Droplet Formation Process Research Articles

Waveform Design Method for Piezoelectric Print-Head Based on Iterative Learning and Equivalent Circuit Model

Piezoelectric print-heads (PPHs) are used with a variety of fluid materials with specific functions. Thus, the volume flow rate of the fluid at the nozzle determines the formation process of droplets, which is used to design the drive waveform of the PPH, control the volume flow rate at the nozzle, and effectively improve droplet deposition quality. In this study, based on the iterative learning and the equivalent circuit model of the PPHs, we proposed a waveform design method to control the volume flow rate at the nozzle. Experimental results show that the proposed method can accurately control the volume flow of the fluid at the nozzle. To verify the practical application value of the proposed method, we designed two drive waveforms to suppress residual vibration and produce smaller droplets. The results are exceptional, indicating that the proposed method has good practical application value.

Pulsed coaxial drop-on-demand electrohydrodynamic printing

This research demonstrates pulsed electrohydrodynamic drop-on-demand (DoD) printing as a novel technique for synthesizing core–shell microparticles in a controlled manner. In this regard, a multiphase and multiphysics model is presented for coaxial electrohydrodynamic printing. The governing partial differential equations of the model are discretized using the finite element method, and a suitable numerical scheme is adopted to solve the system of discretized equations. The experimental results in the literature are used to validate the numerical model. Utilizing the validated model, the effects of continuous-direct current (DC) voltage and pulsed-DC voltage are examined on the behavior of a compound meniscus (composed of ethylene glycol core and olive oil shell) and the droplet formation process. According to the results obtained, the onset voltage of the compound meniscus is 3330 V, which agrees with the scale analysis. Furthermore, increasing continuous-DC voltage results in longer breakup length, shorter breakup time, faster droplet velocity, and shorter jetting start time. In addition, increasing pulsed-DC voltage duration leads to an increase in the breakup length and droplet velocity. Most importantly, it is possible to control the inertia of the coaxial spindle by controlling the pulsed-DC voltage magnitude and duration to ensure that a core–shell droplet separates from the meniscus in every pulse with the shortest breakup length and the minimum satellite droplets possible. It is generally recommended to keep the pulse duration and amplitude low enough to prevent the long breakup length and irregularities in the printed pattern; however, they must be sufficiently large to sustain the micro-dripping mode.

Droplet formation in a step-emulsification microdevice: effect of fluid's viscosity

Particle synthesis, food science and chemical reactions in microchannels often involve highly viscous fluids. In this paper, silicone oils with viscosities of 10 mPa·s, 50 mPa·s and 100 mPa·s respectively are used as continuous phase, and aqueous glycerol solutions with mass fraction of 62%, 81% and 87% are used as dispersed phase. Thus, droplet formation under various viscosities in step-emulsification microdevices is investigated. Based on the liquid-liquid interface evolution, three stages of the droplet formation process are explored. The 2-D expansion process isn't basically affected by the fluid's viscosity. The high viscosity of two phases retards the necking stage and increases the droplet size. The local capillary number Ca of two phases is 10−4 - 2 × 10−2, and the local Weber number We of two phases is less than 10−4. This shows that the necking process is dominated by two-phase viscous force and interface tension. A prediction model for the droplet size is proposed, and the error is within 10%. Finally, the change rule of the flow pattern transition with the viscosities of two phases is determined.

High-speed imaging of giant unilamellar vesicle production in cDICE.

Giant unilamellar vesicles (GUVs) are cell-sized containers that are commonly used as three-dimensional model membranes in biophysics, as in vitro model systems in synthetic biology, and even as cargo carriers in various other research fields. Despite their ubiquitous use, there is still no one-size-fits-all GUV production method. Over the years, numerous methods have been developed, attempting to meet the demanding requirements of robustness, reliability, and high yield while simultaneously achieving robust encapsulation. Double emulsion-based methods are often praised for their apparent simplicity and good yields; hence, methods like continuous droplet interface crossing encapsulation (cDICE) that make use of this principle, have gained popularity in recent years. In cDICE, aqueous droplets that originate from a capillary orifice are continuously forced through an oil-water interface by centrifugal force, thereby forming a lipid bilayer and thus GUVs. Although cDICE and related methods are frequently used in the field, the complexity of the underlying principles and fluid dynamics has not been considered previously, and how exactly the GUVs are being formed remains unknown. To elucidate the process of GUV formation in cDICE, we have developed a high-speed microscopy setup that allows us to visualize GUV formation in real time. We focused on the capillary orifice, where initial droplet formation occurs, and on the oil-water interface, where droplets are converted into GUVs. Our experiments reveal a complex droplet formation process at the capillary orifice and suboptimal droplet transfer through the water-oil interface, which we explain using fluid dynamics and theoretical modeling. Our results are a first step towards explaining the widely observed variation in encapsulation efficiency and size polydispersity in cDICE. Ultimately, these results will contribute to a better understanding of GUV formation processes in cDICE and in extension, in double emulsion-based methods in general.

