Non-dimensional mathematical model of magnetized sugarcane juice by micro-filtration membrane separation

Abstract: The physical properties of liquid and the filtration performance of membrane was easily modified by the magnetization process. It meant that the process of membrane separation was difficult to be analyzed because of applying the magnetic field technology. It was also hard to make clear the relationships of all the influence factors just by a simple mathematical derivation, so a suitable non-dimensional mathematical model of membrane flux was used, in order to simulate the separation process of micro-filtration membrane for the magnetized mixed sugarcane juice. The parameters of micro-filtration membrane, operating conditions and flow characteristics of feed liquid were chosen as the main factors in this process, and mathematical statistics were done aiming at the involved parameters and dimensions. A non-dimensional mathematical model was established according to the π theorem, the dimensional consistency principle and the hydromechanics affinity theory. The results showed that the non-dimensional mathematical model mainly consisted of three important dimensionless parameters. The first one was Reynolds number, which represents the characteristics of fluid during the operating process. The second one was Euler number, which represents the characteristics of micro-filtration membrane. The last one was a new Sy number, which shows the group of dimensionless factors associated with physical property parameters of liquid and intensity of magnetic field. In order to verify the accuracy and the practicability of the model, the mixed sugarcane juice was used as a raw material for solving the non-dimensional mathematical model. The magnetic field intensities of 0.1, 0.2, 0.3 and 0.4 T were applied to deal with the mixed sugarcane juice, and the total reflux experiments were used in the process. The membrane flux was determined under the changed conditions of pressure difference between inlet and outlet of membrane, and flow rate, brix and viscosity of feed liquid. All of these parameters and membrane flux were calculated using the established model. The results showed that the coefficient of determination R2 of the multivariate regression model was 0.905, and the standard error was 0.173. The F value of variance analysis was 413.604, and the significance probability was 3.911×10-134. The P values of q, Reynolds number (x1), Euler number (x2) and two groups of dimensionless factors (x3 and x4) in the model were 7.217×10-96, 7.174×10-127, 4.420×10-6, 0.283 and 8.129×10-24, respectively. The influence order of model factors from high to low was as follows: x1, q, x4, x2 and x3. The results showed that the main flow velocity, operating temperature, intensity of magnetic field and characteristic parameters of membrane tube had great influence on the membrane flux, and the regression analysis model had a high precision. The applied scopes of the model were as follows: 0.050-0.130 MPa pressure difference, flow rate of 2.6-3.9 m/s, brix of 14.5%-16.6%, pH value of 5.00-5.90, operating temperature of 25-60℃, magnetic field intensity of 0-0.4 T, membrane pore size of 0.20-0.45 μm. The model can predict the membrane flux of magnetic mixed sugarcane juice in the micro-filtration membrane separation process under certain parameters, which provides a simple calculation method for the micro-filtration membrane device design and the operating process conditions.