Droplets In Shear Flow Research Articles

Deformation and breakup of a ferrofluid droplet in shear flow under magnetic field

Effects of magnetic field applied perpendicular to a shear plane in shear flow on the deformation of a ferrofluid droplet are numerically investigated. The boundary integral method is employed to solve the two-phase Stokes flow under a uniform magnetic field. When the magnetic field is applied perpendicular to the shear plane, the deformation of the droplet in the shear plane decreases. The magnetic field causes the droplet to elongate in the y-direction, and its cross-sectional radius in shear plane decreases. Consequently, the apparent capillary number in the shear plane decreases, thereby suppressing the droplet deformation. Droplet breakup is also suppressed by imposing a magnetic field perpendicular to the shear plane, thereby increasing the critical capillary numbers. The critical capillary numbers for the magnetic Bond numbers Bo = 2.0 and 4.0 increase to approximately 110% and 130%, respectively, than those without magnetic field. Furthermore, an equation for the theoretical prediction of the droplet deformation under a magnetic field in shear flow is presented, which is based on the small deformation theory, the decrease in the cross-sectional radius, and the boundary conditions at the droplet interface. The theoretical prediction agrees well with the numerical results for the variation in the magnetic susceptibility of the droplet as well as the viscosity ratio between the external fluid and the ferrofluid droplet under a small deformation. The critical capillary numbers under a magnetic field can also be predicted by using the numerical results without a magnetic field.

Hydrodynamic interaction of two droplets covered with insoluble surfactant in shear flow

Despite its significance in various applications, e.g., droplet microfluidics and enhancing oil recovery, the effects of surfactants on the hydrodynamic interactions of droplets in shear flow still need to be clarified. This paper presents a systematic investigation on the hydrodynamic interaction of two droplets covered with the insoluble surfactant in a simple shear flow, which is realized by using our own three-dimensional front-tracking code. Our results indicate that surfactants significantly affect the hydrodynamic interactions of droplets, characterized by the maximum deviation in the z-direction and the shear-induced self-diffusion. Then, we examine the effects of surfactant-relevant parameters, i.e., the surface Peclet number and the elasticity number. Both the maximum deviation in the z-direction and the shear-induced self-diffusion increase with the elasticity number and the surface Peclet number. Specifically, we find two mechanisms underlying the effects of surfactant on the hydrodynamic interaction of two droplets. First, Marangoni stress induced by surfactant sharply increases the maximum deviation in the z-direction when the surface Peclet number is large. It is because that Marangoni stress hinders liquid drainage from the near-contact region and thickens the liquid film between the droplets. Second, hydrodynamic interactions during crossing lead to considerable alterations of the shape and local surfactant concentration, resulting in an irreversible trajectory shift of the droplets. So, the shear-induced self-diffusion sharply rises at the high surface Peclet number.

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

The behavior of a droplet under shear flow in a confined channel is studied numerically using a multi-phase smoothed particle hydrodynamics (SPH) method. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.

Shear flow-driven droplet motion with smoothed dissipative particle dynamics

Droplet motion in shear flow is a typical phenomenon in nature that also plays an important role in the spread of COVID-19 when viruses like SARS-CoV-2 exist in exhalation droplets. In this paper, we adopted smoothed dissipative particle dynamics (SDPD) to simulate the Couette flow and Poiseuille flow. Then, the self-diffusion coefficient and the Schmidt number of the quiescent flow in SDPD are confirmed by comparison with those in DPD. In addition, the SDPD method with pacific coefficients is used to simulate the disintegration of droplets and the collisional aggregation and separation of droplets in shear flow. The applicability of the SDPD method is demonstrated through these simulations, which can be useful in the investigation of many complex fluid flows during the expansion of COVID-19.