Controllable fabrication of millimeter-scale double droplets in co-flowing devices

The fabrication of millimeter-scale water-in-oil-in-water (W1/O/W2) double droplets in five self-manufacturing co-flowing devices is investigated. Double droplets with a diameter range of 1000–4000 µm are successfully fabricated. Three typical flow patterns are observed in a wide range of flow rates, namely squeezing, dripping-like, and jetting-like. A flow pattern diagram is obtained to form double droplets without a single oil droplet and rupture. Furthermore, during the transition from the squeezing to jetting-like patterns, the frequency, filament length and satellite droplet size increase, while the double droplet size and formation period decrease. In addition, due to the increase in middle O and outer W2 phase tube sizes, the double droplet size and its distribution increase, but the frequency decreases. The effect of the flow rate of different phases and the sizes of the tubes on the formation process of millimeter-scale double droplets is also systematically investigated. These results provide more in-depth insight into the formation mechanism of millimeter-scale double droplets and enhance the fabrication controllability of double droplets.

Regulation of droplet size and flow regime by geometrical confinement in a microfluidic flow-focusing device

We have developed a coupled level set and volume of fluid-based computational fluid dynamics model to analyze the droplet formation mechanism in a square flow-focusing microchannel. We demonstrate a flexible manipulation of droplet formation and flow regime based on the modified flow-focusing microchannel with a constricted orifice. Furthermore, we have systematically studied the influence of geometrical confinement, flow rate, and interfacial tension on the droplet formation regime, length, volume, velocity, and shape. Three different flow regimes, namely squeezing, dripping, and jetting, are observed, and the flow regime maps are formulated based on the Reynolds and capillary numbers. After an extensive numerical investigation, we described the boundaries between the different regimes. Droplet shape is also quantified based on the deformation index value. Plug-shaped droplets are observed in the squeezing regime, and near spherical droplets are found in the dripping and jetting regimes. Our study provides insights into the transition of a regime under various geometrical confinement and fluid properties. The results reveal that the modified flow-focusing microchannel can substantially enhance dripping while decreasing the squeezing regime, which is of paramount importance from the standpoint of producing high throughput stable and monodisperse microdroplets. Eventually, this work emphasizes the importance of geometrical confinement, fluid properties, and flow conditions on the droplet formation process in a flow-focusing microchannel that can effectively provide helpful guidelines on the design and operations of such droplet-based microfluidic systems.

Experimental study of the stable droplet formation process during micro-valve-based three-dimensional bioprinting

Three-dimensional (3D) bioprinting offers great potential for the fabrication of complex 3D cell-laden constructs for clinical and research applications. The droplet formation process is the important first step in droplet-based 3D bioprinting, affecting the positional accuracy and printing fidelity. In this paper, the drop ejection behavior, thresholds for stable droplet generation, and formation of satellite drops are studied, under various ink properties, printing conditions, and input cell concentrations using a micro-valve-based 3D bioprinter. Three droplet ejection behaviors are identified under different conditions: an isolated stable droplet, satellites coalescing into a single droplet, and the presence of one/multiple satellites. The droplet state is represented by a phase diagram bounded by a dimensionless Z number (the inverse of the Ohnesorge number) and a jet Weber number, Wej, to define the printability of the utilized bioprinter. The printability range is defined as 2 < Z < 15 and 10 < Wej < 25 by considering characteristics, such as stable single droplet formability and sufficient drop falling velocity. There is no fatal damage on cells within this printability range. The results show there is no strong influence of an actuation system on droplet-based bioprinting printability. As the input cell concentration increases, the bioink's density and viscosity increases, and surface tension decreases, which, in turn, causes the Z number to slightly decrease. The change in the cell concentration (from 0 to 1×107 cells/ml), within a Newtonian bioink, has negligible impact on the droplet volume, falling velocity, drop ejection behavior, breakup time, and ligament length in microvalve-based bioprinting.

