Evaluation and prediction of rise velocity and drag coefficient of an ascending bubble affected by the impurity in continuous and discrete phases, distinctly and concurrently

[Display omitted] •Comparing the obtained drag coefficients of bubbles with several correlations.•Development of two correlations for terminal velocity and drag coefficient.•The observed synergistic effect of NPs and hexane vapor on the bubble hydrodynamics.•Comparison of bubble aspect ratio with proposed correlations in literatures. Obtaining a deep knowledge about the bubbly flow systems, which are widely applied in various chemical and industrial processes, is crucial for scholars and engineers to achieve more accurate equipment design and processes control. This paper is dedicated to experimentally investigate the distinctly and concurrently effects of fumed silica nanoparticles (NPs) and hexane vapor molecules as impurities in continuous and discrete phases, respectively, on the terminal velocity and drag coefficient of a single rising bubble in aqueous solutions. The obtained experimental data were compared to the calculated data by derived correlations in literatures. As a result, none of those can predict the experimental data and a new correlation for considering the SiO2 NPs as an impurity in liquid is required. As a novelty, this work proposed two new correlations for prediction of terminal velocity and drag coefficient of a rising bubble in NPs solutions as a function of NPs concentration in aqueous solutions. The proposed correlations of terminal velocity and drag coefficient are in excellent agreements with the experimental data over the range of Re