Droplet Formation Frequency Research Articles

Regulation of the size and flow pattern of yield stress droplets in flow-focused microchannels by orifice constraints

Although droplet microfluidics have attracted increasing research interest, the regulation of complex polymeric droplets remains incomplete in chemical industry. In this study, we investigate the formation of yield stress droplets in flow-focused microchannels with orifice constraints by means of numerical simulations using a volume-of-fluid method coupled with an adaptive mesh refinement technique. The results show that different orifice sizes induce various flow patterns, including dripping, quasijetting, quasijetting with droplet coalescence, and jetting. A predictive model is established for the extension length of the dispersed phase during the necking stage, considering orifice dimensions interplay. Furthermore, higher yield stress influences the droplet size and formation frequency by expanding the high viscosity distribution in the dispersed phase. The proposed predictive correlations for droplet size, velocity, and formation frequency, accounting for the effects of orifice dimensions and yield stress, are believed to have significant impacts on the preparation of polymeric droplets in microreactors.

Study of droplet formation in parallel flow focusing microchannel under electrostatic field control

To achieve efficient preparation of emulsion droplet, this paper uses a two-dimensional mathematical model coupled with the phase field model and the electrostatic field model to calculate the droplet formation in parallel flow focusing multichannel, and analyzed the effect of electric field strength on the droplet formation process. In addition, the effects of different capillary numbers and dispersed phase viscosity on droplet formation were also analyzed. The results show that the emulsion in the channel always generates droplet by dripping regime, and the droplet have the best monodispersity. Applying appropriate electric field strength can realize droplet formation frequency and size regulation. Increasing the dispersed phase viscosity increases the breakup thread of the dispersed phase fluid, and the droplet size obtained gradually decreases, the difference in droplet size can be slowed down by applying the electric field. Increasing the electrostatic force leads to a higher droplet deformation rate. The droplet shape classification is plotted using the capillary number (Ca) and electrostatic number (CaE). It is found that the droplet flow pattern in the channel remains a circle only when Ca and CaE are sufficiently small.

Study on jetting droplet formation regime in a low-speed annular shear flow field

This study aims to explore the mechanism of droplet generation and the change rule of liquid bridge in an annular shear flow field. With the help of a two-phase system of continuous phase (deionized water)-dispersed phase (fluorescent oil), the process of droplet generation under the jetting mechanism was captured using a camera. By studying the effect of the dispersed phase flow rate on the length of the liquid bridge, it was found that the volume flow rate of the dispersed phase is positively correlated with the frequency of droplet formation and the droplet size, and that the distance of the liquid bridge is also positively correlated with the droplet size under the jetting mechanism. Besides, a prediction mechanism for the maximum stable droplet under the jetting mechanism is proposed based on the droplet formation process.

Performance optimization of droplet formation and break up within a microfluidic device – Numerical and experimental evaluation

Droplet-based microfluidics, including the controlled manipulation of materials in the form of monodisperse droplets on the micrometer scale in microfluidic chips, has gained much attention due to their ability in biological assays. The capillary number of the continuous phase, as the ratio of viscous force and interfacial tension, is so important in the mechanism of droplet formation. This study aims to survey the type of continuous-phase fluid, the change in the parameters of the continuous phase, and the effect of the different flow rates ratios on the droplet formation dynamics, droplet size, distance between droplets and frequency of droplet formation. Three types of oil, including mineral, olive, and paraffin in a flow-focusing microfluidic device have been utilized numerically and experimentally. To characterize the parameters of the continuous phase affecting the droplet size, a microfluidic device has been designed to estimate of the droplet size for three different types of oil used in the assay. The results show that for a constant continuous phase velocity, the diameter of the droplets formed in olive oil has the lowest amount, followed by paraffin and mineral oil, respectively. Regarding the effects of oil type on the frequency of droplet formation and the distance between droplets, the rate of droplet formation in mineral oil, in the ratios of the variable flow rate and the constant continuous phase velocity, is the lowest and, the distance between the droplets has the highest level.

