Abstract
For using microscopic multiphase flows in microreactors, an exact understanding of the underlying hydrodynamic interrelations is key for successful reactor layout and reaction control. To examine the local hydrodynamic behavior, noninvasive optical measurements techniques like particle tracking velocimetry (PTV) or micro particle image velocimetry (µPIV) are the methods of choice, since they provide precise velocity measurement with excellent spatial resolution. Such optical approaches require refractive index matching (RIM) of the involved flow phases to prevent optical distortion due to light refraction and reflection at the interfaces. Established RIM approaches often provide a single degree of freedom, which is sufficient to solely match the refractive index (RI) of the flow phases. Using these approaches, the material properties (Oh number) are fixed and the relevant dimensionless numbers (Ca, Re) may only be altered hydrodynamically or geometrically. To avoid expansive geometric scaling of the microchannels, we propose an approach using two binary mixtures (doublebinary mixtures) to introduce an additional degree of freedom. The approach allows examining liquid–liquid twophase flows at a distinct velocity while being able to change the material properties (Oh number). Thus, Ca and Re can be chosen individually and the proposed RIMapproach provides undisturbed optical access. Furthermore, we present four different binary mixtures, which allow to vary the viscosity ratio of the phases. The relevant material parameters are successfully correlated to measurement data, which delivers a system of equations that determines the mass fractions and the velocities to address Re and Ca individually. A proofofprinciple for the proposed double binary mixture RIMapproach is successfully established using µPIV raw images.
Graphic abstract
1 Introduction and concept
Microfludic processes using liquid–liquid multiphase flows have gained great interest in the past decades (Zhao and Middelberg 2011; Chou et al. 2015; Ahmed et al. 2018; Shi et al. 2019). The applications range from chemical (Kobayashi et al. 2006; Song et al. 2006; Kralj et al. 2007; Lang et al. 2012; Tanimu et al. 2017) to biological (ClausellTormos et al. 2008; Mazutis et al. 2013; Chen et al. 2014; Wolf et al. 2015; Hosokawa et al. 2017) and pharmaceutical applications (Kang et al. 2014; Piao et al. 2015). The large specific surface area in combination with welldefined and allegedly easytocontrol flow structures promise a great potential for process intensification. Thus, optimal reactor design and controllability of the flow are key to raise this potential.
Deep insight into the hydrodynamic interaction of the distinct flow phases enables to tune the mass transfer rates towards more sustainable operation modes close to the optimal working point (Magnaudet and Eames 2000; Ern et al. 2012). To achieve this knowledge, numerical calculations and CFDsimulations enable parameterized studies of, e.g. liquid–liquid Taylor flows (Luis A. M. Rocha et al. 2017). Dimensionless numbers (Re, Ca) and material property ratios (Oh) can be set freely and independently to identify, e.g. critical operation modes. This allows to decrease timeconsuming experimental effort to validation measurements.
The mentioned dimensionless quantities are often based on the material parameters of the continuous phase since it provides the wall contact and drives the flow of the disperse phase. The capillary number compares the viscous forces with the interfacial tension forces \({\text{Ca}} = \frac{u_0 \eta _\mathrm{c}}{\sigma }\) and it is based on the superficial velocity \(u_0\), the dynamic viscosity \(\eta _\mathrm{c}\) of the continuous phase and the interfacial tension \(\sigma\). The Reynolds number relates the inertia forces to the viscous forces \({\text{Re}} = \frac{\rho _\mathrm{c} u_0 d}{\eta _\mathrm{c}}\), where \(\rho _\mathrm{c}\) denotes the density of the continuous phase and d the diameter of the microchannel. The Ohnesorge number \({\text{Oh}} = \;\sqrt {\frac{{{{\text{Ca}}}}}{{{\text{Re}}}}}\) removes the hydrodynamic influences and solely remains as a material parameter.
For macroscopic liquid–liquid flows, the set of dimensionless variables changes with the growing influence of inertia and gravitational forces to Re, We, and the Morton number Mo = Bo \(\cdot \mathrm{Oh}^2\), where the Weber number We = Ca \(\cdot\) Re represents the inertia forces compared to the interfacial tension forces. Mo introduces the buoyancy dependence of the flow’s material system (Araújo et al. 2012) by combining the Bond number \({\text{Bo}} = \frac{\Delta \rho \,g\,d^2}{\sigma }\) with the Ohnesorge number. Since buoyancy forces are small (\({\mathrm{Bo}} \ll 1\)) in microfluidic applications, we base this work on the Oh number only.
