Methods and apparatus for determining the spatial distribution of materials using electromagnetic radiation

1. An apparatus for determining the spatial distribution of materials, the apparatus comprising:

an elongate tubular conducting channel, and a central elongate conducting electrode aligned within the channel such that the channel and the electrode comprises a waveguide for transverse electromagnetic (TEM) modes;

a source of electromagnetic waves across a range of frequencies, wherein the source is configured to emit electromagnetic waves into a sample along an axis;

a detector configured to detect the electromagnetic waves across the range of frequencies emitted by the source, wherein the detector is positioned to receive electromagnetic waves after the electromagnetic waves have interacted with the sample by at least one of: reflection and transmission, and wherein the detector is configured to detect a frequency response of the received electromagnetic waves; and

a controller configured to process the frequency response of the received electromagnetic waves to determine an axial spatial distribution of materials within the sample.

2. The apparatus of claim 1 , wherein the source and detector form part of a vector network analyzer.

3. The apparatus of claim 1 , wherein the detector is configured to receive electromagnetic waves which have interacted with the sample at least 10 cm away from the source.

4. The apparatus of claim 1 , wherein the detector comprises a reflection sensor and a transmission sensor.

5. The apparatus of claim 1 , wherein the range of frequencies spans frequencies between 2 Mhz and 6 GHz.

6. The apparatus of claim 1 , wherein a ratio of the highest frequency to the lowest frequency in the range of frequencies is greater than 1000.

7. The apparatus of claim 1 , wherein the apparatus comprises a waveguide comprising two aligned conductors configured to support Transverse Electro-Magnetic (TEM) modes within the waveguide.

8. The apparatus of claim 1 , wherein the controller is configured to:

determine a time-dependent amplitude of the received electromagnetic waves from the measured frequency response;

based on the time-dependent amplitude of the received electromagnetic waves to determine an axial speed of the electromagnetic waves as a function of axial distance from the source; and

determine an axial spatial distribution of materials within the sample based on the determined axial speed.

9. The apparatus of claim 1 , wherein the apparatus comprises plugs for closing the ends of the channel, the plugs having ports to allow liquid to be exchanged with the channel.

10. The apparatus according to claim 1 , wherein the apparatus comprises one or more of:

a resilient sheath within the channel, and a pump configured to introduce fluid between the sheath and the channel to apply a lateral pressure on the sample within the sheath; and

blocks for closing the ends of the channel, the blocks being moveable to apply an axial pressure on the sample.

11. The apparatus of claim 1 , wherein the channel is impermeable and forms a container for the sample.

12. The apparatus of claim 1 , wherein the channel is porous and is configured to allow fluid communication through the channel.

13. A tank comprising:

an elongate tubular conducting channel, and a central elongate conducting electrode aligned within the channel such that the channel and the electrode comprises a waveguide for transverse electromagnetic (TEM) modes;

a source of electromagnetic waves across a range of frequencies, wherein the source is configured to emit electromagnetic waves into a sample along an axis;

a detector configured to detect the electromagnetic waves across the range of frequencies emitted by the source, wherein the detector is positioned to receive electromagnetic waves after the electromagnetic waves have interacted with the sample by at least one of:

reflection and transmission, and wherein the detector is configured to detect a frequency response of the received electromagnetic waves; and

a controller configured to process the frequency response of the received electromagnetic waves to determine an axial spatial distribution of materials within the sample; and,

wherein the apparatus is arranged such to determine a spatial distribution of materials within the tank along a vertical axis.

14. A method of determining the spatial distribution of materials, the method comprising:

emitting electromagnetic waves across a range of frequencies into a sample along an axis;

pumping fluid comprising nanoparticles through the sample;

detecting electromagnetic waves across the range of frequencies emitted by a source, wherein the detected electromagnetic waves have interacted with the sample by at least one of:

reflection and transmission, and wherein a detector is configured to detect a frequency response of the detected electromagnetic waves; and

processing the frequency response of the detected electromagnetic waves to determine an axial spatial distribution of materials within the sample.

15. The method according to claim 14 , wherein the sample comprises a liquid permeable solid matrix, and wherein the method comprises:

fully saturating the matrix with a first fluid and recording a first-fluid frequency response of the received electromagnetic waves;

introducing a second fluid into the matrix and recording an intermediate frequency response of the received electromagnetic waves;

determining the axial spatial saturation of the second fluid within the matrix based on a comparison between the first-fluid frequency response and the intermediate frequency response.

16. The method according to claim 14 , wherein the method comprises pumping fluid through the sample.

17. The method according to claim 14 , wherein the method comprises pumping saline fluid through the sample and determining salinity concentration profiles.

18. The method according to claim 14 , wherein the sample comprises foam.