Validation and calibration of a millimeter-wave interferometer for concentration measurements in particle-laden flows

Millimeter-wave interferometry is a novel method for measuring absolute concentrations in opaque dispersed multiphase flows. Its advantages include: the ability to penetrate dense particles clouds with minimal transmission loss compared to optical radiation (i.e., near-visible light), a linear response to volume fraction that is mostly independent of particle properties, the use of safe non-ionizing radiation, kilohertz sampling rates, and compact low-cost hardware. Spatial resolution is the main limiting factor of the technique when sub-wavelength resolution is required. In this work, we compare two methods to calibrate a millimeter-wave radar interferometer for absolute concentration measurements: a direct method that uses known particle concentrations, and an indirect method that relies on measuring the relative permittivity of bulk particle samples. Direct calibration results derived from earlier work by the authors are improved through the use of high-resolution X-ray micro-tomography to measure the particle size distribution and overlap-tolerant particle counting algorithms. The indirect calibration method utilizes a custom interference-based technique to measure the relative permittivity of a bulk powder at millimeter-wave frequencies. Results from both calibration methods agree within 0.7% when using the Lichtenecker logarithmic effective medium equation. The agreement between the two independent calibration procedures validates the theoretical framework of millimeter-wave interferometry.