Chemical Engineering Science

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Theoretical and experimental limits of monodisperse droplet generation

Ali Kalantarifard

^a

, Elnaz Alizadeh-Haghighi

^a

, Abtin Saateh

^a

, Caglar Elbuken

^a,b,c,^⇑

aInstitute of Materials Science and Nanotechnology, National Nanotechnology Research Center (UNAM), Bilkent University, Ankara 06800, Turkey

bFaculty of Biochemistry and Molecular Medicine, Faculty of Medicine, University of Oulu, 90014 Oulu, Finland

cVTT Technical Research Centre of Finland Ltd., 90570 Oulu, Finland

h i g h l i g h t s

Investigated the underlying reasons for droplet volume variation in fluidic systems.

Presented 4 design recommendations to improve monodisperse droplet generation.

Presented practical limit of achieving absolute droplet monodispersity, i.e. 0% CV.

Achieved ultra-high droplet monodispersity, less than 0.2% CV in droplet size.

Fluidic evaluation chip design to test parameters under same experimental conditions.

a r t i c l e i n f o

Article history:

Received 13 July 2020

Received in revised form 27 August 2020 Accepted 29 August 2020

Available online 6 September 2020

Keywords:

Microfluidics Microdroplets Monodispersity Numerical modeling T-junction Two phase flow

a b s t r a c t

Droplet microfluidic systems are becoming routine in advanced biochemical studies such as single cell gene expression, immuno profiling, precise nucleic acid quantification (dPCR) and particle synthesis.

For all these applications, ensuring droplet monodispersity is critical to minimize the uncertainty due to droplet volume variation. Despite the wide usage of droplet-based microfluidic systems, the limit of monodispersity for droplet generation systems is still unknown. Here, we present an analytical approach that takes into account all the system dynamics and internal/external factors that disturb monodispersity. Interestingly, we are able to model the dynamics of a segmented two-phase flow system using a single-phase flow analogy, electron flow, in electrical circuits. We offer a unique solution and design guidelines to ensure ultra-monodisperse droplet generation. Our analytical conclusions are experimentally verified using a T-junction droplet generator. Equally importantly, we show the limiting experimental factors for reaching the theoretical maximum of monodispersity.

1. Introduction

Droplet fluidic systems have dramatically improved precision in many applications, such as polymerase chain reaction (Tanaka et al., 2015), biochemical analysis (Kim et al., 2012), and particle synthesis (DeMello, 2006) in which accurate control of sample volume play a significant role. Despite the well-understood physics of squeezing regime droplet formation in two-phase flow systems, the long-sought-after goal of generating identical, equal size droplets is challenging. Although the individual parameters that affect the droplet size were identified as channel dimension (Thorsen et al., 2001), wettability (Xu et al., 2006), viscosity (Nekouei and Vanapalli, 2017), and flow rate or pressure ratio of the two immiscible fluids (Garstecki et al., 2006; Ward et al., 2005; Xu et al.,

2008), the governing mechanism of droplet size variation is not completely analysed. It is shown that droplet length is correlated to the pressure (Ward et al., 2005) or flow rate (Garstecki et al., 2006; Van Steijn et al., 2010; Xu et al., 2008) ratio of the dispersed and continuous phases. There are studies that discuss the root causes of size variation as internal and external pressure fluctuation (Glawdel and Ren, 2012; Korczyk et al., 2011; van Steijn et al., 2008). While the consequences of such fluctuations are still incompletely understood, some methods have been proposed to decrease internal (Pang et al., 2014) and external fluctuations (Crawford et al., 2017; Kalantarifard et al., 2018; Kang and Yang, 2012). These approaches suffer from experimental complexity and do not lead to a comprehensive solution for the elimination of pressure and flow rate fluctuations. Here, we introduce a new approach to analyse droplet size variation that eventually leads to a thorough understanding of the root causes of droplet polydispersity. We demonstrate ultra-monodisperse droplet generation with a coefficient of variation (CV) close to the theoretical limit

⇑ Corresponding author at: Faculty of Biochemistry and Molecular Medicine, Faculty of Medicine, University of Oulu, 90014 Oulu, Finland.

E-mail address:caglar.elbuken@oulu.fi(C. Elbuken).