Controllable generation of core-shell composite droplets in a conical inlet double-focus microchannel

In this paper, a double-focused conical inlet axisymmetric structure with double acceleration is proposed and the evolution of composite core-shell droplets is calculated using the volume of fluid (VOF) method, focusing on the size and droplet formation frequency of composite core-shell droplets as well as the quality control method. The results show that dripping and jetting regimes occur in the channel, and the generation period and flow distribution under the two mechanisms are investigated accordingly. The effect of local geometry on the evolution of composite droplets in the core-shell is investigated and analyzed using the composite droplet size, frequency, maximum extended length, and core droplet relative offset rate at the initial stage. It is found that changing the entrance angle can achieve the regulation of droplet size to a certain extent. With the increase of dimensionless width of the collection channel, the core-shell composite droplets size shows an overall increasing trend and is inversely proportional to the outer phase capillary number. Finally, a quality control method for composite droplet formation based on the maximum relative offset rate of core droplets is proposed for the purpose of controlling the integrity of composite droplets.

Numerical investigation of electrohydrodynamic effect for size-tunable droplet formation in a flow-focusing microfluidic device

ABSTRACT Droplet-based microfluidics has received much attention in biofabrication due to its compatibility with 3D printers that use cell-laden bioinks. In order to tailor the printing resolution, droplet generation under a DC electric field in a flow-focusing device is explored numerically. The major purpose of simulations is to investigate how geometry affects droplet production and electric field intensity. The effects of the orifice’s length, injection angle, and shape are discussed regarding the electric capillary number . Based on the retardation effect, the necking stage of droplet formation changes to expansion, and the frequency of droplet formation declines when the capillary number rises. For a particular value of the applied electric potential, orifice elongation reduces the induced electric field within the orifice. By adjusting the angle of side flow, smaller droplets can be formed, and the linear decrease in droplet size is provided across a wider range. The electric field in the orifice was amplified by 64% by creating a wedge-shaped orifice. In other words, when the notch angle was sharpened, the electric force increased, and the droplet diameter reduced. Since the frequency of droplet production varied only slightly between different notch angles, it could be preferable to generate smaller droplets without significantly altering the frequency of droplet formation.

A numerical study on breakup of a liquid jet in an axial electric field

A liquid jet injected from a nozzle stretches in the direction of the applied electric field and subsequently emits multiple droplets on pinch-off. It is hypothesized that the size and frequency of the drops can be manipulated by varying the electric field strength and flow rate, which is essential in electrohydrodynamic jet printing. Numerical simulations of the electrified jet breakup are performed using an in-house code based on the Dual Grid Level Set Method. To comprehend the impact of the electric and hydrodynamic forces, three dimensionless parameters are introduced: injection velocity (0.01≤Vinj≤0.15), Reynolds number (10≤Re≤100) and electric Bond number (0≤Boe≤30).Our results indicate the transition from dripping to micro-dripping and micro-jetting (at high Vinj) with increasing Boe. The critical Boe, at which this transition occurs, is found to escalate with an increase in Re. The stability of the micro-dripping mode is characterized by the balancing of the electrical and viscous shear stresses. Although the influence of the electric Bond number on the jet breakup length is marginal, it has a significant effect on the droplet diameter and formation frequency. A re-formulated scaling law suggests that the jet breakup length is mainly affected by injection velocity and Reynolds number.

Design and simulation of a novel integrated microfluidic chip for cell isolation and culture.

The lab on a chip is utilized as a background and a substrate for creating a proper flow for cellular processes in medicine. In this study, the concepts of cell isolation and cell transfer methods have been discussed. After that, the device of separation and transfer systems has been designed, simulated, and verified by placing the frequency of particle separation and droplet formation, which is tried to introduce a new device that can be used in cellular studies. The optimal operation conditions for the problem have also been investigated. High separation efficiency (99%) could be achieved when the velocity of the sample inlet in the microchannel separator is 180μm/s. Also, a microfluidic device for droplet generation has been designed to transfer the isolated cells to the culture medium. For this purpose, the frequency of droplet production must be synchronized with particle ejection frequency and equals 9.09Hz.

Liquid-liquid colliding micro-dispersion and general scaling laws in novel T-junction microdevices

Colliding micro-dispersion has been extensively used to generate uniform droplets in liquid-liquid heterogeneous reactions. However, there are few reports on the colliding micro-dispersion. More importantly, only squeezing flow and big size droplets can be generated in the normal colliding micro-dispersion process, and even there exists no general scaling laws for droplet size. We have developed novel T-junction microdevices with new geometric structures to intensify the colliding micro-dispersion and proposed general scaling laws for droplet size in colliding T-junction microdevices. The droplet formation frequency was increased by more than 40 times, and a much wider operating range was allowed in the novel colliding T-junction microdevice. The flow regime distribution under high Weber number was explored for the first time and a complete liquid-liquid flow pattern map under colliding micro-dispersion has been also proposed. We also proved that jetting flow regime can be occurred under high Weber number and low capillary number.

