Logistic fitting model application for evaluation of gas-liquid two-phase mixing effects

The evaluation of mixing effects is crucial in industrial production such as chemical and metallurgical industries. An improved Betti number method is proposed by using a gas-liquid top-blow mixing experiment and a direct contact heat exchange experiment. This method is adapted to the comprehensive evaluation of flow mixing and heat transfer performance under conditions of dispersed particles or bubbles where the target is identifiable. The comparison results and reveals that our method can not only portray the mixing effect by the critical point of the area integration curve of the Betti number time series but also the parameters (i.e., slope and intercept) obtained after the area integration of the Betti number curve by the logistic regression model can effectively characterize the mixing time and heat exchange performance. The intercept variation of the area integral of the Betti number curve was found to have a high correlation with the correlation coefficients of mixing time and heat transfer coefficient. Meanwhile, a new index for evaluating the mixing performance was obtained. The optimal working condition was obtained. This method is simple and easy to implement and can be extended to processes where the target is identifiable in a transparent reactor and where both mixing and heat transfer effects need to be quantified.