Modeling droplets with slippery interfaces

Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential velocity of the inner and outer fluid can differ, with the jump in velocity dependent not only on the material properties of the interface but also the stresses applied by the surrounding fluid. In this work a numerical model is presented which is capable of investigating general multiphase fluid systems involving interfacial slip in both two- and three-dimensions. To make the system computationally feasible, a hybrid Navier-Stokes projection method is used, whereby the viscosity, density, and pressure are assumed to be continuous across the interface while the velocity field can experience a jump, which is handled via the Immersed Interface Method. The numerical model is compared to experimental results involving polymer-polymer mixtures and computational results for droplets in extensional flows, showing excellent agreement with both. It is then used to explore the influence of interfacial slip in a number of common multiphase fluid systems, including the shearing of a planar interface, droplet and filament relaxation, and droplets in shear flow, both unbounded and wall-bound.

Role of particle-laden interfaces in shear-induced deformation of colloidal droplets

In this study, basing on the level-set and point-particle methods, we have developed a numerical methodology for simulating the dynamics of colloidal droplets under flow conditions in which the particle–particle, particle–interface and particle–fluid interactions are all taken into account efficiently. By using this methodology, we have determined the essential role of particle-laden interfaces in the deformation of colloidal droplets in simple shear flow with relatively low particle concentrations. Generally, adsorbed particles strongly enhance the deformability of the whole droplet, which is principally attributed to the particle-induced reduction of the effective surface tension. Systematic simulations are performed to reveal the detailed roles of interparticle interactions and particle surface coverage in the deformation of particle-covered droplets. Most importantly, we find the promotion effect of adsorbed particles on the droplet deformation cannot be completely included via the effective capillary number characterizing the particle-induced overall reduction of the effective surface tension, which is particularly obvious at high particle coverage. We propose two potential reasons for this surprising phenomenon, i.e. the convection-induced non-uniform distribution of adsorbed particles over the droplet surface and the particle-induced reduction of the droplet surface mobility, which have not been discussed yet in previous numerical and experimental studies of particle-covered droplets in shear flow.

Janus Nanoparticle and Surfactant Effects on Oil Drop Migration in Water under Shear.

The effects of surface-active nanoparticles and surfactants on the behavior of oil-water interfaces have implications for a variety of industrial processes related to multiphase flows including separation processes, enhanced oil recovery, and environmental remediation. In this work, the migration of an oil droplet in shear flow is investigated with the presence of surface-active molecules and nanoparticles at the oil-water interface. Pure oil (heptadecane) in water and oil with the presence of Janus nanoparticles (JPs) and/or octaethylene glycol monododecyl ether, a nonionic surfactant, were examined using coarse-grained computations. The shear flow field was created utilizing a Couette flow, where the top wall of a channel moved with a specified velocity and the bottom wall was kept stationary. The dissipative particle dynamics (DPD) method was applied. The oil drop was placed on the stationary wall, and its displacement was recorded over time. When surfactants were added at the oil-water interface, the slip of the water over the oil drop was reduced, leading to a larger displacement of the drop. Moreover, surfactant molecules tended to concentrate toward the rear side of the oil drop rather than the front as the drop moved in the flow field. The presence of only JPs on the oil-water interface resulted in slower droplet migration. In the presence of both JPs and surfactants, the effect of JPs on the oil-surfactant-water system was investigated by changing the number of JPs on the drop surface while keeping the concentration of the surfactant constant. Under the same shear rate, the droplet's migration speed increased in the presence of both surfactants and JPs compared to the case of bare oil. The JPs appeared to follow a repeated pattern of motion while residing close to the solid substrate-oil drop contact line. These findings elucidate the contribution of both surfactants and JPs on oil drop displacement for enhanced oil recovery or remediation of an oil-contaminated subsurface.

