## 3 Results and Discussion
### Overrun, Air Phase Fraction and Rheology of Liquid Foams  
The foamability of analyzed WPI solutions is expressed as foam overrun (OR). Table 2 shows the overrun and corresponding air phase fraction (\(\Phi\)) values for liquid foams. The OR and \(\Phi\) values increased with the increasing sugar concentration up to 10%. The highest OR was observed for the WPI/10% sucrose solution. For the sample containing 15% of sugar, significant decrements in the OR and \(\Phi\) were recorded. A similar effect of sucrose on protein foamability was observed by [PERSON] et al. (2011) and [PERSON] (2011). According to [PERSON] and [PERSON] (2017), the rheological properties of WPI foams depend on the \(\Phi\) values. The values of \(\Phi\)\(\geq\) 0.88 indicate that their bubbles have a polyhedral shape and the increase in air fraction volume leads to an improvement in the rheological properties and stability of the foams. Since foams are unstable systems, small strain rheology was used to determine their rheological properties. The G\({}^{\prime}\) (storage modulus), G\({}^{\prime\prime}\) (loss modulus) and tan (\(\delta\)) values of the obtained foams are shown in Figure 3. Tan (\(\delta\)) demonstrates the relative input of elastic and viscous properties of the sample (tan \(\delta\) = G\({}^{\prime\prime}\)/G\({}^{\prime}\)). When tan (\(\delta\)) is less than 1, the structure is elastic and G\({}^{\prime}\) value is greater than G\({}^{\prime\prime}\). The findings show that G\({}^{\prime}\) dominated over the G\({}^{\prime\prime}\) in all frequency ranges indicating a solid-like behavior of the analyzed foams. For the samples, G\({}^{\prime}\) is about 4 times greater than G\({}^{\prime\prime}\), which is characteristic of weak physical gels. For stronger gels, tan (\(\delta\)) is closer to 0.1 ([PERSON] et al., 2017). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **OR (\%)** & \(\Phi\) \\ \hline
20\% WPI/0\% sucrose & 661.82 \({}^{\circ}\) \(\pm\) 8.44 & 0.867 \({}^{\circ}\)\(\pm\) 0.001 \\
20\% WPI/5\% sucrose & 699.13 \({}^{\circ}\)\(\pm\) 7.63 & 0.874 \({}^{\circ}\)\(\pm\) 0.001 \\
20\% WPI/10\% sucrose & 724.21 \({}^{\circ}\)\(\pm\) 6.76 & 0.878 \({}^{\circ}\)\(\pm\) 0.001 \\
20\% WPI/15\% sucrose & 642.05 \({}^{\circ}\)\(\pm\) 5.16 & 0.864 \({}^{\circ}\)\(\pm\) 0.001 \\ \hline \hline \end{tabular}  
* The differences among the mean values in the column designated with different letters are statistically significant (\(p<0.05\)).  
\end{table} 
Table 2: Overrun (OR) and air phase fraction (\(\Phi\)) values measured for the liquid foams. Figure 3: Frequency sweep experiment of the analyzed liquid foams. The graph represents one replication. The G\({}^{\prime}\) and G\({}^{\prime\prime}\) results show that frequency demonstrates a significant impact on the structure of the foams. Initially, the G\({}^{\prime}\) values decreased, which indicates the changes in the foam structure, most probably by breaking unstable laminar layers in the bubbles. Next, an increase in elasticity is observed most likely due to merging of bubbles, which simultaneously proves greater stability and higher G\({}^{\prime}\) value. An increase in elasticity with the increasing frequency follows directly from the Deborah number. The materials with the low Deborah number are elastic substances, also characterized by the high value of the G\({}^{\prime}\) relating to G\({}^{\prime\prime}\)[33]. Increasing the sugar content up to 10% increased the rheological properties of foams while the WPI/10% sample was the strongest foam, which was reflected in the G\({}^{\prime}\) and G\({}^{\prime\prime}\) values. The lowest G\({}^{\prime}\) and G\({}^{\prime\prime}\) values were observed for the WPI/15% sample, which confirms the decrease in its rheological properties. The lowest value of tan (\(\delta\)) was recorded for the WPI/10% sample.