Numerical Study on the Formation and Solidification of LMPA Microdroplet in a Microfluidic Device

LMPA droplets or particles have contributed to many fields such as the application of sensors and valves, and droplet-based microfluidics has been applied to the preparation of LMPA droplets. Understanding how flow rate, interfacial tension, and temperature affect the formation and solidification of droplets is helpful to design a microfluidic platform. In this study, a coupled VOF and enthalpy-porosity method will be used to numerically simulate how these factors affect the LMPA droplet formation and solidification process. We find that increasing the velocity of the continuous phase or decreasing the interfacial tension will reduce the LMPA droplet size and simultaneously increase the frequency of droplet formation. In addition, increasing the interfacial tension will decrease the required solidification time of LMPA droplets, and the solidification time of droplets will first increase and then decrease with the growth of continuous-phase velocity. On the other hand, increasing the continuous-phase temperature or cooling wall temperature will reduce the solidification time of LMPA droplets, but has no obvious influence on the size and frequency of droplet generation.

Insights into the dynamics of non-Newtonian droplet formation in a T-junction microchannel

The non-Newtonian shear-thinning droplet formation mechanism in a T-junction microchannel is experimentally investigated using the aqueous solutions of xanthan gum as the dispersed phase and mineral oil as the continuous phase. Influences of both phase flow rates and polymer concentration on flow regime transition are explored. It is observed that the initial vertical expansion stage is present only for the Newtonian and lower shear-thinning systems. The droplet evolution rate shows the influence of continuous phase flow rate and shear-thinning properties on the dynamics of necking stages, viz., squeezing, transition, pinch-off, and filament thinning. Analysis of Ohnesorge number (Oh) reveals that inertial force dominates in the squeezing stage, whereas viscous and interfacial force control in the filament thinning stage. Longer and stable filament generation is detected as a discerning feature for non-Newtonian systems that appears more prominent with increasing dispersed phase shear-thinning properties. The results also indicate an inverse relation of droplet length with the continuous phase flow rate and xanthan gum concentration, while the droplet formation frequency and its polydispersity vary directly with those parameters.

The preparation of mono- and multicomponent nanoparticle aggregates with layer-by-layer structure using emulsion templating method in microfluidics

We report on the preparation of multicomponent hollow aggregates by an emulsion templating method adapted to microfluidic format. The method exploits partial miscibility of aqueous colloidal solutions as discrete phase and n-butanol as continuous phase. The aggregates consisted of an inner inorganic shell composed of iron oxide (IO) and gold nanoparticles (Au NPs) covered with polycaprolactone (PCL) NPs. The aggregates of smaller sizes were prepared compared to immiscible phases due to the diffusion-controlled shrinkage of aqueous droplets. The aggregate surface properties were controlled by using different mobilities and affinities of IO, Au, and PCL NPs to the water:n-butanol interface. The biocompatible surface layer enclosing an inorganic shell with a core space for possible cargo loading endowed these constructs with properties appreciated in medicinal applications. A computational fluid dynamics model enabled the prediction of the droplet size and formation frequency together with flow field properties at the point of droplet detachment.

Generation and Dynamics of Janus Droplets in Shear-Thinning Fluid Flow in a Double Y-Type Microchannel.

Droplets composed of two different materials, or Janus droplets, have diverse applications, including microfluidic digital laboratory systems, DNA chips, and self-assembly systems. A three-dimensional computational study of Janus droplet formation in a double Y-type microfluidic device filled with a shear-thinning fluid is performed by using the multiphaseInterDyMFoam solver of the OpenFOAM, based on a finite-volume method. The bi-phase volume-of-fluid method is adopted to track the interface with an adaptive dynamic mesh refinement for moving interfaces. The formation of Janus droplets in the shear-thinning fluid is characterized in five different states of tubbing, jetting, intermediate, dripping and unstable dripping in a multiphase microsystem under various flow conditions. The formation mechanism of Janus droplets is understood by analyzing the influencing factors, including the flow rates of the continuous phase and of the dispersed phase, surface tension, and non-Newtonian rheological parameters. Studies have found that the formation of the Janus droplets and their sizes are related to the flow rate at the inlet under low capillary numbers. The rheological parameters of shear-thinning fluid have a significant impact on the size of Janus droplets and their formation mechanism. As the apparent viscosity increases, the frequency of Janus droplet formation increases, while the droplet volume decreases. Compared with Newtonian fluid, the Janus droplet is more readily generated in shear-thinning fluid due to the interlay of diminishing viscous force, surface tension, and pressure drop.