Inner and outer flow of an adhering droplet in shear flow

Adhering droplets in shear flow start to move downstream when a critical velocity ucrit is reached, i.e. the adhesion force is overcome by aerodynamic force. It is still not clear, whether drag-coefficient-estimation based on an approximation of the droplet as a rigid spherical cap is a valid approach. In contrast to rigid hemispheres there is a gas-liquid-interface, i.e. the velocity of the interface is not zero by all means. Therefore, there is a fluid transport inside the drop that depends on the outer flow structure. We report on a combined numerical and experimental investigation to find out the characteristic inner and outer flow structure of an adhering droplet in shear flow in order to evaluate the rigid-hemisphere-approach.The inner flow structure of the droplet is measured by particle-image velocimetry (PIV) while the wake flow of the droplet in the gas-phase is measured by a modified laser-doppler-velocimeter (laser-doppler profile sensor). Numerical simulations of a droplet have been carried out using a modified volume of fluid (VOF) model taking into account contact angle hysteresis effects in OpenFOAM®. The complete two-phase fluid motion of the liquid droplet and surrounding gas phase is simulated, i.e. the inner and outer flow of the droplet are captured with a three-dimensional simulation model.Experimental and numerical results agree very well concerning flow pattern inside and outside the droplet. There is a strong connection between the inner and outer flow of the droplet. For lower Reynolds numbers based on droplet diameter (Red < 800) the flow inside the droplet rotates in direction of the channel flow. On the leeward side of the droplet there is a small wake flow with slightly decreased flow velocity. At higher Reynolds numbers (Red ≥ 800) the flow pattern inside the droplet changes completely: A strong reverse flow close to the droplet surface appears. Concurrently a strong recirculation zone emerges in the wake of the droplet. This is due to the roll-up process of a separated shear layer originating from the droplet. Due to the coupling of the inner flow with the outer flow via the gas-liquid-interface our data show that at higher Reynolds numbers flow separation takes place on the windward half of the droplet. This is in contrast to the case of a rigid hemisphere, where the separation is located at approximately 90°, i.e. the top of the droplet, and does not move upstream with increasing Reynolds number. The height of the separation zone increases up to 1.29 times the droplet height, which is not observed for rigid hemispheres. Since the pressure field around an obstacle is governed by the flow separation location and the corresponding size of the recirculation zone, the coupling of the inner and outer flow changes the pressure distribution around the droplet with respect to a similar rigid structure. This will affect the aerodynamic forces acting on the droplet, which is why the approximation by a rigid spherical cap does not seem to be a suitable approach. Nevertheless, additional experimental and numerical efforts need to be done to assess the flow structures, pressure distributions and forces acting on the droplet in a suitable precision also considering possible aero-elastic effects.

Effect of the Molecular Structure Change of a Matrix Polymer (Nylon 6) on the Deformation of Dispersed Phase (a Thermotropic Liquid Crystalline Polymer) Droplets in Shear Flow.

In this work, we investigated the effect of a change in the molecular structure and ensuing molar mass change of a matrix polymer (polyamide 6, Ny 6) on droplet deformation of a dispersed thermotropic liquid crystalline polymer (TLCP, a poly(ester amide)) in shear flow. This study focuses on a total capillary number (the sum of the shear capillary number and the elasticity capillary number) and the viscosity ratio between the TLCP and Ny 6, for the morphological development and mechanical performance of TLCP/Ny 6 blends. In contrast to Ny 6, which has a lower melt viscosity than the TLCP melt, a modified Ny 6 (m-Ny 6) with ca. 2 orders higher melt viscosity than that of Ny 6 at a shear rate of 1 s–1 was found to facilitate the deformation of the TLCP phase. A total capillary number was defined to characterize the viscoelasticity effect on droplet deformation in the blend system. The first normal stress difference obtained from the viscosity curve using Steller’s method was used for the evaluation of the elasticity capillary number. The total capillary number for the Ny 6 blend was far less than the critical capillary number and was insufficient for the dispersed TLCP droplets to be deformed. The shear capillary number of the m-Ny 6 blend was greater than the critical capillary number but was still insufficient for droplet deformation into fibril shapes. The total capillary number, including the elastic capillary number, was sufficiently greater than the critical capillary number for deformation of the dispersed TLCP droplets. Morphological observations and a comparison with the theoretical work confirmed the importance of the viscoelasticity of the melt in the immiscible Ny 6/TLCP blends for in situ composite fabrication in shear flow. Both the high viscosity and the first normal stress difference of m-Ny 6 promote the deformation and fibrillation of the dispersed TLCP droplets.