Contents lists available atScienceDirect

Chemical Engineering Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c e s

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of 0% CV. We extend the basic electric circuits analogy of fluidic circuits (Mosadegh et al., 2010; Oh et al., 2012) to develop a methodology to study the key parameters that affect droplet size variation.

Applying high identical pressure from a single pressure supply and using a low hydrodynamic resistance droplet channel are the key factors for monodisperse droplet generation.

2. Theory

The existing models that predict droplet size in microdroplet systems correlate the length of a droplet with geometrical parameters, volumetric flow rate ratio of dispersed and continuous phases, and capillary number (Garstecki et al., 2006; Korczyk et al., 2019; Van Steijn et al., 2010; Xu et al., 2008). Ideally, keeping the flow rate ratio constant would result in the generation of identical droplets, since channel geometry, fluid viscosities and interfacial tension do not change during droplet generation. The use of Hagen–Poiseuille Law is a common practice when studying microfluidic circuits as a first approximation;DP¼ RQ, whereDP, R and Q are pressure difference, hydrodynamic resistance and volumetric flow rate, respectively. For a pressure-driven two-phase flow system schematically shown inFig. 1(a), we can write the volumetric flow rate ratio of the two immiscible fluids as

Qd

Qc¼^P_P^di_ci^P_P^dj_cj^R_R^c_d, where subscriptsc and d represent continuous and dispersed phases and i and j represent channel inlet and junction, respectively. Variation in the inlet and junction pressures leads to fluctuation in flow rate ratio and droplet length, which in turn leads to droplet polydispersity. We demonstrate that droplet volume variation can be minimized by two fundamental approaches:

flow source configuration and channel network design.

Unlike single-phase flow systems, generation and movement of the droplets in a microfluidic system lead to inevitable pressure variations, which are referred to as internal fluctuations. In addi- tion, there is pressure variation at the inlets due to pressure/flow source imperfections, which are referred to as external fluctuations. In theory, we can keep the flow rate ratio constant under a particular condition, that of having identical pressure for continuous and dispersed phases at the inlet (Pd_i¼ Pc_i) and the junction (Pdj¼ Pcj). In this case, the flow rate ratio would be independent of any pressure fluctuations, Q_d=Qc¼ Rc=Rd. Applying identical pressure for both phases at the inlet is a viable option, since inlet pressure is dictated by the user [Fig. 1(b)]. However, it is not possible to have the same pressure for continuous and dispersed phases at the junction due to the inherent Laplace pressure difference at the interface between the two phases (Pdi–Pci). Still, it is worth analysing the effect of having equal inlet pressures for a pressure driven droplet fluidic system. For this analysis, we rewrite the flow rate ratio equation as:

Q_d

Q_c¼ Pdi Pdj

Pci Pcj

! Rc

Rd

¼ Pd_i Pcj

Pci Pcj

Pdj Pcj

Pci Pcj

! Rc

Rd

¼

a

DPcDPL

DPc

Rc

Rd

ð1Þ

whereD^PL¼ Pdj Pc_jis Laplace pressure,D^Pc¼ Pc_i Pc_jis the pressure drop between the inlet and junction for the continuous phase and

a

^isP^di Pcj. Note thatD^PL,D^Pcand

a

are the fluctuating terms in Eq.(1).

Fig. 1. Schematic representation of fluidic and electric circuit and numerical results for the effect of fluctuating terms on droplet generation using the conventional (a) and proposed (b) method. (c) Equivalent circuit of a droplet generator driven by pressure supplies. Both two source and single source (grey background)-driven architectures are shown. Fluctuation ofa⁰=DVc(d),DVL=DVc(e) terms and the resultant system (f) for the conventional and proposed methods.

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3. Numerical modeling

To investigate the effect of the fluctuating terms in this equation, we performed a numerical study based on the analogy between fluidic and electrical systems. We made an electrical circuit equivalent of a T-junction droplet generator driven by a pressure supply [Fig. 1(c)]. Flow rate ð Þ, pressureQ ð Þ andP hydrodynamic resistor Rð Þ in the fluidic system are analogous to current Ið Þ, voltage Vð Þ and electrical resistor R ⁰

in the electrical circuit, respectively (⁰denotes electrical resistances throughout the text). The hydrodynamic resistance of the microchannel (Rm) between droplet generator junction and outlet fluctuates, since the pressure drop is a function of the number and the position of droplets (Cybulski et al., 2019). Similarly, there is a variation in Laplace pressure ðD^PLÞ, and the corresponding analogous resistance (R⁰LP) at the junction due to the varying interface geometry between the immiscible phases during droplet formation.