Preferably noninvasive experimental methods need to be applied to investigate the hydrodynamic behavior of liquid–liquid multiphase flows supporting the numerical findings. Even in microchannels, a high spatial resolution of an entire flow field is accessible with, e.g. optical measurement techniques (Park and Kihm 2006; Kinoshita et al. 2007; Khodaparast et al. 2013). However, undistorted optical access is necessary to avoid measurement deviation due to light refraction and reflection at the experimental setup, as well as the flow phases themselves.
Often the hardwarerelated refraction effects of the setup can be compensated by adjusting the experimental design, e.g. avoiding curved surfaces and using corrective optics. The curved interfaces (interfacial areas) of microscopic liquid–liquid flows themselves are commonly counteracted applying refractive index matching (RIM) with one degree of freedom (Miessner et al. 2008; Ma et al. 2014; Liu et al. 2017). A broad overview of possible liquid–liquid, as well as solid–liquid refractive index matching possibilities, is given in the works of Budwig (1994) and Wright et al. (2017). Furthermore, recently several approaches have been made using refractive indexmatched systems not only to gain optical accessibility, but also to mimic special application cases like specific rheology for blood (Najjari et al. 2016; Brindise et al. 2018), highdensity differences or for a buoyant jet (Clément et al. 2018; Krohn et al. 2018).
In microscopic liquid–liquid flows RIM with one degree of freedom solely allows matching the RI of one phase to the other. The material system of the phases like density, viscosity, and interfacial tension are fixed for the desired RI. The governing dimensionless numbers such as Re, Ca may only be parameterized hydrodynamically (superficial velocity) or geometrically (microchannel diameter). The monetary effort to parameterize the diameter of the microchannel is high, while the velocity alters both quantities simultaneously. Alternatively, surfactants can be added to change the interfacial tension of the material system solely, which allows to vary the ratio between Ca and Re. Since at surfactant concentrations well below the critical micelle concentration the viscosity of the host phase is not changed significantly, this approach addresses Ca only. However, the use of surfactants might introduce severe effects such as altering the hydrodynamics of the flow as well as its mass transfer properties.
In order to solve this problem, we suggest an approach using two immiscible binary mixtures to match refractive indices (Saksena et al. 2015; Cadillon et al. 2016), i.e. adding an additional degree of freedom to the system by introducing a binary mixture for each of the liquid phases. By this means, the material system becomes flexible enough to match the immiscible binary liquid mixtures optically using the entire range of RI. Hence, the simultaneous velocityrelated change of Ca and Re may be compensated for by adequately adapting the material composition of the mixtures (Oh).
We carefully determine the mass fractiondependent material properties of the involved mixtures, establish dedicated correlation functions and provide an approach to identify the necessary mass fractions of both binary mixtures and the needed superficial velocity to use this RIM system. A proof of principle is given using µPIV rawimages of two fluorescence particleseeded microscopic Taylor flows at two Re and constant Ca at different channel heights.
Recently, the viscosity ratio of both flow phases \(\lambda = \frac{\eta _{\text{d}}}{\eta _\mathrm{c}}\) is reported to influence the local hydrodynamics of microscopic Taylor droplets (Rao and Wong 2018). However, the available measurements are limited to a narrow parameter range without refractive index matching (Kovalev et al. 2018; Liu et al. 2017). We suggest four combinations of wellquantified doublebinary mixtures for the disperse phase as well as the continuous phase. This allows to additionally alter the viscosity ratio of the flow phases by changing the flow system.
2 Materials and methods
Within this section, the choice of the basic mixture compounds, the experimental procedures to retrieve the properties of the fluids, and the numerical approach are described. All measurements are referenced to mass fractions \(\xi\) to compensate for nonlinearities in the mixing behavior.
2.1 Basic mixture compounds
