Study On The Breakage And Coalescence Processes Of Droplets/Bubbles Under Turbulent Conditions

The breakage and coalescence of fluid particles(i.e.,droplets or bubbles)are common phenomena in the chemical industry.The size distribution of the fluid particles determined by the breakage and coalescence processes will have a significant effect on the mixing,transfer and reaction performance of the multiphase reactor.Therefore,it is helpful to develop,design and optimize the multiphase reactor by deeply understanding the breakage and coalescence processes of the fluid particles and establishing reasonable theoretical models.Through analysis breakage mechanism of droplets in the turbulence,in the framework of entire energy spectrum a multiple breakage model for low viscosity droplets was proposed by this paper.Unlike the previous models,the proposed model was not restricted by the assumptions of binary breakage and the droplet size always falls into inertial sub-range.In the entire energy spectrum range,starting from the physical processes of breakage,this work proposed the breakage frequency models and daughter size distribution models for binary,ternary and quaternary breakages respectively.The proposed model considered the effects of surface oscillation and initial shape of parent droplet on the collision frequency and breakage probability.According to the proposed model,two kinds of contradictory academic views existing in the literature were explained theoretically.The model was validated by the existing experimental data.The results predicted by the proposed model showed an agreement with the breakage frequencies and daughter size distributions measured by different authors under different operating conditions.For the evolution of droplet size distribution in the stirred tank reactor,the satisfactory results were predicted by coupling the proposed model with the population balance equation.The coalescence of fluid particles induced by turbulence was studied in the entire energy spectrum.This paper proposed two different coalescence mechanisms.Based on the concept of solid angle,the collision probability between fluid particles as well as the collision probability between turbulent eddies and fluid particles can be derived,and the corresponding coalescence model was proposed for each coalescence mechanism based on the concept of joint probability.The proposed coalescence model was closed by the critical coalescence velocity predicted by coupling the approach equation and liquid film drainage models between two fluid particles.Unlike the previous work only considered the contribution of the turbulent eddies of size equal to the fluid particles,this work considered the contribution of turbulent eddies of different sizes in the entire energy spectrum to the coalescence of given fluid particle sizes.Simultaneously,the influences of the average collision free path between fluid particles and turbulent eddies as well as the lifetime of turbulent eddies on the coalescence were considered.This work also proposed a novel second-order longitudinal structure function valid for entire energy spectrum.Furthermore,the critical coalescence velocity and evolution of droplet size distribution in the stirred tank predicted by the proposed model were in agreement with experimental data.Furthermore,by using the open source fluid mechanics software,this paper performed the direct numerical simulation on the droplet coalescence.Based on the simulation results,the assumptions adopted in the existing drainage mechanism models were analyzed.According to the calculated results,we can draw the following conclusions:(1)the Reynolds lubrication approximation has its limitations,and the film drainage mechanism models may lead to unreasonable results if the axial pressure gradient was neglected arbitrarily;(2)the axisymmetric liquid film assumption may be reasonable in the early stage of film drainage,while in the late stage of film drainage,the assumption may be invalid;(3)the constant force boundary condition are reasonable in some degree,but the constant velocity boundary condition was not in agreement with the numerical results.Those conclusions were beneficial to establish more reasonable film drainage mechanism model.