We propose an equivalent circuit for the droplet generation system in which the Laplace pressure is taken into account in the electrical circuit analogy. To achieve the equivalence to the fluidic circuit, the main channel resistance was shown as identical parallel channels inFig. 1c. Then for R⁰_LP¼ 0, main channel resistance is equivalent to R⁰_m. The flow rate ratio and, consequently, the droplet length is related to the current ratio Iðd=IcÞ in the equivalent circuit.

The electrical equivalent of Eq.(1)is written as:

Id

Ic¼

a

⁰ D^VcD^V^L

D^Vc

R⁰_c R⁰_d !

ð2Þ

We have studied the effect of having identical inlet pressures/- voltage and external fluctuations on the variation of the fluctuating terms in Eq.(2). Simulations were performed using a SPICE software (LTSpice, see supplementary Fig. S1), which gives the dynamic system response. We analysed the effect of the first term in Eq.(2),

a

⁰=DVc

, second term,ðDVL=DVcÞ, and their difference,

a

⁰=D^Vc

ðD^VL=D^VcÞ [Fig. 1(d)–(f)]. The calculation of the numerical values is explained in the supplementary document.

For the identical inlet pressures/voltages (V_d_i¼ Vc_i) shown in Fig. 1(b), we have:

Id

Ic¼ 1 D^VL

D^Vc

R⁰_c R⁰_d !

ð3Þ

which shows that fluctuations due to the first term are cancelled out. InFig. 1(d)–(f), the time-dependent change of fluctuating terms are plotted when a single source is used to drive the system (red cir- cle – case 1), which is also shown as the dashed line configuration in Fig. 1(c). For comparison, the simulations were repeated with the conventional architecture for two separate pressure sources with different (blue triangle – case 2) and same values (green square – case 3). In practice, for a two pressure source driven configuration even if inlet source pressures are kept constant, there are minor pressure fluctuations at the inlets due to inherent noise, which are included in the simulations as random white noise. The numerical simulation results show that using a single source not only eliminates the undesired flow rate fluctuations due to the first term, but also compensates the imperfections of the source fluctuations, as shown inFig. 1(d). The decrease in fluctuations from case 2 to case 3 is due to equating the inlet pressures and addresses the polydispersity due to the first term in Eq.(2). The further improvement from case 2 to case 1 is due to the immunity of the single source- driven system to source imperfections. Still, absolute monodispersity, i.e. 0% CV, is not possible due to the fluctuations of the second term in Eq.(2), as seen inFig. 1(e). Increasing inlet pressure/voltage

(D^Vc) and/or decreasing the Laplace pressure (D^VL) would minimize the fluctuations due to this term.

Design Recommendation 1: Supply the pressures to the two inlets of the microfluidic droplet generation system from a single source. For experimental implementation, a T- connector can be used to split the single source into two as schematically shown inFig. 1b.

4. Results and discussion

For experimental verification of these results, a PDMS/glass microfluidic chip was used. The width and height of all

channels were 300mm and 80 mm, respectively. The length of the continuous phase channel was 1 cm; dispersed phase and main channel were 18 cm long. Water droplets were formed inside sili- cone oil (50 mPa.s) using a pressure controller using four inlet pressure values (400, 500, 600, 700 mbar). The single pressure source configuration is shown inFig. S3b. The CV% measurement was performed by analysing the video recording of at least 150 consecutive droplets (Basu, 2013). The results were obtained at varying pressures, for four inlet pressure configurations. According to the experimental (Fig. 2(a)) and numerical (Fig. 2(b)) results, the single-source configuration leads to the smallest CV% values at all pressures.

Additionally, increasing the inlet pressure reduces the CV%, and an experimental CV% value of 0.11% was obtained the reason of which is not explicit and is explained further below in the text.

Increasing pressure not only improves droplet monodispersity, but also increases droplet generation frequency. The details of the channel geometry are given in the supplementary document (Table S1). These results verify that having a single source supply improves monodispersity. Still, a detailed analysis is required to develop strategies to minimize the other fluctuating terms and to approach the asymptotic theoretical limit of 0% CV, i.e. absolute monodispersity.