For the binary mixtures of this work, we focused to mainly use nontoxic, nonhazardous, Newtonian substances. A wide range of addressable refractive indices is accomplished, when mixing substances of high and and low RI in each phase. The polar phase is chosen to be aqueous for practical reasons. The range of RI of the aqueous binary mixture is defined when using either DMSO or glycerol as Newtonian liquid to elevate the RI. The nonpolar phase is based on hexane, as it represents a tradeoff between a lower RI and hazardous properties. The nonpolar binary mixture is complemented by either anisole or sunfloweroil, which establishes a high RI range. Rheometry measurements show that in the observed range sunfloweroil also behaves Newtonian.
Combining the suggested aqueous mixtures with the nonpolar systems, the viscosity ratio \(\lambda\) between the phases of the flow can be changed by either inverting the flow phases or changing the combination of the materials. For that reason, we introduce and characterize different binary mixtures for the polar as well as for the nonpolar phase. For low viscous mixtures with viscosity ratio below one, we suggest water/DMSO and nhexane/anisole, while for highviscosity ratio we propose to apply water/glycerol and nhexane/sunflower oil. Please note that the viscosity ratio cannot be chosen freely. However, it is possible to choose a ratio below or above unity to investigate the hydrodynamic consequences.
With these mixtures, we reach a broad range of refractive indices between the pure substance’s RI of nhexane (\({\text{RI}} \approx 1.375\)) and glycerol/DMSO (\({\text{RI}} \approx 1.47\)). The material properties of the binary mixtures (density, viscosity, interfacial tension), as well as the refractive index, are given in Sect. 3.
2.2 Determination of material properties
The refractive indices of the used fluids were measured using a Krüss Abbe refractometer AR2008, temperated at 20 °C. The refractive indices were measured using a light wavelength of 589 nm (Sodium D1line) with three independent measurements each. For volatile or liquids with low viscosity or low surface tension, no stable film forms between the prisms of the refractometer, which leads to a high deviation. For this reason, the refractive indices of the nhexane/anisole system for high mass fractions of anisole could not be acquired reliably. Instead, literature data are used in this case.
The interfacial tension of the doublebinary mixtures was measured using a Lauda TVT drop tensiometer with a syringe of 2.5 ml and a stainless steel capillary at a temperature of 20 °C. The interfacial tensions were acquired using the volume drop method (the interfacial tension is measured based on the balance of buoyancy and surface tension of a detaching droplet). The dispersed droplet was detected with a light barrier and the interfacial tension was calculated from the droplet volume. The interfacial tension is a timedependent property for nonpure or mixed systems. Thus, droplets with differently aged interfacial area were formed such that the interfacial tension for infinite time \(\sigma _{\inf }\) can be derived (Wilkinson 1972; Sinzato et al. 2017). Within our work, the droplet formation times and, therefore, the surface age range between 2.5 and 60 s.
The light barrier, which detects the detachment of the ascending droplets, cannot work properly when the refractive indices are matched. Thus, we deliberately detune the mass fraction of the nonpolar phase such that a sufficient detection difference exists between the refractive indices of both phases (\(\Delta\) RI = 0.01). The droplet detachment, as well as the interfacial tension, is determined at these detuned fluid compositions. The actual interfacial tension for the matched case is then retrieved by linear interpolation using the lever rule. The linear interpolation is considered valid since only the mass fraction of one of both phases is varied and the change in the mass fraction is kept small.
The measurements of the viscosities of the volatile compounds (nhexane/anisole) were performed using a Malvern Kinexus Ultra Plus with solvent trap, coneplate setup, 1° opening angle, and a stationary shear rate table 10–100 s^{−1} with 5 % stationarity tolerance. The remaining measurements were performed using a Bohlin Rheometer CS and a 30 ml doublegap system. All measurements were performed at 20 °C.
The densities of the mixtures are retrieved from literature data except for the mixture water/glycerol.
2.3 Massfraction and superficial velocity identification approach
