CFD-PBM Investigation On Droplet Size Distribution In A Liquid-liquid Stirred Tank

Accurate prediction and control of droplet size distribution(DSD),which is one of the most important indexs for the function and quality of liquid-liquid dispersion products,has been a pressing problem in industry.For liquid-liquid dispersion systems in stirred tanks,existing experimental methods are difficult to measure the local flow field and DSD conveniently and inexpensively and to predict them accurately.Computational fluid dynamics(CFD)can predict the variation of the flow field in a stirred tank with geometry,impeller design and operating conditions,and population balance modeling(PBM)can simulate the spatial and temporal size distribution of droplets due to coalescence and breakage.The combination of CFD and PBM has been applied to study liquid-liquid dispersion systems in different dispersion equipment.However,the study of liquid-liquid stirred tanks by CFD-PBM is still not deep and comprehensive enough.The mechanism of the influence of the flow field formed by different impellers on DSD is still to be explored,the existing simulation schemes ignore the interaction between surfactant and droplets,and the accuracy of DSD prediction in liquid-liquid stirred tank in the presence of surfactant is still to be improved.Based on the experimental validation,this paper adopts the numerical simulation method of three-dimension CFD-PBM coupling,and firstly explores the relationship between the action of impeller design,flow field and liquid-liquid dispersion characteristics in the absence of surfactant;for the liquid-liquid dispersion system containing surfactant,innovatively proposes to adopt the inter-phase mass transfer model to modify CFD-PBM,analyzes the modification effect of three coalescence models,and the mechanism of the effect of surfactant type and concentration on DSD was investigated in depth;the modified CFD-PBM coupled model was used to investigate the complex effects of the rheological characteristics of the dispersed phase and the corresponding flow field on the DSD of the surfactant-containing system,and to provide a basis for the prediction and control of the DSD in the liquid-liquid mixing tank of industrial processes.The main work and conclusions of this paper are summarized as follows.(1)CFD-PBM was used to simulate the flow field characteristics,two-phase dispersion and DSD of Rushton turbine(RT),parabolic blade turbine(PB)and 45°down flow pitched-blade turbine(PBT)in the absence of surfactant,and to deeply analyze the relationship between flow field and DSD,and the mechanism of turbulent flow distribution on droplet breakage.The CT coalescence model and the Alopaeus breakage model are equipped in the PBM as source terms by programming with userdefined functions(UDF).Particle imaging velocimetry(PIV)and image analysis verified the reliability of the flow fields and DSDs simulated by CFD and PBM,respectively.Compared to the axial flow impeller PBT,the radial flow impeller RT and PB discharge liquid with higher flow velocity and stronger turbulence within the impeller region,promoting two-phase dispersion and increasing droplet breakage frequency.For radial flow impellers,the turbulent inertial regime is the dominant mechanism for droplet breakage in the impeller region;for axial flow impellers,the turbulent viscous regime has a higher degree of influence on droplet breakage in the impeller region.the DSD of PBT is less sensitive to the effect of the volume fraction of the dispersed phase than RT and PB.(2)The CFD-PBM with the original CT,Prince and Das coalescence models were used,and the simulation results were close to the experimental values for liquid-liquid dispersion DSD in the absence of surfactant,but the simulation results were unsatisfactory in the presence of surfactant,and the simulation errors increased as the surfactant concentration increased.The mechanism of surfactant hindrance to droplet coalescence was analyzed,and a modification scheme of the coalescence model based on the interphase mass transfer model was established.Modification of CFD-PBM by interphase mass transfer model implemented by UDF,and the modification factor of the coalescence model was calculated to modify the CFD-PBM based on the experimentally measured surfactant adsorption parameters and the adsorption density simulated by the interphase mass transfer model.For the three coalescence model:CT,Prince and Das,the modified CFD-PBM could simulate the DSD more accurately,and the simulation results were close to the experimental values for different surfactant concentrations.The modification factor decreases when the volume fraction of the dispersed phase is increased,and the effect of surfactant on droplet coalescence hindrance is enhanced.The coalescence repulsion force generated by the surfactant after droplet adsorption is the dominant effect on DSD,and the coalescence model modification factor,which represents the strength of the repulsion force,is related to the equilibrium rate constant of the surfactant.(3)CFD-PBM modified by interphase mass transfer model was used to simulate the flow and dispersion of two phases with different rheological properties of dispersed phase when the impeller in the stirred tank was PB,to deeply analyze the complex mechanism of the effect of surfactant and dispersed phase rheological properties on droplet behavior,and to investigate the mechanism of their joint influence on DSD.The viscosity of the dispersed phase increases,the overall flow weakens,the circulating flow contracts,the two phases are unevenly distributed,and the dispersed phase aggregates near the impeller,near the stirring shaft,and at the center of the circulating flow.The droplets of disperse phase with high viscosity are difficult to break,the distribution of droplet size becomes wider,and the control of droplet size is difficult.The enhanced shear thinning characteristics of the dispersed phase promote the overall flow in the upper circulation stream,and the two phases are more uniformly dispersed in the whole tank,and significantly increase the droplet breaking frequency in the impeller region,and the average droplet diameter in different areas of the tank decreases and the difference increases.The increase of surfactant concentration helps to eliminate the problem of uneven mixing of two phases caused by high viscosity dispersed phase,inhibit the coalescence of droplets,reduce droplet size,and narrow the distribution of droplet size.