Modification of the Young–Laplace equation and prediction of bubble interface in the presence of nanoparticles

•A new method is developed to predict the bubble shape while (a) bubble is oscillating in bubble growth period, (b) bubble is stretched upward in bubble departure period or (c) shear stress and inertial force are not negligible when gas flow rate is relatively high.•Using the new method, the pressure difference between gas and liquid is calculated at the bubble interface while bubble is fluctuating.•The bubble fluctuation and oscillation of liquid–gas interface are observed only when bubble is grown from substrate nozzles. For the same conditions, the bubble formation from needle is noticed to be steady.•Effect of concentration of gold nanofluid on dynamics of triple line and bubble growth is investigated.

Bubbles are fundamental to our daily life and have wide applications such as in the chemical and petrochemical industry, pharmaceutical engineering, mineral processing and colloids engineering. This paper reviews the existing theoretical and experimental bubble studies, with a special focus on the dynamics of triple line and the influence of nanoparticles on the bubble growth and departure process. Nanoparticles are found to influence significantly the effective interfacial properties and the dynamics of triple line, whose effects are dependent on the particle morphology and their interaction with the substrate. While the Young–Laplace equation is widely applied to predict the bubble shape, its application is limited under highly non-equilibrium conditions. Using gold nanoparticle as an example, new experimental study is conducted to reveal the particle concentration influence on the behaviour of triple line and bubble dynamics. A new method is developed to predict the bubble shape when the interfacial equilibrium conditions cannot be met, such as during the oscillation period. The method is used to calculate the pressure difference between the gas and liquid phases, which is shown to oscillate across the liquid–gas interface and is responsible for the interface fluctuation. The comparison of the theoretical study with the experimental data shows a very good agreement, which suggests its potential application to predict bubble shape during non-equilibrium conditions.

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