Modeling droplet formation in microfluidic flow-focusing devices using the two-phases level set method

Droplet-based microfluidics is an emerging field that has found its way in different applications like material science and biotechnology. Knowing how factors like capillary number, surface tension, velocity ratio, viscosity ratio, and contact angle affect droplet formation is of upmost importance for the design of microfluidic platforms. In this study, we evaluate how these factors affect droplet formation by using the two-phase level set method, measuring its length and frequency. Additionally, to assess how channel geometry affects droplet length and frequency, we considered the three most commonly used flow-focusing geometries in microfluidic platforms. As a general conclusion, we found that the droplet length decreases when the capillary number, velocity ratio, and viscosity ratio increase, while it increases when surface tension increases as well. The frequency of droplet formation augments when the capillary number, velocity ratio, and viscosity ratio increase, while it decreases when surface tension increases. We found that geometry influences droplet length, while it has minor effects on droplet formation frequency. Moreover, the contact angle has a low effect on both droplet length and formation frequency in flow focusing devices compared to other studies carried out using different geometries like the T-junction.

Experimental Investigation on the Dynamics of On-Demand Ferrofluid Drop Formation under a Pulse-Width-Modulated Nonuniform Magnetic Field.

Drop formation has been the focus of many studies because of its vast application in biomedicine and engineering, as well as its rich underlying physics. Applying a magnetic force on ferrofluids can provide more control over the formation process of the droplet. In this study, a time-dependent, nonuniform magnetic field was used for the formation of ferrofluid droplets using a nozzle. A pulse-width-modulation signal (PWM) was utilized to induce the time-dependent magnetic field, and a drop-on-demand system was designed using the capability of the PWM magnetic field. Three kinds of drop formation regimes under the PWM magnetic field were seen. Also, a new droplet generation regime was observed in which the drop is formed while it bounces back to the nozzle during the off-time period of the magnetic excitation. As compared to other techniques, the main advantage of droplet formation in this regime is that there will be no satellite droplet during the pinch-off. The regime map of drop formation based on the magnetic Bond number and the dimensionless induced frequency was obtained. Also, the effect of the duty cycle, the induced frequency, the magnetic induction, and the vertical interval between the coil's top surface and the nozzle on the drop formation evolution, the equivalent diameter of the droplets, the frequency of droplet formation, and the pulses that are necessary to form a drop was studied. Additionally, it was illustrated that by prolonging the duty cycle, the magnetic induction, or by decreasing the induced frequency, the equivalent diameter of the drop and the pulses that are necessary to form a drop reduce, while the frequency of drop formation increases. Eventually, a correlation for predicting the nondimensionalized diameter of the droplet, based on dimensionless variables, was presented with a maximum relative error of 8.1% and an average relative error equal to 2.2%.

Non-dimensional groups for electrospray modes of highly conductive and viscous nanoparticle suspensions

Multiple modes of atomization in electrosprays are affected by viscosity, surface tension and electrical conductivity of the semiconductor nanosuspensions. While the effect of gravity is dominant in the dripping mode, the electric field degenerates the electrospray mechanism into a microdripping mode that can potentially allow the deposition of semiconductor nanodots on a substrate. Drop size and frequency of droplet formation are obtained as functions of non-dimensional parameters, which agree well with experimental data. The analysis shows that it is possible to produce the desired size and frequency of ejection of monodisperse droplets by manipulating the electrode voltage for any nanosuspension.

Ferrofluid droplet formation from a nozzle using alternating magnetic field with different magnetic coil positions

