Measurement of liquid foam flow through a diverging nozzle

The theory of pneumatic foam describes the transport of liquid by foam rising continuously in a vertical column. At constant cross-sectional area, the liquid foam is assumed to move similar to a plug flow with a uniform distribution of the liquid phase. To assess the pneumatic foam theory in the case of foam flowing through an expansion, we mapped the liquid fraction and measured the local velocity of a steady-state foam flow in a vertically aligned diverging nozzle by means of optical and X-ray imaging techniques. This paper presents and discusses the experimental findings in comparison with the theoretical predictions assuming different models of foam permeability. X-ray radiography revealed that the liquid fraction is decreasing with increasing cross-sectional area in nominal flow direction, which is consistent with the pneumatic foam theory, although the measured liquid fraction was at an overall higher level than predicted. In radial direction, the liquid fraction was found to increase slightly towards the nozzle wall. Similarly, non-uniform velocity profiles that deviate from the expected plug flow were revealed by X-ray particle tracking velocimetry inside the nozzle, combined with foam-adapted particle image velocimetry at the transparent nozzle wall. In conclusion, the advective transport of liquid measured in the nozzle is lower than predicted by the pneumatic foam theory.