A Study of the coarse droplet formation from the liquid film in steam turbines

For all the deployment of the non-fossil energy sources the steam turbine remains the most important energy transforming device. In the current situation when the daily operation of the turbines is not predictable due to electricity supply from the photovoltaic and the wind power plants, the turbines work in the non-design conditions, the danger of the blade’s erosion caused by the coarse droplets is assumed. The purpose of this paper is to suggest the possible formation process of the coarse droplets in the steam turbine. The current studies were focused mostly on the measurement or identification of the coarse droplets in the steam turbine, but the explanation of the archived results was not sufficient. An analysis of the droplets formed in the wind tunnel indicates, for the majority of the measurements, the part of the formed droplets is bigger than the critical Weber number limit. Similar, but less detail, experience was achieved for measurement in the steam turbine. This paper introduces simple analysis of the optically measured coarse droplets size distribution with the modelled flow field behind the blade fitted by measured velocity field. A detailed hot wire measurement was performed in the vicinity of the trailing edge where the liquid film is disrupted to the coarse droplets.

Computational fluid dynamic study of polycaprolactone nanoparticles precipitation in a co‐flow capillary micro‐tube

AbstractPolycaprolactone nanoparticles (NPs) were produced in the co‐flow glass capillary device with tip dimension. NPs size was 990 nm for continuous phase velocity, and and 426 nm for . The droplet formation process in the co‐flow microchannel was also simulated using computational fluid dynamic (CFD). Employing a digital image analysis technique, a cut‐off value of 0.81 for the dispersed phase volume fraction was proposed for the determination of droplet size. A scenario was expressed for NP formation from micro‐droplets. Moreover, after conducting 27 CFD simulations, a dimensionless exponential form correlation was proposed for droplet size estimation. In this generalized map, there were three distinct regions based on the relative capillary numbers of continuous to dispersed phases. It was revealed that at a constant dispersed phase velocity, by increasing the continuous phase velocity, more small NPs are formed. The results show that the ratio of micro‐droplets to NPs size was between 735 and 755.

Investigation of Cell Aggregation on the Printing Performance in Inkjet-Based Bioprinting of Cell-Laden Bioink.

During 3D bioprinting, when the gravitational force exceeds the buoyant force, cell sedimentation will be induced, resulting in local cell concentration change and cell aggregation which affect the printing performance. This paper aims at studying and quantifying cell aggregation and its effects on the droplet formation process during inkjet-based bioprinting and cell distribution after inkjet-based bioprinting. The major conclusions of this study are as follows: (1) Cell aggregation is a significant challenge during inkjet-based bioprinting by observing the percentage of individual cells after different printing times. In addition, as polymer concentration increases, the cell aggregation is suppressed. (2) As printing time and cell aggregation increase, the ligament length and droplet velocity generally decrease first and then increase due to the initial increase and subsequent decrease of the viscous effect. (3) As the printing time increases, both the maximum number of cells within one microsphere and the mean cell number have a significant increase, especially for low polymer concentrations such as 0.5% (w/v). In addition, the increased rate is the highest using the lowest polymer concentration of 0.5% (w/v) because of its highest cell sedimentation velocity.

Experimental and numerical study of droplet formation with Marangoni instability

The Marangoni effect produces some complex phenomena during droplet formation and has an important influence on the mass transfer state. In this paper, the droplet formation process of toluene/acetone/water droplet extraction system accompanied by Marangoni instability was numerically simulated, and the actual mass transfer states of droplets were photographed using schlieren imaging technology. The results reveal that: suspended droplets may have mass transfer states such as diffusion layer, natural convection, jet and turbulence, and the Marangoni instability causes the droplets to jet solute intermittently. Compared to droplets with constant surface tension, the Marangoni effect increases the mass transfer rate during droplet formation, and the Marangoni stress generates Marangoni convection at the interface, whose mutual annexation with the internal circulation leads to droplet oscillations. The Marangoni effect also causes pulsations in droplet vorticity, increasing the solute concentration exacerbates the vortex disorder, while increasing the injection rate may suppress the pulsations, which are physically dependent on the relative advantage of droplet internal circulation over Marangoni convection.