Keeping in mind the definition of Re and Ca, refractive index matching at these properties is a minimization problem with the superficial velocity \(u_0\) as the objective value. The mass fractions of the continuous phase \(\xi _\mathrm{c}\) and disperse phase \(\xi _\mathrm{d}\) are the control variable, which influences the material properties.
If the fluid properties of the pure substances as well as of the mixtures are known, Ca and Re can be calculated. The equations can be changed such that the superficial velocity \(u_0\) for both numbers is a function of the continuous phase mass fraction \(\xi _\mathrm{c}\):
For a minimum residuum of this optimization (\(u_{0,{\text{Re}}}=u_{0,{\text{Ca}}}\)), the correct \(u_0\) is known as well as the corresponding mass fraction of the continuous phase \(\xi _\mathrm{c}\). The mass fraction of the disperse phase \(\xi _\mathrm{d}\) can be calculated via the refractive index of the continuous phase. A working example is given in the supplementary resources.
3 Experimental results
Within this section, the material properties of the binary and RImatched doublebinary mixtures are experimentally investigated.
3.1 Properties of binary mixtures
To successfully determine the correct mass fractions of both binary mixtures and the superficial velocity, the used algorithm needs a steady optimization function to work with. However, the measurement data consist of discrete points including measurement errors. Thus, a transition of the discrete data sampling to continuous functions is necessary. As established in our last work (Helmers et al. 2019), we correlate the data with polynomial approaches for simplicity.
The equation for a polynomial function follows:
where y is the desired property (e.g., density, viscosity or interfacial tension), \(\xi\) the mass fraction of the mixture, and \(A_4\)–\(A_0\) fitting coefficients for the polynomial. The polynomial coefficients for the different material properties as well as the experimental data and the range of validity are shown in the following:
At first, the densities of the binary mixtures are investigated in Fig. 1a for the polar and in Fig. 1b for the nonpolar media. The system water/glycerol shows a nearly linear behavior, while the system water/DMSO shows a peak at approximately \(\xi = 0.8\). This is caused by nonlinear mixing behavior due to the similarity of water/DMSO and also effects the viscosity. The system nhexane/anisole shows a nearly linear behavior, while nhexane/sunflower oil shows a deviation from linearity. The correlations extracted from the measurement and literature data are shown in Table 1 together with the resulting adjusted coefficient of determination \(R^2_\mathrm{{adj}}\).
In Fig. 2 the refractive index of the water/glycerol mixture features a linear behavior (empty squares), while water/DMSO shows a nonlinearity for higher DMSO mass fractions (Fig. 2a, triangles). For the nonpolar substances the system nhexane/sunfloweroil (filled squares) behaves nearly linear, while nhexane/anisole (filled triangles) increases the slope indicating nonlinear dependence (Fig. 2b). For all mixtures, the measurements confirm the available literature data. The correlation coefficients are shown in Table 2.
The viscosities of the four binary mixtures are given in Fig. 3. Both of the highly viscous mixtures (water/glycerol Fig. 3a, and hexane/sunfloweroil Fig. 3d) exhibit similar behavior. As intended, with a higher mass fraction of the more viscous substances, the viscosity rises. The less viscous mixtures water/DMSO (Fig. 3b) and nhexane/anisole (Fig. 3c) show different behavior. While the viscosity of nhexane/anisole mixtures increases quadratically with a rising mass fraction of anisole, the viscosity of water/DMSO reaches a peak at \(\xi = 0.70\). For nhexane/anisole no own measurements could be performed, since the high evaporation rate of the volatile hexane/anisole mixture leads to a significant deviation in the mass fraction of the mixture during the measurement. Instead, literature data are used. The correlation coefficients are shown in Table 3.
3.2 Properties of RImatched doublebinary mixtures
Since the doublebinary system consists of four substances, the interfacial tension is influenced independently and possibly nonlinearly by the mass fractions of both binary mixtures. Thus, the interrelations are linearized to obtain a manageable experimental effort for the required measurements: For the use in RImatched measurements, only the mass fractions of the matched solution need to be observed. As it is visible in Fig. 4 this simplifies the problem to a twodimensional problem.