Regime mapping of multiple breakup of droplets in shear flow by phase-field lattice Boltzmann simulation

Multiple breakup refers to a sequence of events through which a single droplet eventually produces multiple daughter droplets in a shear flow. It is a more common phenomenon than binary breakup. Using a phase-field lattice Boltzmann method, this work investigates the effects of Reynolds number, capillary number and soluble surfactant on multiple breakup in shear flow. We find that the regime map for a droplet in a surfactant-free shear flow can be segmented into the non-breakup, elementary breakup, multiple breakup, filament and coalescence regimes. By contrast, the multiple-breakup regime widens and the coalescence regime narrows in the system of surfactant. This difference on macroscale regimes originates from the mesoscale behaviour caused by the interaction of surfactant and shear flow. While surfactant hinders droplet breakup at lower Re, it promotes breakup at higher Re. The interfaces around the breaking points are stretched by the opposite reaction of Marangoni stress. While the regime map gives the number of daughter droplets in a given shear flow, a correlation is proposed to calculate the composition of breakup events, viz. the number of binary breakup and of ternary breakup events.

Electric field induced dynamics of viscoplastic droplets in shear flow

We investigate the dynamics of viscoplastic droplets under the combined action of electric field and shear flow by performing direct numerical simulations. The electro-hydrodynamic equations are solved in a two-dimensional finite volume framework, and the interface is captured using a volume-of-fluid approach. The rheology of the viscoplastic droplet is modeled as a Bingham plastic fluid. Both the drop and the surrounding medium are considered to be perfect dielectric fluids. The simulations reveal that in the sole presence of the shear flow, the plasticity of the fluid plays a pivotal role in deciding the magnitude of droplet deformation and orientation. The local viscosity inside the drop is significantly augmented for higher plasticity of the fluid. Under the action of the electric field, the droplet deformation and orientation can be suitably tuned by varying the magnitude of the permittivity contrast between the fluids. The droplets experience enhanced deformation and preferred orientation against the flow direction when the permittivity ratio is greater than unity. Increasing the droplet plasticity leads to reduction in the droplet deformation. Conversely, by increasing the electric field strength, the deformation of the droplets can be notably enhanced, with a stronger response observed for a permittivity ratio beyond unity. Finally, it is observed that by suitably manipulating the strength of the shear flow and the electric field, droplet breakup can be engendered. The mode of droplet disintegration differs due to variation of the parameters, which can be attributed to the competing influence of shear and electric forces on the droplet.

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5ε added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pε,in−Pε,out satisfies the Young-Laplace law for droplet radius greater than 3.5ε and otherwise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non-local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Confinement effect on electrically induced dynamics of a droplet in shear flow.

Deformation and breakup of droplets in confined shear flows have been attracting increasing attention from the research community over the past few years, as attributable to their implications in microfluidics and emulsion processing. Reported results in this regard have demonstrated that the primary effect of confinement happens to be the inception of complex oscillating transients, monotonic variation of droplet deformation, and droplet stabilization against breakup, as attributable to wall-induced distortion of the flow field. In sharp contrast to these reported findings, here, we show that a nonintuitive nonmonotonic droplet deformation may occur in a confined shear flow, under the influence of an external electric field. In addition, we demonstrate that the orientation angle of a droplet may either increase or decrease with the domain confinement under the influence of an electric field, whereas the same trivially decreases with the increase in degree of confinement in the absence of any electrical effects. Unlike the typical oscillatory transients observed in microconfined shear flows, we further bring out the possibility of an electrohydrodynamically induced dampening effect in the oscillation characteristics, as governed by a specific regime of the relevant dimensionless electrical parameters. Our results reveal that instead of arresting droplet deformation, the unique hydrodynamics of microconfined shear flow may augment the tendency of droplet breakup, and is likely to alter the droplet breakup mode from midpoint pinching to edge pinching at high electric field strength. These results may bear far reaching implications in a wide variety of applications ranging from the processing of emulsions to droplet based microfluidic technology.

