## 1 Introduction  
Thermal pasteurization and sterilization are crucial in ensuring food safety and extending shelf life, primarily due to their ability to destroy enzymes and microorganisms. When designing preservation processes for liquid foods, it is essential to maintain the natural quality of the food. However, the nonspecific effects of heat can impact the nutritional and sensory qualities and alter the foods' functional properties. Over the years, various research groups have studied how ultrasound may affect microbial inactivation [1] and physicochemical and nutritional parameters in liquid foods [2], such as juices, purees, and pulps of fruits and vegetables [3], e.g., avocado puree [4], strawberry puree [5], and cashew apple bagasse puree [6], and also cow milk [7] and other beverages, e.g., coconut milk [8; 9]. Food's behavior varies based on the food matrix, necessitating the evaluation of each product before marketing [10]. Carrots are widely cultivated in Poland and are available throughout the year due to their long-term storage capabilities. However, the seasonality of plant materials often results in the overproduction of fruits and vegetables, producing carrot juices and pureses to manage the surplus. Carrot puree is particularly valuable due to its high content of carotenoids and polyphenols, known for their potential health benefits, including boosting immune response and preventing diseases such as eye diseases, cardiovascular diseases, and cancer. Carrot puree is rich in \(\beta\)-carotene and \(\alpha\)-carotene, with steam-blanched puree showing high levels of these nutrients (94.56 \(\upmu\)g/g and 86.62 \(\upmu\)g/g, respectively), which contribute to its nutritional value and color [11]. It also contains significant amounts of total soluble solids (5.50 \({}^{\circ}\)Brix) and specific color values. However, the sensitivity of carotenoids to thermal or physical degradation due to their long conjugated chain of C-C double bonds poses challenges for consumers and producers. Typically, carrot puree used in the food industry contains an extract ranging from 9 to 15%, or 29% in the case of concentrated carrot puree [11]. The viscosity of carrot puree decreases as the shear rate increases, a behavior known as shear thinning. This behavior can be accurately described by the Ostwald-de Waele (Power Law) model with a flow behavior index of 0.34 at 20 \({}^{\circ}\)C [12]. Various preparation methods can affect the consistency of carrot puree. High-pressure homogenization and high-temperature blanching reduce water separation (syneresis), while low-temperature blanching increases it. The order of thermal and mechanical treatments also impacts consistency, with higher consistency achieved when high-temperature treatment is followed by homogenization [12]. Moreover, the apparent viscosity of vegetable juices increases with higher concentrations of carrot puree, with significant changes observed at concentrations above 17.5% [13]. In the literature, the viscosity of carrot puree can be influenced by particle size and the presence of pectin. In blended carrot purees, water-soluble pectin (30.3%), chelator-soluble pectin fraction (42.6%), and sodium-carbonate-soluble pectin fraction (19.9%) were observed in non-heated samples [14]. Homogenization, commonly used in the food industry, tends to reduce particle size, resulting in a smoother consistency, while low-temperature blanching can increase consistency due to enhanced intercellular adhesion [12; 13; 15]. These rheological properties are important for various processes, such as pumping, mixing, pasteurization, and evaporation. Additionally, the physicochemical properties of carrot puree serve as indicators of the product's quality. Furthermore, applying new methods, such as sonication, can enhance the quality of the product [16]. Ultrasounds (USs) are sound waves with frequencies starting from 20 kHz, and their mechanical waves propagate in solids and liquids.