Bubbles with different sizes have different dynamic and kinetic behavior in a two-phase bubbly flow. A common two-fluid model based on the uniform bubble size assumption is not suitable for a bubbly flow with non-uniform bubble sizes. To deal with non-uniform bubbly flows, a multi-fluid model is established, with which bubbles are divided into several groups according to their sizes and a set of basic equations is derived for each group of bubbles with almost the same size. Through analyzing the bubble-bubble and bubble-pipe wall interactions, two new constitutive laws for the wall-force and pressure difference between the liquid phase and interface are developed to close the averaged basic equations. The respective phase distributions for each group of bubbles measured by a specially designed three-dimensional photographic method are used to check the model. Comparison between model-predicted values and experimental data shows that the model can describe laminar bubbly flow with non-uniform bubble sizes.