To retrieve the specific mass fractions of both phases for the matched case, the correlations for the RI of both phases are equated and a fit function is numerically retrieved. The behavior of the RImatched doublebinary systems is a combination of the binary mixtures. The results are shown for all doublebinary mixture systems in Fig. 4.
The system water/DMSO–hexane/anisole (Fig. 4c) shows the most prominent nonlinear behavior. This is caused by the larger increase of the RI of anisole for elevated anisole mass fractions and the nonlinearity of water/DMSO. For the system water/glycerol–nhexane/anisole (Fig. 4a) this behavior is as not prominent since the binary mixture water/glycerol in contrast to water/DMSO is nearly linear. As expected from the binary mixture’s behavior, this also holds for the system water/glycerol–hexane/sunfloweroil (Fig. 4b), while again caused by water/DMSO, for water/DMSO–nhexane/sunfloweroil nonlinearities are present at higher DMSO mass fractions (Fig. 4d). The correlation coefficients for the matched systems are shown in Table 4.
Every matched system consists of two binary mixtures with exactly one RI for the matched case and one specific mass fraction and viscosity for the polar as well as the disperse phase. Changing the mass fraction of one phase, the mass fraction of the other phase needs to be adjusted to keep the RI matching. This changes the viscosity ratio, as it also depends on the ratio of the binary mixtures of each phase. The viscosities of polar continuous phase of the high viscous systems are shown in Fig. 5. The combinations with water/glycerol show a broad range of available continuous phase viscosities.
Considering the viscosities of both flow phases, the viscosity ratio \(\lambda\) of the respective RImatched material systems can be calculated. The results are shown in Fig. 6 separated for polar and nonpolar continuous phase.
In addition to the determination of the material properties that depend only on the binary mixtures themselves, the interfacial tension depends on the forces of the energetic state of the interfacial area. Thus, the determination for a quaternary fluid system is complex. For the following measurements, only the interfacial tension of the RImatched case is of interest. Thus, we only determine values at the mass fractions of the RImatched interfacial tensions to minimize the experimental effort. The measurement data, as well as the derived correlations, are shown in Fig. 7.
The interfacial tension between the RImatched liquids exhibits different behavior for each system. The system water/glycerol–hexane/anisole (Fig. 7a) shows an unpredictable interfacial tension development for rising mass fractions of glycerol or anisole. The interpolated values of the single measurements deviate around the correlation function. This is a sign for strong nonlinear interrelations between the four substances. Probably caused by weaker intermolecular forces between glycerol and anisole depending on the composition of the mixture. The system water/glycerol–hexane/sunfloweroil shows a minimum for equivalent fractions of all four substances (\(\xi _\mathrm{p} \approx 0.5\), \(\xi _\mathrm{n} \approx 0.5\)), while the interfacial tension increases for higher amounts of glycerol or sunflower oil (Fig. 7b). As the \(R^2_{{\text{adj}}}\) implies, the interfacial tension of this system is weakly correlated to the massfractions of the flow phases. Nevertheless, the correlation is sufficient to apply the proposed RIMapproach with sufficient accuracy.
The systems involving water/DMSO expose a decreasing interfacial tension with decreasing massfraction of nhexane. Especially the water/DMSO–hexane/anisole shows a very low interfacial tension for lower mass fractions of hexane (Fig. 7c), which is caused by a diminished structural difference to hexane. Water/DMSO–nhexane/sunfloweroil shows a similar decrease of the interfacial tension (Fig. 7d).
The most significant deviations (Fig. 7a, b) are situated in a range of 2 mPas. These deviations between the correlation and the interpolated data of single measurements can be caused by either the linearization or confined effects at distinct mass fractions as well as measurement errors. Since the results of the single measurements are based on at least 20 independent droplets, we consider possible measurement errors to attribute from diminutive contaminations of the volume tensiometer. The correlation coefficients for the interfacial tension for all four systems are shown in Table 5. To take care of the nonideal behavior, we introduce a secondorder polynomial fit to cover the parabolic behavior (see “Appendix”).
4 Results and discussion
In this section, we discuss the experimentally determined material properties of the doublebinary mixtures and deliver a proofofprinciple for the doublebinary approach.
