Towards a model of bubble breakup in turbulence through experimental constraints

Abstract

Complex bubble breakup in turbulence has been studied and modeled extensively by employing the population balance equation. This equation hinges on two quantities, i.e. daughter bubble size distribution and breakup frequency. Since there is no first-principle equation that can be solved to calculate these two quantities, many phenomenological models based on different physical mechanisms have been proposed. A large number of possible mechanisms at play leads to models with drastically different, and even contradictory, predictions. In contrast, experimental measurements of these two quantities, including several previous works and our own results collected in a vertical water tunnel that features a large homogeneous and isotropic region, seem to be consistent with one another. To resolve the difference between models and experiments, rather than following another physical argument, we approach the problem from a different direction by asking how to constrain a model based on experimental results. The specific constraints extracted from eight experimental results include: (i) direct measurements of daughter bubble size distribution; (ii) Super-Hinze-scale bubble size spectrum for constraining breakup frequency; (iii) Sub-Hinze-scale bubble size spectrum for modeling daughter bubble size distribution; (iv) Convergence time to an equilibrium state. Finally, based on these experimental constraints, a new breakup model that incorporates a corrected formulation for breakup frequency as well as a simplified function for daughter bubble distribution is developed to meet all constraints. Although the new model is deliberately not connected to any specific physical arguments for simplification, it appears to be robust and consistent with all experimental constraints mentioned.