Material jetting for advanced applications: A state-of-the-art review, gaps and future directions

The proven ability of additive manufacturing (AM, also known as 3D printing) to fabricate complex components with substantial reductions in material wastage and reduced lead times has made it a key enabling technology for numerous important industrial applications. Of current AM processes, material jetting (MJ) is demonstrating considerable potential for producing multi-material, intricate, 3D components and systems with integrated functionality, with the additional benefit that the process can be easily integrated with other manufacturing procedures. However, material jetting of functional materials to produce advanced applications still poses numerous technological challenges which hinder its full industrial exploitation. These extend from the limited range of high-performance materials with consistent properties usable for MJ, through the need to enhance the process itself by optimizing the droplet formation process, tuning waveforms for specific processes, modification of substrate and substrate/jetted material interactions, the complexities of curing and post-processing procedures, and the challenge of characterizing the 3D printed parts. In this context, this article attempts to provide a comprehensive discussion of the principles and characteristics of the most recent material jetting technology and review the state-of-the-art research and development being conducted. This review identifies existing gaps with regards to high-performance UV-curable inks, printing behavior of non-Newtonian fluids, optimum jetting and curing strategies and effective measures for achieving high-precision MJ. Future work should bridge the aforementioned gaps in order to improve the performance of the technology, thereby making it more attractive for large-scale adoption by industry and increasing market acceptance and penetration of material jetting for advanced applications.

Dynamic of centrifugal step emulsification and prediction of droplet diameter

Studies show that centrifugal step emulsification is an effective method for high throughput droplet generation and has been widely used over the past ten years. However, there is no in-depth understanding of the physics underlying emulsification and the effect of centrifugal force on the droplet volume. Aiming at resolving this shortcoming, this article is focused on the dynamics of the droplet formation process subjected to centrifugal acceleration, and a theoretical model is proposed for accurately predicting the droplet size. A critical time and a critical bulb length are introduced to describe the droplet formation and divide this process into stable and rapid filling regimes. It is worth noting that the centrifugal force was considered in the dispersed phase profile. Finally, a theoretical model was established to predict the droplet size. Numerical simulation and high-speed measurements demonstrate that there is a critical time and bulb length, and the critical bulb length is in good agreement with the proposed theory. To evaluate the performance of the model, experiments with different centrifugal accelerations, terrace heights, and terrace lengths were carried out. The obtained results are in excellent agreement with the experiments, and the relative diameter error was less than 4%. The performed analyses demonstrate that the established model can be applied to accurately calculate the droplet size and obtain the correlation between the droplet size and different parameters, such as terrace height, terrace length, and centrifugal acceleration. This model has great potential in guiding the designs of centrifugal step emulsification systems.

Experimental study on the dispersed phase droplet formation process in a circumferential shear flow in dripping regime

A simplified experimental device was designed to simulate the shear flow in a liquid-liquid cyclone reactor. And the dispersed phase droplet formation process in the shear flow in dripping regime was investigated. Four characteristic parameters, droplet growth time (Tg), shrink time (Ts), formation time (Tf) and size (d) were used to describe the formation process. All the parameters presented fluctuation with different serial droplet numbers. Therefore, the effect of dispersed phase inlet flow rate (vd) on the value and uniformity of the parameters are analyzed. The results indicate that with the increase of vd, Tg, Ts, Tf decrease firstly and then increase, while the droplet size gradually increases. Meanwhile, the uniformity of Tg decreases first and then basically tends to be stable, while that of Ts, Tf and d decreases firstly and then increases. Eventually, the optimal range of vd under different continuous phase inlet flow rate is provided.

Dynamic wetting characteristics during droplet formation in a microfluidic T-junction

• Dynamic wetting characteristics during droplet formation in a microfluidic T-junction are investigated. • The three-phase contact line dynamics are influenced by the channel wettability and other flow properties. • The dynamic contact angle increases with an increase in Capillary number, static contact angle, and dispersed phase viscosity. • In contrast it decreases with an increase in flow rate ratio and slip length. Droplet formation in a microfluidic T-junction is dominated by the interfacial force arising between the two fluids. The three-phase contact line at the channel wall is affected by the surface energy or the wettability of the channel wall and other hydrodynamic forces. The dynamics of a three-phase contact line can be evaluated in terms of dynamic contact angle, which a moving contact line makes with a wall. The present work investigates the influence of wall hydrophobicity and fluid properties on the three-phase contact angle during droplet formation in a microfluidic T-junction. Experimental and numerical investigations are performed to study the effects of flow properties on the dynamic wetting of the channel during the droplet formation process. A level-set-based numerical model is employed to predict the moving contact line for different operating parameters and wettabilities of channel walls. Further, a simplified analytical model is developed to express the influence of flow parameters on the dynamic wetting behavior of the wall. The interface is more stressed out for a low viscous dispersed fluid, whereas the interface is less affected by a high viscous dispersed phase fluid. During the transient droplet stage, the dynamic contact angle increases with time with the increase in channel wall hydrophobicity. The dynamic contact angle increases with time for a higher static contact angle, and the variation decreases at a lower static contact angle. At the steady-state, the dynamic contact angle increases with the static contact angle and dispersed phase viscosity. In contrast, it decreases with an increase in the flow rate ratio and the slip length. The droplet with a higher length tends to increase the wetting line in the channel wall. The wettability of the channel wall influences the droplet interface along the lateral direction resulting in corner leakage flow, which further affects the dynamic contact angle.

