**4.1 Effect of foam quality and texture**

 Foam quality and its texture have a strong impact on the viscosity of CO2 foam [45, 46]. A simultaneous study of foam texture is important during the foam rheology measurements [47–49]. Before starting the viscosity measurements, it is important to ensure that the flow loop is completely filled with the foam of known foam quality. It has been reported by many researchers that the rheology of foam is dependent on foam quality and foam apparent viscosity [38, 48, 50–53]. Foam quality (*fq*) is defined as the volume fraction of gas in foam [54–56] and is expressed as Eq. (1).

$$f\_q = \frac{V\_\mathcal{g}}{V\_\mathcal{g} + V\_l} \tag{1}$$

 where *Vg* and *Vl* are gas and liquid volume in foam, respectively.

When the foam is relatively wet, i.e., at low quality, the foam bubbles are less in number and are far apart with no interaction with each other during the foam flow. Therefore, the foam viscosity is low.

 When the foams have low foam quality (i.e. relatively wet foam), the interaction of dispersed gas bubble is insignificant during the foam flow and due to this reason viscosity of foam decreases ; whereas at high foam quality, i.e., when the foam is dry, the interaction of bubble will be quite significant during the foam flow and the friction between the individual bubbles will result in the drastic increase in foam apparent viscosity. In the case of dry foam with very high foam quality, the bubble cannot sustain and breakdown occurs during which a sharp decrease in foam viscosity occurs [43].

### **4.2 Effect of shear rate**

The applied shear rate has a significant impact on foam apparent viscosity. The changes in the foam apparent viscosity at different shear rate display power law behavior. Ahmed et al. [84] tested high quality polymer free foams and reported

a typical shear thinning behavior within the shear rate range (10–500 s<sup>−</sup><sup>1</sup> ). The viscosity of foam decreases in shear flow due to Rayleigh-Taylor instability, which causes the tensile deformation, stretching, and rupturing of lamella [41, 57].