A point-mass particle method for the simulation of immiscible multiphase flows on an Eulerian grid

We present an Eulerian-Lagrangian approach for the modeling and simulation of immiscible multiphase flow systems. The Naiver-Stokes equations are solved on a traditional Eulerian grid while the fluid mass and phase information is discretized by Lagrangian particles. The method is novel because the particles move with a velocity that enforces consistency between the particle field density and the fluid density. The approach is advantageous in that (i) an arbitrary number of phases are easily represented, (ii) the particles remain well-distributed in space, even near merging and diverging characteristics, (iii) mass conservation is easily controlled, and (iv) the methodology is applicable to a wide range of Courant numbers. The governing equations are derived and a numerical method is presented that is applicable to incompressible flows. Performance is assessed via standard two-dimensional and three-dimensional phase transport tests as a function of both Eulerian grid resolution and Lagrangian particle resolution. Results show that the shape error converges with first-order with respect to increasing either Eulerian grid resolution or particle resolution, while mass conservation errors converge with the square root. The method is shown to successfully simulate expanding elliptical regions, stationary and oscillating droplets, a droplet in shear flow, a Rayleigh-Taylor instability, and the air blast atomization of a droplet.

Deformation of clean and surfactant-laden droplets in shear flow

In this work we study the deformation of clean and surfactant-laden droplets in laminar shear-flow. The simulations are based on Direct Numerical Simulation of the Navier–Stokes equations coupled with a Phase Field Method to describe interface topology and surfactant concentration. Simulations are performed considering both 2D (circular droplet) and 3D (spherical droplet) domains. First, we focus on clean droplets and we characterize the droplet shape and deformation. This enables us to define the range of parameters in which theoretical models well predict the results obtained from 2D and 3D simulations. Then, surfactant-laden droplets are considered; the main factors leading to larger droplet deformation are carefully described and quantified. Results obtained indicate that the average surface tension reduction and the accumulation of surfactant at the tips of the deformed droplet have a dominant role, while tangential stresses at the interface (Marangoni stresses) have a limited effect on the overall droplet deformation. Finally, the distribution of surfactant over the droplet surface is examined in relation to surface deformation and shear stress distribution.

A comprehensive SPH model for three-dimensional multiphase interface simulation

Smoothed particle hydrodynamics is a typical Lagrangian meshless method, which has unique advantages in modelling multiphase phenomena with interface deformation and fragmentation. Current study proposes a comprehensive multiphase SPH model, which takes the advantages of some numerical techniques such as numerical interfacial force and damping technique. An improved boundary model is also introduced to deal with the solid walls. Additionally, the multiphase phenomena are investigated by solving an enhanced continuous surface force (CSF) model. In order to verify the proposed model, the droplet in shear flow is firstly considered and the results are consistent with the analytical solutions. Furthermore, the oscillations of square droplets are simulated under different particle resolutions, density and viscosity ratios. Finally, two and three dimensional bubble rising at high density ratios (up to 1000) are tested.

Influence of electric field on deformation of a drop in shear flow

The dynamics of a droplet in shear flow under the influence of an external electric field are investigated by performing extensive numerical simulations. The study is carried out by solving two-dimensional electrohydrodynamic equations, and the interface is captured using a volume-of-fluid approach. It is observed that with an increase in the drop size, a confined drop exhibits enhanced deformation and preferred orientation with the flow direction. For the case of dielectric fluids, the deformation of the drops can be either enhanced or reduced by varying the permittivity ratio and electric field strength. The nature of the polarisation forces acting at the interface can be either compressive or tensile depending on the magnitude of the permittivity ratio. The local electric field intensity inside the drop is significantly altered due to the permittivity contrast between the fluids. The computations for leaky dielectric fluids reveal that the deformation of the drop can be effectively tuned by altering the permittivity as well as the conductivity ratios. The nature of charge accumulation and the electric forces acting at the interface are critically dependent on the relative contrast between the electric properties of both the phases. The conductivity ratio decides the magnitude and nature of charge at the upper and lower portions of the droplet interface, thereby fundamentally maneuvering the droplet dynamics under the applied electric field.

