the membrane and the rate of oxygen entering the probe is a function of the partial pressure of oxygen in the air or water being measured.

Since the partial pressure of dissolved oxygen is a function of temperature of the sample, the probe must be calibrated at the sample temperature or the probe’s meter must automatically compensate for varying sample temperature. Note that this thermal effect is different from the thermal response of the membrane discussed above.

The reading of a DO probe must be corrected for the amount of salt in the sample. As noted above, the salt in solution will reduce the actual concentration of oxygen.

In all DO Probes, the membrane/sample interface should have a few cm/sec flow of the sample for precision performance. Without flow at the interface, the surrounding oxygen will be consumed and the local reading drops. The output of the probe increases with relative movement between the probe and sample.

DISSOLVED OXYGEN MEASUREMENT

The amount of oxygen that a given volume of water can hold is a function of the atmosphere pressure at the water-air interface; the temperature of the water; and the amount of other dissolved substances (such as salts or other gases) in the water. Recall seeing bubbles in a pot of water just before it starts to boil. These bubbles are the air which was dissolved in the water at room temperature. When the water boils, the dissolved oxygen is ejected—warmer water contains less DO. When other substances, such as salts, are dissolved in a unit volume of water, there is less room for oxygen to dissolve—oxygen is less soluble than most salts

The following table shows the relationship of dissolved oxygen (mg/L) to temperature and salinity:

The relationship between temperature, salinity, and dissolved oxygen is approximated with the following exponential equation:

ln( C ) = -139.34 + (1.5757 x 10⁵/T) - (6.6432 x 10⁷/T²) + (1.2438 x 10¹⁰/T³)

- (8.6219 x 10¹¹/T⁴) - S [1.7674 x 10^-2 - (10.754/T) + (2.1407 x 10³/T²)]

T = Temperature in degree Kelvin

S = Salinity in parts per thousand (ppt)

C = Concentration in mg/L

As the pressure of the air above the water is increased, more oxygen will be dissolved in the water. This increases the concentration of the dissolved oxygen. The solubility of a gas in a liquid is directly proportional to the pressure of that gas above the liquid—Henry’s law. This is often expressed as:

p = k C (C = concentration of DO)

If different gases are mixed in a confined space of constant volume and at a definite temperature, each gas exerts the same pressure as if it alone occupied the space. The pressure of the mixture as a whole is the total of the individual or partial pressure of the gases composing the mixture—Dalton’s law of partial pressures. The partial pressure of each gas is proportional to the number of molecules of that gas in the mixture. Air is 20.948% oxygen. When air bubbled through water, only 20% as much oxygen dissolves as would dissolve if pure oxygen were used instead of air, at the same pressure.

Combining Henry’s and Dalton’s Laws for the concentration of dissolved oxygen:

Concentration of dissolved oxygen is also measured in units of % saturation. % saturation is simply the ratio of the measured mg/L of dissolved oxygen divided by the mg/L of dissolved oxygen at saturation—as given in the above tables, saturation levels is dependent upon the temperature, salinity, and pressure. Since % saturation is a ratio, it is not affected by these conditions if the calibration at 100% saturation was performed under the same conditions.

Solubility of solutes as a function of temperature (mg of solutes per liter of water):

Solubility of gases in water (ml/L):

With stationary, continuously monitoring Dissolved Oxygen Probes, the source of the oxygen being measured is air. Thus, Dissolved Oxygen in air saturated water (mg/l or ppm) as a function of temperature is determined by:

Solubility (ml/L) x Density (mg/ml) x % in air = saturated DO in mg/L (ppm)

Solubility (mg/L) x % in air = saturated DO in mg/L (ppm)

Increasing temperature usually increases the solubility of solids and liquids whereas it reduces the solubility of gases. Also keep your units straight--mg/L, ppm, ml/L, % saturation.