Simulation of Droplet Formation in T‐Inlet Microchannels with Different Junction Angle

AbstractThe level set method was used to numerically simulate the droplet formation process in T‐junction microchannels with different junction angle. The effects of flow rate ratio, capillary number, and contact angle on droplet formation under different junction angles were discussed. The numerical simulation results show that the dimensionless length and generation frequency of microdroplets increase with the flow rate ratio. It was observed that the droplet transforms from the squeezing regime to the dripping regime when the capillary number Ca is ≥ 0.02. For Ca ≤ 0.04, the smallest droplet was generated in the microchannel with 120° junction angle. Finally, the results also indicate that the effect of the contact angle is discrepant at different junction angles.

Enhanced droplet formation in a T-junction microchannel using electric field: A lattice Boltzmann study

The electric field-driven droplet formation technique can effectively improve the formation throughput and control the droplet size, which is important for the application of microscale droplets in biopharmaceuticals and chemical analysis. In this paper, the droplet formation characteristics in T-junction microchannels under the action of electric field are investigated by coupling a three-dimensional lattice Boltzmann method (3 D LBM) with the leaky dielectric model, focusing on the effects of electric capillary number, a flow ratio, and a viscosity ratio on the droplet size. It is shown that as the electrical capillary number increases, the non-uniformly distributed electric force stretches the dispersed phase to form a Taylor cone and increases shear force at the interface of the two liquids to overcome the surface tension force. This facilitates the transition from squeezing to dropping and reduces the droplet size. At high flow ratios, increasing the electric capillary number leads to a pinning effect between the dispersed phase and the wall, which intensifies the compression of continuous phase on the neck of dispersed phase, resulting in a significant decrease in the droplet size. As the viscosity ratio increases, the vortex resistance caused by electrical force decreases, and thus, the electric field effect will dominate the droplet formation process.

Prediction of Newtonian Droplet Breaking Time from a Capillary at Low Weber Numbers.

Droplet formation and growth processes have numerous scientific and industrial applications. Experimental and numerical studies on the formation, growth, and breaking of droplet are carried out in present work. The numerical results are in good agreement with the experiment. This work focused on the effect of different Weber numbers (We) on the droplet breaking time. The results show when We < 0.05, the length and volume of the droplet increase, and the breaking time decreases rapidly. The resultant force acting on the main droplet suddenly drops around the critical breaking time. The difference rate between the time tn (when the resultant force is zero) and the breaking time tb is less than 8.49%. For the dimensional analysis of the numerical results, a prediction formula of breaking time on the Weber number is modeled as aWeb + c for We < 0.5.

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.

Effect of Sea Salt AOT on Precipitation Processes Associated with Red Sea Moisture Flux on Iraq, a Case Study

Sea salt acquires importance in the process of precipitation formation through its hygroscopic nature. and its role in accelerating the droplet formation process within a moisture saturation less than if it was not present. In this work, the maps of precipitation distribution with sea salt aerosol optical thickness (AOT) as well as moisture flux and wind at an altitude of 50 meters were compared. The data of Three rainy cases, characterized by heavy rains and moisture feeding from the Red Sea were selected. They are respectively 13 to 15 November 2018, 1 December 2018, and 27 to 29 January 2019. Cloud top temperature (CTT) data were obtained from Meteosat satellites (Meteosat 9, and 10). Total Precipitable water (TPW) and sea salt (AOT) were obtained from Model projects: a modern-era retrospective analysis for research and applications 2 (MERRA-2). the correlation coefficient (R) was used to test the relation between the variables like Total Precipitable water (TPW), Cloud top temperature (CTT), precipitation, and Sea Salt AOT. The results showed that there is a good correlation between the sea salt AOT and the amount of precipitation. The work also showed the roles that other variables play in the precipitation process. Where the relationships showed values of correlation coefficients about 0,6 to 0,7 between the variables, leading to the enhancement of precipitation.