Study On Electric Field Mediated Droplet Dynamic Behavior

Due to the unique enclosed liquid-liquid interface structure,microdroplets have significant applications in biomedical engineering,chemical technology,materials processing,etc.Therefore,finding an effective method to achieve the controllable generation of microdroplets has always attracted great attention.In recent years,with the rapid development of advanced technologies including bio-pharmacy,cell sorting,and inertial confinement fusion,higher control accuracy and efficiency are needed in the droplet generation and following dynamic behaviors.Comparing to the common microfluidic method which relies on the organization of multiphase fluid flow to control the dynamic behaviors of microdroplets,applying an electric field provides an opportunity for improving the performance of droplet generation and controlling the dynamic behaviors of droplets actively.Therefore,investigation of electric control on microfluidic droplet generation and control will be not only useful to develop the microfluidic technology for droplet generation but also good for enriching the basic theory of multiphase flow and interface science.Although many experimental and theoretical efforts have been devoted to exploring the electric control performance,the mechanism of electric mediated droplet generation and following dynamic behaviors have not been fully understood.In addition,there is still a lack of deep insight into the effects of key parameters such as electric field parameters,electric properties,and hydrodynamic parameters on the droplet generation performance and following dynamic behaviors.Therefore,based on phase field method and electrostatic or electric currents model,a mathematical model of electric meditated droplet generation,sorting,and deformation is developed and the experiment of droplet deformation under the combined effect of shear flow and electric field is designed and established.A combined numerical and experimental study is conducted to study electro-hydrodynamic behaviors of droplets.Electro-hydrodynamic behaviors of droplet generation,sorting,and deformation under the combined effect of electric field and external flow field are investigated.The mechanism of electric mediated droplet dynamic behaviors is clarified.And the influence of electric intensity,fluid electric properties,flow field intensity,and droplet size on the droplet dynamic behaviors are revealed.In summary,the main results are concluded as follows:（1）A numerical study is performed to investigate the electro-hydrodynamics of droplet generation in a co-flowing microfluidic device under electric control.The mechamism of droplet generation regime and evolution under electric control is revealed,and a droplet generation regime is plotted.The influence of electric and flow field parameters on the droplet generation frequency,monodispersity and deformation rate are clarified.It is indicated that four flow regimes during droplet generation are observed:dripping,dripping-jetting transition,jetting and threading with no droplets generated.Increasing the electric force can suppress the role of interfacial tension,which restrains the head-growth of the inner fluid in the dripping regime and the Rayleigh-Plateau instability appearing in the jetting regime.The squeezing,necking and breakup of the inner fluid thread is also enhanced by increasing the electric force,leading to increments in the droplet generation frequency and deformation rate as well as decrement in the droplet size.Depending on the hydrodynamic capillary number（Ca）and electric capillary number（Ca _E）,a droplet generation regime diagram is plotted to quantitatively represent the flow regimes,which indicates that,when the Ca and Ca _E are low enough（Ca≤0.20and Ca _E≤0.8）,only the dripping regime is observed,and the threading regime is only able to appear at sufficiently low Ca（Ca≤0.125）and high Ca _E（Ca _E≥2.68）.（2）To study the electric-field-controlled droplet sorting in the microfluidic chip,an unsteady numerical model of droplet sorting controlled by a nonuniform electric field is developed.The hydrodynamic behaviors of a droplet in a bifurcating channel are studied under different electric field strengths and fluid properties.The results indicate that both the shape and trajectory of the droplet are dependent on the permittivity ratio（S=ε_o/ε_i）and electric conductivity ratio（R=κ_i/κ_o）between the fluids when flowing through the electric field.Under the condition of RS<1,the droplet is squeezed and deflected into the right bifurcating channel.In contrast,the droplet is stretched and deflected into the left bifurcating channel when RS>1.The behaviors of the droplet are summarized in a sorting regime diagram according to the droplet size（r^*）and electric Euler number（Eu_e）.In the case of RS<1,a small droplet（r^*≤0.25）flowing through the horizontal channel is observed under the condition of weak electric intensity(Eu_e≥1×10^-4).As Eu_e decreases,the sorting regime of the droplet transits to turning right.Pinning on the grounded channel wall occurs when Eu_e≤7.21×10^-5.Eventually,droplet breakup is triggered(r^*≥0.3,Eu_e≤1.17×10^-4).In the case of RS>1,droplets are observed flowing through the main channel in the sorting process of both small and large droplets at large Eu_e(r^*≤0.25,Eu_e≥4.9×10^-4 and r^*≥0.3,Eu_e≥2.44×10^-4).A strong electric intensity(Eu_e≤2.44×10^-4)contributes to the breakup regime of large droplets（r^*≥0.3）.（3）The visualized experiment is conducted to investigate droplet deformation under the combined effect of shear flow and electric field.The influence of the capillary number and electric capillary number on droplet deformation is explored.It is indicated that the droplet rotates and deforms under the pure shear flow field.With the increase of capillary number,the deformation rate increases and the tilt angle decreases.In the pure electric field,the droplet only deforms.The droplet of castor oil is stretched in the direction of the electric field and the deformation rate increases with the increase of electric capillary number.When the electric field is imposed in the shear flow,the rotation of droplet is weakened while the deformation is enhanced.The tilt angle of the droplet in steady state depends on the competitive relation between shear flow and electric field.When the shear flow is stronger,the droplet rotates towards shear flow direction,while when the electric field is stronger,the droplet rotates towards electric field direction.Both shear flow and electric field promote droplet deformation,and the deformation rate increases with the increase of capillary number of electric capillary number.（4）Electric field mediated double emulsion droplet spheroidizing in an extensional flow is investigated numerically and the underlying electro-hydrodynamics is clarified.Regime diagrams are plotted to quantitatively recognize the operating regimes for different droplet morphologies,from which the critical electro-hydrodynamic criteria for droplet spheroidizing are summarized.It is indicated that a pure extensional flow deforms the outer droplet into an oblate shape,deforms the inner droplet into a prolate shape without the electric field.The deformation of a double emulsion droplet subjected to extensional flow can be counterweighted by a proper applied electric field.The droplet deformation rate can be controlled by adjusting the intensity of the electric field according to the intensity of the flow field and the electrical parameters of fluids.The electric force changes under the same electric field with different electrical parameters of fluids.As the value of the product of conductivity ratio and permittivity ratio of the outer droplet and continuous phase(R₀₁S₀₁)increase,more inductive charges are produced at the droplet interface,and the droplet is subjected to stronger electric force.In particular,the relation between the capillary number（Ca）and the electric capillary number（Ca _E）for the droplet to maintain spherical is linear,which can be expressed as Ca _E=a Ca.The coefficient a decreases with an increasing R₀₁S₀₁.The droplet electro-hydrodynamic behavior in the process of droplet generation,sorting,and deformation is studied both numerically and experimentally.The mechanism of different flow regimes is revealed,and the meditation of electric field on droplet dynamic behavior is clarified.Moreover,the effects of fluid properties,flow field intensity and electric intensity on the droplet dynamic behavior are discussed.This work could not only enrich the electro-hydrodynamics of the droplet but also be used to precisely control the droplet morphologies in the external flow via the electric control.