Optimization of the channel network design is the second route we explored to further improve droplet monodispersity. To this end, we rewrite the flow rate ratio equation by applying Kirchhoff current law to the equivalent circuit inFig. 1(c) (seesupplemen- tary filefor details). When a single pressure source is used to drive both fluids, as recommended above, (Vdi¼ Vci¼ Vi), we obtain the following equation:

Id

Ic

¼4R⁰_mR⁰_c 2R⁰mR⁰_LPþ R⁰cR⁰_LP

4R⁰_mR⁰_d 2R⁰mR⁰_LPþ R⁰dR⁰_LP ð4Þ Rewriting the current ratio (flow rate ratio) for the two input channels (fluid inlets), gives us a unique insight into how to further reduce the fluctuations. From a purely mathematical analysis of Eq.

(4), we can see that decreasing either (i) R⁰_LPor (ii) R⁰_mto zero causes the current ratio and, consequently, the droplet size to depend merely on resistance ratio R⁰_c=R⁰d, which is constant. Thus, by designing the system with minimal R⁰_m and R⁰_LP would lead to higher monodispersity. Additionally, when (iii) R⁰_c=R⁰d ratio approaches unity, the current ratio approaches one and higher monodispersity values are expected. These arguments are related to the channel network design and depend on the type of fluids, since viscosity effects hydrodynamic resistance. Thankfully, these three points can be studied using our previously discussed numerical model and can also be verified experimentally.

Firstly, the effect of decreasing RLP has been studied. Although Laplace pressure could be reduced by adding surfactant, the change is marginal due to critical micelle concentration (CMC) limit. We have added 0.5 wt% concentration SDS into water and

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decreased the interfacial tension from 38 to 5 mN/m. The monodispersity of the droplets with and without surfactant was measured and 20% decrease in CV% was obtained (Fig. 3(a)).

Design Recommendation 2: Minimize the interfacial tension between the dispersed and continuous phases at the device junction,DPL! 0. Note that increasing inlet pressures is equivalent to decreasing Laplace pressure relatively, hence in Fig. 2we observe increased monodispersity at higher inlet pressure settings.

Secondly, we studied the effect of decreasing main channel hydrodynamic resistance, Rm. We used microfluidic designs with five different main channel lengths (L = 1, 4, 10, 16, 21 cm) and performed monodispersity measurements. Experiments for each channel length were repeated four times, each analysing 150 consecutive droplet to obtain experimental CV values. Both numerical and experimental results demonstrate that decreasing main channel length decreases the CV% of droplet size and improves monodispersity. For the shortest main channel of 1 cm length, we accommodated 20 droplets in the main channel and obtained a CV of 0.24%

[Fig. 3(b)].

Design Recommendation 3: Minimize the hydrodynamic resistance of the main channel that accommodates the droplets.

Finally, Rc=Rdratio was varied using a screw valve placed on the dispersed phase inlet section of the device, as shown inFig. 3(c). Tight-

ening the screw increases hydrodynamic resistance of the dispersed phase inlet channel (Rd) by decreasing channel height. Measuring the ratio of the dispersed phase and continuous phase volumes in the main channel by using image processing, we obtained quantita- tive values of Rc=Rd ratio (details are given in the supplementary document). The smallest experimental CV% was obtained when Rc=Rdwas approximately 1 at a screw angle ofh^°=135° that is in line with our expectations obtained from Eq.(4).

Design Recommendation 4: Equate the hydrodynamic resistance of continuous and dispersed channel inlets by considering the fluid viscosity, channel geometry and all the fluidic path from the source to the junction.

Our experimental and numerical results given inFigs. 2 and 3show that droplet monodispersity can be improved by optimizing several parameters, such as having a single pressure source supply that is set at high pressure, decreasing the interfacial tension, using a short main channel, and equating the resistance of the inlet channels.

Another interesting study at this point is to compare the effects of each of these modifications on monodispersity improvement to be able to prioritize when it is required to design for an application where all the design recommendations given above are not possible to implement concurrently. To tackle this problem, we designed another microfluidic device (fluidic evaluation chip), which can vary the hydrodynamic resistance of main channel and one of the inlet channels, to quantify the effect of changing inlet pressure (Pin), main channel length (Lm) or resistance (Rm) and hydrodynamic resistance ratio of inlet channels (Rc=Rd). We owe this idea to electrical circuit evaluation boards which enables system optimization where multi- Fig. 2. Experimental (a) and numerical (b) results of droplet monodispersity values, %CV, obtained for single-source and two-source configurations. Error bars denote standard deviation of four experiments. The insets show the normalized size of individual droplets for 700 mbar/7.0 V inlet pressure/voltage.