Migration of ferrofluid droplets in shear flow under a uniform magnetic field.

Manipulation of droplets based on physical properties (e.g., size, interfacial tension, electrical, and mechanical properties) is a critical step in droplet microfluidics. Manipulations based on magnetic fields have several benefits compared to other active methods. While traditional magnetic manipulations require spatially inhomogeneous fields to apply forces, the fast spatial decay of the magnetic field strength from the source makes these techniques difficult to scale up. In this work, we report the observation of lateral migration of ferrofluid (or magnetic) droplets under the combined action of a uniform magnetic field and a pressure-driven flow in a microchannel. While the uniform magnetic field exerts negligible net force on the droplet, the Maxwell stresses deform the droplet to achieve elongated shapes and modulate the orientation relative to the fluid flow. Hydrodynamic interactions between the droplets and the channel walls result in a directional lateral migration. We experimentally study the effects of field strength and direction, and interfacial tension, and use analytical and numerical modeling to understand the lateral migration mechanism.

Numerical study of deformation and breakup of a multi-core compound droplet in simple shear flow

In this paper, we present the numerical simulation results of deformation and breakup of a multi-core compound droplet. The method used is a two-dimensional front-tracking method with a modification for multi-layer droplets. The droplet is placed at the center of the domain whose top and bottom boundaries move in the opposite directions to create the shear flow. We vary the values of various parameters in specific ranges to investigate their effects on the deformation and breakup of the multi-core compound droplet in shear flow. We mainly focus on the two-core compound droplets. Basing on the numerical results, we reveal various patterns (i.e. modes) of deformation and breakup: non-breakup types 1 and 2, breakup types 1, 2, 3 and 4. For the first non-breakup type (type 1), the outer interface is deformed with two inner droplets accumulating at the center whereas in the other non-breakup type (type 2), the inner droplets move to the two furthest ends. The non-breakup type 1 generally changes to the breakup type 4, at some critical parameters, in which the compound droplet breaks up into simple droplets at its ends with a smaller daughter compound droplet in between. The non-breakup type 2 transits to the breakup type 1 or type 2, depending on the flow conditions, with the formation of two smaller daughter compound droplets at the ends. The remaining breakup mode (type 3) is a mixed breakup mode that is a combination of the breakup types 2 and 4. These deformation and breakup patterns are mapped onto a Re–Ca diagram. We also propose some other diagrams based on the variations of the inner droplet location. In addition, we investigate the effect of the number of the inner droplets encapsulated in the compound droplet on its deformation and breakup.

Effect of surfactants on the deformation of single droplet in shear flow studied by dissipative particle dynamics

ABSTRACTThe behaviour of a single droplet in shear flow is a fundamental problem in immiscible liquid–liquid multiphase fluid systems. In this article, the deformation and inclination angle of single droplet covered with surfactants in shear flow at moderate Reynolds number, when both the inertial effects and interfacial tension are the key governing factors, were simulated by dissipative particle dynamics (DPD). Weber number We was adopted to indicate the force state of the droplet and a linear relationship between the deformation parameter D and We was found when Reynolds number Re is about 1–10, which is similar to the relation of D and Capillary number Ca when Re ≪ 1. When the surfactant concentration is lower than the critical micelle concentration (CMC), the distribution of surfactants, the droplet inclination angle θ and the droplet deformation parameter D were investigated at different surfactant density at interface ds and shear rate . When the droplet size is close to the characteristic size of surfactant molecules, phase interfaces of water in oil (W/O) and oil in water (O/W) systems have different microstructures, which result in differences in the surfactant distribution, the droplet inclination angle and deformation of the two systems.