Effects of wall temperature and temperature-dependent viscosity on maximum spreading of water-in-oil emulsion droplet

Abstract

The study is focused on the spreading dynamics of the droplets of n-decane and water-in-oil emulsions based on n-decane and isoparaffinic oil stabilized by different nonionic surfactants. The droplets fall on a solid glass surface heated up to 70–390 °C at Weber numbers of 100–500 and Ohnesorge numbers of 0.001–0.008. Five hydrodynamic outcomes of the droplet impact on a heated surface are experimentally identified, including deposition, bouncing, contact splashing, film splashing, and rebound. The maximum spreading of droplets of the liquids is quantified given their temperature-dependent dynamic viscosity. As a result, a universal empirical model for maximum droplet spreading diameter, βmax=(T*WeOhT–1)1/8 + 0.15, is proposed, taking into account the overall effects of temperature-dependent dynamic viscosity, surface tension, and explicit impact surface temperature term. The model has been successfully tested using the experimental data on the maximum droplet spreading diameters for pure hydrocarbons, commercial hydrocarbon liquid fuels, and biofuel at Weber numbers of 60–900, Ohnesorge numbers of 0.002–0.015, and impact surface temperature of 25–210 °C. The values of the maximum droplet spreading diameter predicted by the model are compared with those determined by the empirical expression by Bhat et al. (2019) for single- and multi-component liquid fuels, also involving an explicit surface temperature term. The model by Bhat et al. (2019) is modified by introducing the temperature-dependent viscosity leading to the significant decrease in the relative mean error between the experimental and predicted values of the maximum droplet spreading diameter. The findings related to the no-slip condition for the viscous liquids are critically important in modeling the conjugate problems of fluid mechanics and heat mass transfer used in the fuel-air mixture formation in combustion chambers.