Fig. 3. Experimental and numerical results of droplet monodispersity, CV% as a function of (a) Laplace pressure (RLP), (b) main channel length (Rm) and (c) (Rc=Rd) ratio. (b) n denotes the number of droplets accommodated in the main channel; error bars denote standard deviation of four experiments. (c) The inset shows the photo of the microfluidic device with a screw valve.

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ple parameters can be varied simultaneously under same operating conditions. Using a single pressure source and bifurcation, inlet pressures of the fluids were set as identical and changed simultaneously, Pin = 360, 400, 440 mbar. As shown inFig. 4(a) and (b), a screw valve was placed over the dispersed phase channel to change the channel height to vary (Rc=Rd) by setting the screw angle (h° = 0, 90, 180). The serpentine main channel section was designed with multiple outlets, only one of which was used, while the others were kept closed using microplug valves (Guler et al., 2017); hence different main channel lengths were obtained (Lm= 13, 16.5, 20 cm). For real-time analysis of droplet size variation, we used impedimetric droplet measurement (iDM) (Saateh et al., 2019). The results are in accordance with our previous conclusions. Droplet monodispersity improves by increasing inlet pressure (Pin), decreasing main channel length (Rm), and equal inlet channel hydrodynamic resistances (Rc=Rd). These results not only replicates our previous conclusions given using a different microfluidic chip, but also provides a second verification using a different droplet size analysis tool, which is based on electrical impedance change whereas previous experimental results (Figs. 2 and 3) were obtained using an optical droplet size analysis tool.

We employed a randomized full factorial study to compare the effects of three factors (Pin, Rm, Rc=Rd) on the monodispersity of droplets, CV%. The Pareto chart inFig. 4(c) shows that Pin, Rm, Rc=Rdand the interaction between P_inand R_mare significant parameters in improving droplet monodispersity. The monodispersity results of all 27 experiments and a multivariable chart for the main and interaction effects are given in the supplementary document.

When we compare the monodispersity values given in the liter- ature, which mainly used displacement (syringe) or pressure pumps, we see a victory of syringe pump-driven systems that are immune to the pressure fluctuations and are primarily affected by the variation of inlet volumetric flow rates (Bauer et al., 2010;

Hwang et al., 2014; Link et al., 2004; Wang et al., 2015; Xu and Nakajima, 2004). The intrinsic internal fluctuation’s effect on droplet monodispersity in syringe pump-driven systems is less than pressure-driven systems (Kalantarifard et al., 2018). Also, negative pressure-driven systems performed better than positive pressure supplies (Murata et al., 2018; Tanaka et al., 2015). A negative pressure-driven droplet generator is equivalent to setting the inlet pressures to the same value (P_d_i= P_c_i= P_atm). Hence, the retrospec- tive monodispersity comparison is in accordance with our findings (refer to Table S3 for a detailed comparison). Another broadly

agreed fact is that increasing capillary number improves monodispersity (Abate et al., 2012; Li et al., 2012; Sivasamy et al., 2011; Yan et al., 2012; Zagnoni et al., 2010). The capillary number can be increased by increasing the flow rate or by decreasing the interfacial tension, both of which are equivalent to decreasing the effect of Laplace pressure.

These results demonstrate that using a pressure driven droplet generation system that is fed from a single pressure source and optimizing the channel network leads to very high monodispersity droplet generation. It is also worth emphasizing that implementation of the four design recommendations given above is straight- forward for any droplet fluidic system. One concern might be losing a degree of freedom when two inlets are controlled using a single source, since droplet size adjustment is usually done on- the-fly by tuning the inlet pressure or flow rates. To overcome this shortcoming and making ultra monodisperse droplets of any size, the channel geometry should be engineered so that the droplet volume for the recommended equal inlet hydrodynamic resistance configuration yields the desired droplet volume, which is dictated by the channel design. An easier solution can be changing the hydrodynamic resistance of the dispersed or continuous phase inlet channels in-situ during an experiment. In Fig. 5, we show two techniques that allow discrete and continuous changes of inlet channel hydrodynamic resistances using plug (Guler et al., 2017) and screw valves, (Elizabeth Hulme et al., 2009) respectively.

