## 1 Introduction  
Over the last three decades, significant progress has been witnessed in the theoretical understanding of liquid-liquid binary mixtures [1, 2], keeping in view that the prediction of the few important properties like density, viscosity, and the excess properties, is related to their engineering performance. Studies on the theoretical modelling of thermodynamic and engineering properties have been carried out on alcohol-based binary/ternary mixtures like water and ethanol [3], 1,3,5-trimethyladamantane + 1,2,3,4-tetrahydronaphthalene + n-octanol and corresponding binary systems [4], n-hexane, ethanol, and cyclopentyl methyl ether [5],pentanol + ethyl cyclohexane + methyl myristate and corresponding binary systems [6] and ethylene glycol-based ternary mixture [7]. The knowledge of the thermodynamic and transport properties of alcohol-based binary mixtures can be used to develop theoretical models and for the design of new technologies. Importantly, information on the dynamic viscosity of liquid mixtures can be used in chemical engineering calculations involving fluid, heat, and mass transfer [8]. The experimental viscosity data of ethanol-based liquid mixtures (ethanol + 1-hexanol and ethanol + 1-heptanol) have been reported [9]. The viscosity for binary mixtures containing n-hexanol and ethyl valerate or hexyl acetate, as well the details on negative viscosity deviations over the entire composition have been presented [10]. The viscosity of binary systems containing n-hexanol and other related details has been reported [11; 12; 13; 14]. The deviation in the viscosity data was correlated with its composition using polynomial models, and details on the interpretation of molecular interactions, as well as on the transport and ultrasound properties of binary liquid solutions are presented [15; 16; 17; 18; 19; 20; 21]. Studies on viscosity, a transport property, have been used in terms of modelling and simulation, and the activation energy values as determined by Arrhenius plots have been detailed [22; 23]. It has been notified that liquid viscosity is highly affected by the heat and decreases with an increase in temperature [22]. Most liquids have an exponential relationship between temperature and viscosity rather than linear dependence. Ultrasonic properties and their variation within the composition of the binary mixture are useful to design engineering processes and in chemical and biological industries. Ultrasonic velocity is useful to investigate the molecular interactions between the components of the mixture. The measurement of ultrasonic velocity is the only direct method to determine isentropic compressibility, which then provides further access to the related thermodynamic properties of the liquids and liquid mixtures [24; 25; 26]. Ultrasound measurements are one of the most widely used techniques in the investigation of liquids and are essential in the construction and validation of fundamental equations of its state. The present investigation is focused on the first-time theoretical evaluation of the viscosity, density and ultrasonic properties of two binary liquid mixtures: ethanol + 1-hexanol and ethanol + 1-octanol at 303.15 K, to decide on the deviation of the values of the properties as well to know the average percentage of deviation (APD). In this work, the experimental value of the properties was taken as reference from the literature [27]. The experimental viscosities were compared with various theoretical methods like the [PERSON] relation (\(\eta\)H) [28], [PERSON] and [PERSON] relation (\(\eta\)K-M) [29], [PERSON] relation (\(\eta\)B), Arrhenius-Eyring relation (\(\eta\)AE), Croenauer-Rothfus Kermore relation (\(\eta\)CRK) and [PERSON] relation (\(\eta\)G) [30]. Turning to the other study in this work, the experimental densities were compared by deriving the values through theoretical methods like the [PERSON] model (\(\varrho\)MNM) [31], [PERSON] and Thomson model (\(\varrho\)HT) [32], [PERSON] and Gunn model (\(\varrho\)YG) [33] and [PERSON] et al. model (\(\varrho\)R) [34].