If the equation relating to isotope dilution (11.15) is deducted not to material vol­ume (V), but to tracer volume (Vj), the reverse isotope dilution equation is obtained:

(11.24)

This equation is valid not only for volumes but also for the mass of materials.

When applying the reverse isotope dilution method (discussed in Section 10.1.6.2), the volume of the tracer is intended to determine. This requires knowledge of the total volume in which the radioactive tracer of known activity is mixed.

Such investigation is, for example, a wear study carried out with the radiotracer technique (Figure 11.16). The plug of a motor vehicle is a part that is particularly exposed to wear. For the study, a plug in its full mass is neutron-irradiated in the research reactor or locally irradiated with charged particles in a cyclotron, and then the radioactive part is inserted into the motor. Fine particles from the plug of the running motor get into the lubrication oil as the result of wearing. The oil volume/ mass and activity on the plug are measured prior to the test. This is followed by measuring the radioactive concentration/specific activity of the oil contaminated with worn particles. Then, using the equation related to reversed isotope dilution, either volume or mass of the radioactive tracer (worn particles in the oil) can be calculated.

In addition to wear studies, other corrosion processes can be tested by the reverse isotope dilution method. Such tests are wear of enamels, removal of surface degreasers at galvanization, and chromium loss at welding technologies.

Figure 11.16 A wear study of a radioactive plug built into the motor of a vehicle.

11.2.1 Groundwater Flow Studies

The linear velocity of groundwater can be determined by determining the dilution of a tracer as a function of time. Concentration decreases over time t at a ground­water flow with a Q flow rate according to the following equation:

dc _ Qc d t _ ~V

where V is the volume of the labeled water column, and c is the radioactive con­centration of the tracer at a time t.

Introducing an internal cross section of the well (A), the groundwater velocity v can be determined by integrating Eq. (11.25) as follows:

Consequently, for determining the flow velocity of groundwater, a continuous decrease of radioactive concentration of the tracer injected instantaneously into the well is measured (Figure 11.17).

A measuring probe automatically detects the residual concentration of the radio­active tracer diluted continuously with groundwater, while a connected meter records the concentration versus time plot (Figure 11.18).

To determine the direction of the groundwater flow, the intensity plot of the radioactive tracer escaping from the well is recorded for every direction. This can be done by rotating a probe sunken into the well which is collimated (opened) in one direction. The plot of a rotating probe is shown in Figure 11.19. The flow direction of the groundwater corresponds to the direction of the longest drawn tracer spot on the plot.

Groundwater flow velocity and flow direction studies serve typically to determine local conditions, while large field flow conditions are better determined by measuring

1— Scintillation detector

2— Lead shielding

3— Sealing balloon

4— Sealing balloon

5— Tracer injector

6— Tracer mixer

7— Rotating detector

8— Scaler

9—

Data logger

water level changes in several drilled wells. Mapping groundwater local flow condi­tions were executed in practice in the surrounding of industrial waste repositories.