In the plug valve technique, parallel channels equipped with a plug valve are used to supply the dispersed or continuous phase.

The inlet channel hydrodynamics resistance can be varied by turn- ing the valves on/off; discrete resistance values are obtained, which can be calculated for channels of rectangular cross sections (Oh et al., 2012). We implemented this technique using three valves for the dispersed phase inlet as shown inFig. 5(a). The average droplet lengths (n = 100) obtained for various valve combina- tions at constant shared inlet pressures are given inFig. 5(b).

Similarly, the hydrodynamic resistance of inlet channels can be varied using other types of valves. To demonstrate continuous tuning of channel hydrodynamic resistance, we employed a screw valve placed over the dispersed phase inlet channel. Tightening the screw presses over the channel and decreases the channel thickness [Fig. 5(c)]. Expectedly, this lowers the droplet length as shown inFig. 5(d). It should be noted that the screw valve enables droplet generation in a broader range with much finer control in comparison to the plug valve. The two types of valves given in

Fig. 4. The schematic drawing (a) and the photo (b) of the monodispersity evaluation chip, (c) Pareto chart of effects. The inlets were connected to a single pressure supply (Pin) using a bifurcated tubing. The effective main channel length (Rm) was varied using plug valves.

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Fig. 5are simply to demonstrate the tunability of droplet size even when the two inlets are fed from a single pressure source. Any microfluidic valve can be used to change the hydrodynamic resistance ratio of dispersed and continuous phases. Droplet size depends on the microfluidic device dimensions. Therefore, it is preferable to adjust the volume of monodisperse droplets at the chip design stage instead of in-situ tuning which may violate Design Recommendation 4.

5. Conclusions

Achieving high monodispersity is a necessity for all droplet fluidic applications that require precision analytics. We demonstrated a holistic approach studying the external and internal factors that cause polydisperse droplet generation. We concluded that supply- ing the inlet pressures from the same source (Design Recommen- dation 1) and equating inlet channel hydrodynamic resistances (Design Recommendation 4) minimize the pressure difference between the dispersed and continuous phase at the junction. Low- ering the interfacial tension (Design Recommendation 2) serves the same purpose. Hence, the underpinning effect of our suggested design guidelines is to minimize pressure discontinuity at the droplet formation junction and to approach a single-phase-like system. Additionally, lowering the main channel hydrodynamic resistance (Design Recommendation 3) is also important to improve monodispersity. We modelled the dynamics of a segmented two-phase flow system using a one-phase flow analogy,

electron flow in electrical circuits. We determined the governing factors and their effect on droplet monodispersity. Eventually, we offered a flow source configuration and channel network design recommendations to minimize external and internal fluctuations.

We achieved a droplet monodispersity of less than 0.2% CV. More importantly, we showed the limitations of reaching the maximum theoretical limit of monodispersity. The analytical, numerical and experimental results given in this manuscript not only explain the underlying physics of droplet size variation in microchannels, but also provide practical design guidelines to obtain very high droplet monodispersity.

CRediT authorship contribution statement

Ali Kalantarifard: Methodology, Formal analysis, Investigation, Validation, Visualization, Writing - original draft. Elnaz Alizadeh- Haghighi: Validation, Investigation. Abtin Saateh: Software.

Caglar Elbuken: Conceptualization, Methodology, Validation, Pro- ject administration, Funding acquisition, Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing finan- cial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 5. The device and experimental results of using two different techniques to make monodisperse droplets in different sizes. (a) Photograph of the microfluidic T-junction device with three parallel dispersed phase channels equipped with micro plug valves. (b) Droplet lengths for different pressures and hydrodynamic resistance ratios for various micro plug valve configurations. (c) Photograph of the microfluidic T-junction device equipped with screw valve. (d) Droplet lengths for different pressures and rotation angles of the screw valve. The results are the average length of 100 droplets for each case.

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Acknowledgements

This project was partially supported by TÜBITAK (no. 215E086).

C.E acknowledges the support from The Science Academy, Turkey through the Young Scientist Award Program.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ces.2020.116093.

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