Volume equalized constitutive equations for foamed polymer solutions

In order to develop a constitutive equation for foamed polymer solutions their flow behavior was investigated in a large‐scale vertical tube. Starting from theoretical considerations, two new constitutive equations are proposed. A new variable−the specific volume expansion ratio−is introduced to characterize the relative gas content of the foam. With the new variable the proposed constitutive equations take simple forms and obey the principle of volume equalizing, i.e., the corresponding Reynolds numbers possess a certain invariance property. The proposed models are fitted to the experimental data. The principle of volume equalizing is checked in light of the current knowledge on foam flow behavior.