## 3 Results
### Rheological Properties  
The relationship between the consistency coefficient (K) and viscosity in carrot juices and purees is well documented. The consistency coefficient measures the thickness or resistance to flow in non-Newtonian fluids, such as carrot puree. It is influenced by factors including mixture concentration and the presence of thickeners [13; 44], which were not present in the tested carrot purees (information from the company). Flow curve analysis (Figure 2) characterized carrot puree as a pseudoplastic fluid with shear thinning behavior (n < 1), exhibiting decreased viscosity with increased shear rate. Power equations were used to describe the resulting flow curves for each temperature (Table 3). Shear thinning behavior is associated with multiphase materials like vegetable and fruit pulps formed by a dispersion of insoluble components (cellular wall materials) in a water solution [45]. As the concentration of carrot puree in vegetable juices increases, there is a corresponding rise in apparent viscosity and yield stress, as shown in Figure 2 and Table 3. The viscosity of carrot puree decreases with rising temperature, following an Arrhenius-type relationship (Table 3). This relationship validates the observed decrease in viscosity as the puree's temperature increases [46; 47]. This trend is also evident when the carrot puree concentration exceeds 17.5% [13]. The study revealed that ultrasound treatment significantly influenced the viscosity of the puree under investigation (Figure 2, Table 3). A noticeable decrease in viscosity was associated with lower extracted values. Notably, no statistically significant changes were observed in the viscosity of carrot puree with 9% extract, possibly due to the more efficient evaporation of water during sonication at lower concentrations [48; 49]. In the literature, it has been observed that ultrasound can both increase the viscosity of avocado puree [50] and decrease the viscosity of orange juices [41]. This effect primarily depends on the concentration of the juice or puree rather than the source, while the presence of small particles can also play a role. An increase in the extract content led to a statistically significant rise in the consistency coefficient K. However, the analysis of the flow behavior index n did not reveal any discernible trend during the increase in extract and the use of US treatment (Table 3). Moreover, elevating the measuring temperature resulted in a decrease in the consistency coefficient K across all the presented experiments, irrespective of the carrot puree extract and US treatment. Nonetheless, this decrease was statistically significant only in the case of the highest carrot puree extract. Similar findings were reported by [PERSON] et al. [51] for aracq pulp and [PERSON] et al. [47] for carrot juices; however, those authors did not use sonication before testing the viscosity and other descriptive values for purees. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Concentration** (°Brix)} & **US** & **Temperature for** & **Apparent Viscosity** & **Consistency** & **Flow Behavior** & **Activation** \\  & **(kHz)** & **Rheology Test** & **(n)** & **Coefficient** & **Index** & **Energy (Ea)** \\  & **(°C)** & **(Pa-s)** & **(Pa-s)** & **(Pa-s)** & **(-)** & **(kJ/mol)** \\ \hline \multirow{6}{*}{9} & \multirow{6}{*}{0} & 20 & 7.79 \(\pm\) 0.01 \({}^{\text{\text{\text@underline{\text{\text{\text{\textasci  
A comparison of the temperature values for each extract and each US treatment revealed a significant increase in the consistency coefficient K in the samples containing 12 \({}^{\circ}\)Brix and 21 \({}^{\circ}\)Brix. However, for the 9 \({}^{\circ}\)Brix extract, the decrease was not significant. Additionally, the tendency for the flow behavior index n to increase with an increase in US frequency was significant only for carrot puree with 12 \({}^{\circ}\)Brix.