4.1 Features and limits of the doublebinary approach
Based on the conducted measurements and literature data, the proposed doublebinary mixture systems are described by means of correlation functions with sufficiently high accuracy. This allows to calculate the relevant dimensionless quantities Ca and Re for all accessible mass fractions and superficial velocities. This is done via the MATLAB program, which we supply with the supplementary material. Alternatively, the mass fraction and the superficial velocity can be retrieved graphically from the nomograms presented in the Appendix (Figs. 10, 11). Regarding liquid–solid refractive index matching, RI up to 1.4714 for the system water/glycerol and 1.4738 water/DMSO can be achieved. This allows to match two phase flows to the reactor material PDMS. The microreactor’s coverglass is usually aligned orthogonally to the flow and, therefore, does not need refractive index matching since on orthogonal surfaces no distortions occur. However, fused silica could still be matched.
4.2 Proof of principle
The practicability of the proposed approach for optical measurements and especially the possibility to reach the desired Re and Ca independently at a matched refractive index is proven in an experimental approach. A microscopic Taylor flow is established and optical measurements are performed in the symmetry plane (channel center plane), the channel top wall, and at an intermediate plane at 0.75 of the channel height at two different Re numbers while Ca is held constant (Fig. 8a). The experimental setup to record the PIV rawimages is described in the Appendix. In the symmetry plane at the half channel height, distortions can be quantified that arise from nonideal refractive index matching and accumulate (Fig. 8b). In this setup, the tracer particle position in proximity of the interfacial area cannot be determined reliably, leading to a decrease of measurement precision.
Utilizing the proposed RIMapproach, the required mass fraction of the binary mixtures for the continuous and disperse phase and the superficial velocity are determined minimizing the difference of Eqs. 1, 2 as described in Sect. 2.3. Subsequently, the microscopic Taylor flow is reestablished using the calculated parameters. In the µPIV raw images, the droplet interface is not visible and optical distortions caused by the interfacial area do not occur (Fig. 8c, d). The apparent reduction of droplet length is caused by the curved droplet cap shape when the focal plane is moved towards the channel top wall. Only the tracer particles in the focal plane contribute to the image. Interfacial reflections from out of focus regions are note visible. Thus, the correlations for the refractive index as well as the solver algorithm work well.
5 Conclusion
In this study, we present and successfully validate a novel approach using doublebinary mixtures for both immiscible flow phases to establish refractive indexmatched microscopic multiphase flows. In comparison to classical monobinary mixture approaches, Re and Ca can be addressed individually in a material restricted parameter set, since viscosity and interfacial tension (and thus the different flow forces) do not change in the same order of magnitude if the mass fractions of the phases’ binary mixtures are varied. Alternatively, multiphase flows at different Oh at a fixed RI can be established to match the reactor material (e.g. simulating threephase flows via monolith). We introduce two binary mixtures for a polar and nonpolar phase to enable the investigation of, e.g., different viscosity ratios \(\lambda\) or flow systems with simultaneously high or low viscosities are possible too.
Measurements for the relevant material properties (densities, viscosities, refractive index) of the binary mixtures as well as the RImatched compositions (interfacial tensions) are carried out and compared to literature data to characterize the system. The task to establish multiphase flows at specific Re and Ca independently is identified as an optimization problem. For that purpose the material properties as well as the interfacial tension are successfully described with correlations that allow the use of a solver algorithm.
In first measurements, the capability to establish refractive indexmatched Taylor flows at freely chosen Ca and Re is proven. This proof of principle is successfully conducted using recorded µPIV raw images. With the proposed doublebinary RIMapproach the specific influences on the local velocity of droplets can now be independently examined via optical flow visualization techniques (PTV, PIV).
Abbreviations
 µPIV:

particle image velocimetry
 µPTV:

particle tracking velocimetry
 DMSO:

dimethyl sulfoxide
 DOF:

depth of field
 NA:

numerical aperture
 RI:

refractive index
 RIM:

refractive index matching
 \(\lambda\) :

Viscosity ratio (−)
 Bo:

Bond number (−)
 Ca:

Capillary number (−)
 Mo:

Morton number (−)
 Oh:

Ohnesorge number (−)
 Re:

Reynolds number (−)
 \(\eta\) :

Dynamic viscosity (\(\mathrm {Pa\,s}\))
 \(\lambda\) :

Light wavelength (\(\mathrm {nm}\))
 \(\rho\) :

Density (kg m^{−3})
 \(\sigma\) :

Interfacial tension (N m^{−1})
 \(\xi\) :

Mass fraction (kg kg^{−1})
 A :

Correlation factor (−)
 d :

Characteristic length (m)
 g :

Gravitational acceleration (m \({\text{s}}^{2}\))
 u :

Velocity (mm \({\text{s}}^{1}\))
 R:

Coefficient of determination (−)
 0:

Superficial
 1, 2, 3:

Order of correlation factor
 adj:

Adjusted
 c :

Continuous phase
 d :

Disperse phase
 ex:

Excitation
 n :

Nonpolar phase
 p :

Polar phase
 s :

Slug
 tot:

Total
 tr:

Tracer particle
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Acknowledgements
Open Access funding provided by Projekt DEAL. The contribution of P. Kemper has been supported by the German Research Foundation (DFG), Priority Program: “Reactive Bubbly Flows”, SPP1740 under Grant TH 893/172. The authors gratefully acknowledge the financial support.
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Appendix
Appendix
1.1 Experimental setup of proof of principle
The experimental design follows Fig. 9: A Simicrochannel (manufactured by IMSAS Bremen) with 198 µm nearly rectangular crosssectional area is located on a Zeiss LSM210 inverted microscope with a motorized nosepiece and twoaxis stage for precision movement. The microscope is controlled via a selfwritten LabView program using serial port communication.
The microscope is equipped with a Zeiss LD LCI Plan Apochromat 25x/0.8 objective to provide a high spatial resolution at a small depth of field (DOF = 1.034 μm) to receive a high resolution in the zdirection. A pulsed Nd:YAG laser (New Wave Research SoloPIV III) with a 15 Hz repetition rate, 50 mJ pulse intensity, and a pulse length of 3 to 5 ns with frequency doubling (wavelength: \(\lambda _\mathrm{{ex}}\) = 532 nm) serves as a light source for the measurement. Images of the flow are acquired using an activecooled high quantumefficient PCO.sensicam qe 670 LD 3078 double CCDcamera with an acquisition rate of 4 Hz at a resolution of 1376 px × 1040 px. The continuous phase is seeded with particles of 1.61 µm particles. The particles are coated with FluoRed as fluorescence dye (excitation peak 530 nm, emission peak 607 nm) and are dispersed in the water/glycerol phase using an ultrasonic bath for 15 min at 20 °C.
Two syringe pumps (Dolomite Mitos Duo XS) supply a steady flow such that the volume flow of both phases can be individually controlled. The excitation light from the pulsed Nd:YAG laser is guided into the Zeiss LSM210 microscope and the laser is widened with a convex lens of short focal length. The illumination is additionally averaged with a holographic diffuser.
A dichroic mirror separates the green excitation light from the red fluorescence light and directs it to the camera. To further improve the cutoff, an additional longpass filter is mounted in the lightpath to shield the camera from laser light (Fig. 9). A timing unit synchronizes the laser and the camera.
An overview of the experimental and optical parameters is given in Table 6.
1.2 Nomograms for massfraction determination
In addition to the MATLABscript also the relevant properties are provided with this supplementary material, where they can be retrieved from nomograms (Figs. 10, 11). The desired Ca and Re are chosen on the according axis and the corresponding matched Oh and RI of both phases, as well as the superficial velocity, can be received. The RI determines the mass fractions of both phases \(\xi\) (Fig. 4) and the associated viscosity ratio (Fig. 6). Via the continuous phase viscosity (Fig. 5) and \(\lambda\) the disperse phase viscosity can be determined. Generally, the systems with a high viscous continuous phase (Fig. 10a, b) cover a larger range of possible Ca and Re, while for the lower viscous continuous phase the parameter range is smaller.
1.3 2Dprojection of interfacial tension measurements
Regarding the correlations of the interfacial tensions of the doublebinary mixture of the refractive indexmatched massfractions, the 3D visualization of Fig. 7 complicates the assessment. We provide 2D projections of the correlations for the refractive index matched massfractions in the following (Fig. 11).
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Helmers, T., Kemper, P., Mießner, U. et al. Refractive index matching (RIM) using doublebinary liquid–liquid mixtures. Exp Fluids 61, 64 (2020). https://doi.org/10.1007/s0034802028921
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DOI: https://doi.org/10.1007/s0034802028921