Numerical Study On Hydrodynamic Behaviors Of Emulsion Droplet Under The Combination Of External Flow And Electric Field

Due to the unique enclosed liquid-liquid interface structures,emulsions have become the ideal templates for the functional micro elements such as storage units,reactors,core-shell materials and so on.Emulsion droplets are often manipulated by the external flow field which determines their main characteristics,e.g.droplet size,monodispersity,and interface shape.The construction of functional micro elements is accomplished by means of polymerization,crosslinking,solvent evaporation,curing,assembly and other physical and chemical processes.Hence,the dynamic behaviors of emulsion droplet,including deformation and breakup,would significantly affect the structure and characteristic of micro device.To precisely control the construction of micro emulsion devices via microfluidics,it is of significance to fully explore the fluid dynamic behaviors and active manipulation approaches of the emulsion droplet under external flow fields.In recent years,with the development of electrohydrodynamics,the electric fields provide promising routes to actively control droplet dynamics.However,in practical engineering process,lack of theoretical guidance limits the development of active control of emulsion droplets based on electric fields due to the incomplete understanding of droplet dynamics under the coupling of electric field and flow field.Especially,the regulation mechanisms of coupled flow field force and electric force require further revealing.In this context,numerical simulation based on the electric current model is conducted to study the charge process of the droplet and as well as estimate the effect of electric force.While a phase filed method based on Cahn-Hilliard equation is adopted to capture the motion of the interfaces.The dynamic behaviors during the deformation of emulsion droplet under linear flow field combined with external electric field are studied,the coupling mechanism of viscous drag,interfacial tension and electric force in droplet deformation dynamic is analyzed.A series of important results and conclusions are obtained as follows:The deformation of incompressible single emulsion droplet under the condition of linear flow field coupled with external electric field is investigated numerically by computational fluid dynamics simulation.The characteristics and regimes of dynamic deformation behavior are investigated.The results indicate that,single droplet deforms due to viscous drag force in single linear flow field and when capillary number is small(Ca<0.06),the deformation parameters D increase linearly with the increasing capillary number.When electric field is induced,two different types of inductive charge distribution are observed at the droplet interface and are affected by the ratio of electrical conductivities R and the ratio of permittivity S between the droplet and the continue phase,.When the electric field is parallel to the flow direction and the electric parameters of droplet and continue phase satisfy RS>1,electric force can restrain the deformation of droplet effectively.The deformation of incompressible double emulsion droplet under the condition of elongational flow field coupled with external electric field is investigated numerically by computational fluid dynamics simulation.The characteristics and regimes of the dynamic behaviors during double emulsion droplet deformation are studied.The results indicate that,in elongational flow,the outer droplets are subjected to oblate deformation due to the viscous drag from the outer fluid,while the inner droplets are subjected to prolate deformation caused by the viscous drag from the middle fluid.When electric field is induced,four different types of deformation is observed due to four different types of inductive charge distribution based on different ratio of electrical conductivities R and different ratio of permittivity S between the droplet and the continue phase.When electric field is parallel to the flow direction of elongational flow,various types of deformation including O-P,O-O,O-S,P-P,P-O,P-S,S-O,S-S and S-P,(O-oblate,P-prolate,S-spherical)are observed on the interfaces of double emulsion.Especially,passive deformation of double emulsion droplet can be restrained to obtain perfect spherical interface of double emulsion by varying the ratio of conductive R and the ratio of permittivity S between inner droplet,outer droplet and continuous phase,.Further study on the splitting of single emulsion droplet is conducted based on the study of dynamic behavior of single droplet deformation.The results indicate that,the droplet breakup is occurred when capillary number(electric capillary number)exceeds a critical value in flow filed or electric field.Moreover,the breakup regime varies with relative permittivity rate and conductivity rate under the domination of electric force.When electric field is parallel to the flow direction and electric parameters of droplet and continue phase satisfy RS>1,the droplet breakup is facilitated due to the electric force.