Ferrofluid has been used in many fields, such as microfluidics, droplet formation, and heat transfer, due to its potential to be attracted in the presence of a magnetic field. Droplet formation, itself, has many applications such as emulsions, 3D micro-printers, MEMS, and electro-sprays. In this study, the mechanism of ferrofluid droplet formation from the nozzle in the presence of an alternating magnetic field was investigated. The magnetic coil was fixed at different angles with respect to gravity and the effect of the alternating magnetic field and the angle of the magnetic coil axis with respect to gravity on the produced droplet volume, satellite droplet, and droplet formation frequency were studied for the first time. Also, by using a reservoir instead of syringe pump, a drop-on-demand (DOD) platform was introduced. The results showed that with increasing magnetic force, the volume of droplets in both DC and AC cases decreases, whereas the droplet formation frequency increases. It was also observed that by using a DC magnetic field for all angles, the droplet formation was accompanied by a satellite droplet, whereas in the presence of the AC magnetic field, the satellite droplet was eliminated. So, a new regime of droplet formation was observed. Also, by tuning the alternating magnetic field, a larger droplet with respect to DC magnetic field was detected. Interestingly, it was shown that by increasing the angle of the magnetic coil axis with respect to gravity from zero to 90°, the volume of the produced droplet has a minimum at 45°.

Controlled retention of droplets and the enhancement of mass transfer in microchannel with multi-groove structure

A simple and novel droplet-based microfluidic device with multi-groove structure has been developed to achieve stay-collision-transfer process of droplets. After summarizing the scaling law of droplet diameter and formation frequency with two phase flow rates, we got the optimum operating range of continuous phase flow. During the retention of droplet in groove, the existence of internal vortex was observed, which lead to the homogeneity of internal concentration field. For the process of solvent-microextraction with high phase ratio, due to multi-groove structure, the actual volume phase ratio in microchannel can be much smaller than injection phase ratio to improve extraction efficiency. And two-phase acid-base reaction and fluorescence extraction experiments further validate the enhancement of mass transfer process by this kind of microchannel.

Determining the flow-related cap deformation of Taylor droplets at low Ca numbers using ensemble-averaged high-speed images

Droplets of microscopic Taylor flows can act as stirred batch microreactors, while the continuous phase compartments supply good mixing and mass transfer to the channel walls. The design of reliable reactors, however, requires a priori information about droplet formation frequency and droplet length, which is difficult to obtain. Here, we report about a new method to reliably describe the droplet deformation, which could act as a flow indicator. The flow-related interface shape deformation of liquid–liquid Taylor flows in square micro channels for $$Re < 5$$ and $$Ca < 0.02$$ is quantified by experimental studies and ensemble image averaging. We deduce an easy-to-access droplet cap deformation model, which allows reducing the complex interface curvature information to an ellipse and provide correlation functions to link this deformation ratio to the flow conditions quantitatively. In addition, we introduce an experimental approach using a ternary liquid–liquid material system that allows adjusting $$Re$$ and $$Ca$$ numbers independently without surfactant addition by changing the mass fraction of two liquids forming the continuous phase. In combination, we suggest an image processing method to overcome the optical issues arising from the poor image contrast of Taylor droplets with low differences of refractive index to the bulk material. The presented approach opens the possibility to benchmark numerical studies of the interface deformation and paves the way for improved flow modeling, e.g., pressure drop or relative velocity of Taylor droplets, since the flow-induced curvature could serve as an indicator of the forces acting on the droplet front and rear.

Mixing efficiency and pressure drop analysis of liquid-liquid two phases flow in serpentine microchannels

When fluids flow in microchannels, due to the relative low hydraulic diameter and low flow velocity, the flow is usually laminar flow, which hinders the effective mixing between two liquid-liquid phases. In this paper, the mixing efficiency at both droplet forming stage and droplet moving stage are investigated with the volume of fluid (VOF) method. The user defined scalar (UDS) is defined in the dispersed phase to analyze the mixing efficiency quantitatively. The droplet moves in the microchannel with the constant velocity, while serpentine microchannels are designed with different bend radius ranging. \( \overline{R} \) and ed are defined as the ratio of the bend radius to the width of the microchannel, and the ratio of the dispersed phase velocity to the droplet moving velocity, respectively. They are used for illustrating the effect of the bend radius and the dispersed phase fraction on the mixing efficiency in the droplet. Results indicate that the smaller dispersed phase fraction and smaller bend radius show the better mixing efficiency. However, the droplet production frequency changes in a parabolic trend with the variation of the dispersed phase fraction. The suitable dispersed phase fraction should be less than 0.5 in order to achieve a higher mixing efficiency and higher droplet formation frequency. In addition, the pressure drop in microchannel is increased with the decrease of the bend radius. The pressure drop observed in the micorchannel with square turn (\( \overline{R} \) = 0) and the microchannel with a bend radius of \( \overline{R} \) = 1 is nearly the same. This paper can be referred by someone dealing with the micromixer design and mass transfer in micro scale.