Time and surfactant types dependent model of foams based on the Herschel-Bulkley model

- Drainage rate of foams including three stages was investigated.
- The drainage of AFFF (3%) has obvious effect on apparent viscosity before 600 s.
- A Herschel-Bulkley modified model was built, which was relating to time and foam index.
- Foam index of the modified model is decided by surfactant types and concentration.

Due to the special topological structure of foams changing with time, the instantaneously rheological properties of foams was difficult to study. Then an online measurement was designed to explore the relation of drainage time and rheological behavior. Foams evolution and drainage process from generation to demise were firstly investigated by SiGe300 image analysis system and electronic scale at atmospheric pressure, respectively. The evolving images of foams show that the polyhedron foams begin to appear at almost 200 s, however, the sphere (or ellipsoid) foams almost become polyhedron at 550-600 s. The drainage rate is divided into three stages: increasing stage, dropping stage and stabilizing stage. Meanwhile, the superficial velocity associating with gas and liquid for dropping stage is calculated, it indicates that gas phase will be beneficial to liquid-hold. A modified rheological model is theoretically proposed that combines with Herschel-Bulkley model, structural damage coefficient and foam index (m). In addition, the foam index is decided by surfactant types and concentration rather than shear rate and drainage time; structural damage coefficient is related to the initial expansion ratio and instantaneously mean expansion ratio. The continuously apparent viscosity of AFFF (3%) at any shear rates and drainage time can be obtained with instantaneously mean expansion ratio less than 48× (48 times). Finally, modified model was imported into the commercial software ANSYS Fluent-15.0 to build material properties of foams. It shows that the distribution of apparent viscosity changes with instantaneously mean expansion ratio.

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