# A T-junction device allowing for two simultaneous orthogonal views: application to bubble formation and break-up

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## Abstract

A novel design for the classical microfluidic device known as T-junction is proposed with the purpose of obtaining a simultaneous measurement of the in-plane velocity components in two orthogonal planes. A crucial feature of the proposed configuration is that all three velocity components are available along the intersection of the two planes. A dedicated optical set-up is developed to convey the two simultaneous views from the orthogonal planes into the sensor of a single camera, where a compound image is formed showing on either half one of the two views. A commercial micro-particle image velocimetry system is used to measure the velocity in the two planes. Feeding the T-junction with a liquid continuous phase and a dispersed gas phase, the velocity is measured by phase averaging along the bubble formation and break-up process showing the potentialities of the new design. The accuracy analysis shows that the error is dominated by a systematic component due to the thickness of the measurement slice. The error can be reduced by applying confocal microscopy to the present system with no further modifications so as to reduce the thickness of the measurement slab thereby reducing the error. Moreover, by sweeping the planes across the region of interest, a full three-dimensional reconstruction of the velocity field can be readily obtained. Finally, the simultaneous views offer the possibility to extract the principal curvatures of the bubble meniscus thereby providing access to the Laplace pressure.

## Keywords

Micro-particle image velocimetry Bubble dynamics## 1 Introduction

In microfluidics, different methods are used to produce microbubbles, exploiting laminar flow conditions to allow for high reproducibility and high production rate at relatively low energy and mass transfer rates (Chen et al. 2014). Among the different devices conceived to manipulate fluids at the microscale (Whitesides and Stroock 2001), the T-junction is one of the most fundamental and widely used device. It consists of two orthogonally intersecting microchannels. The device is used to produce bubbles or droplets of a secondary phase into the main continuous one. Since its original development in the first few years of the present century, see, e.g., Thorsen et al. (2001), it has been repeatedly addressed by a number of investigators (Tice et al. 2003; Günther et al. 2004; Garstecki et al. 2006; Menech et al. 2008). In micro electro-mechanical systems (MEMS) and lab-on-chip (LOC), such geometry can be exploited to obtain two-phase flows (Zhao and Middelberg 2011), where two partially miscible or immiscible fluids interact in the microfluidic networks with well-defined and controlled conditions (Graaf et al. 2005; Garstecki et al. 2006; Fu and Ma 2015. The possible applications are countless. In the medical/biological field, LOCs featuring the T-junction configuration have been developed to deliver drugs at a precisely controlled rate, e.g., in Okushima et al. (2004) and Stride and Edirisinghe (2008). In micro- and nano-technology, T-shaped channels have been employed to produce regular-sized polymeric particles (Nisisako et al. 2004) typically used, e.g., in liquid chromatography (Ugelstad et al. 1983) or for flow measurements (PIV and microPIV) (Melling 1997). The generation of microbubbles is also relevant for fabricating porous biomaterials (Wang et al. 2011), for mixing enhancement in chemical processes (Günther et al. 2005; Kreutzer et al. 2005) and for different biomedical applications, e.g., to form liposomes (Swaay 2013).

Since two immiscible fluids are present, surface tension is dynamically important. On the other hand, given the scale of the order of hundreds micrometres and the velocities of tens of millimetres per second, inertial effects are usually negligible and viscous forces dominate over inertial forces. In these conditions, the Navier–Stokes equation can be linearised to describe a “creeping flow”. However, although the familiar convective non-linearity of macroscopic fluid mechanics is ineffective, instability may still set in due to competition between surface tension and viscous forces (Landau and Lifshits 1959; Taylor 1934). As a consequence, despite the simple geometry, the dynamics leading to bubble/droplet formation is far from being trivial. In particular, the complex bubble shape and the strong three-dimensional and time-dependent velocity and pressure distributions are rather difficult to measure directly when the characteristic size falls below the millimetric range. In simple cases, important information can be inferred from numerical simulations (Menech et al. 2008; Soh et al. 2016; Steijn et al. 2010; Amaya-Bower and Lee 2011).

However, a way to resort to experiments is clearly needed both for validation of the numerical models and for the investigation of more complex cases when, e.g., rheologically complex fluids are involved. The experimental analysis has been mainly focused on the global characterisation of the device addressing the influence of global parameters, such as characteristic length scale, flow rates and capillary number (Yamamoto and Ogata 2013; Wehking et al. 2014; Nunes et al. 2013; Fu et al. 2010). Attention has been given to unsteady phenomena, as in the case of bubble break-up (Garstecki et al. 2006; Fu et al. 2011; Fu and Ma 2015).

The velocity field can be obtained using micro-particle image velocimetry (\(\mu\)PIV), a non-invasive technique that allows to measure the velocity on planar sections (Steijn et al. 2007; Sinibaldi and Romano 2017). The accuracy is limited by the thickness of slab over which the field is implicitly averaged. A better resolution may be achieved by coupling \(\mu\)PIV with confocal microscopy, to reduce the thickness of the measurement volume, see Lima et al. (2006) and Oishi et al. (2009) for applications to the T-junction configuration. Still working with planar section, the third component of velocity can be acquired using stereo PIV (Lindken et al. 2006) at the prize of a considerably more complex system. By sweeping the measurement plane across the flow domain, a complete three-dimensional field can be reconstructed from the two-dimensional fields.

The purpose of this paper is to illustrate the concept of a novel set-up able to allow for the simultaneous measurement of the two-dimensional velocity field in two orthogonal planes in the T-junction. The fabrication technique used to build the proof-of-concept is described in some detail, but the reader should be aware that other alternative procedures and materials can be used. The process we adopted should then only be considered as an inexpensive and easy way to manufacture the microchip.

Concerning the velocity measurement, the advantage of the new configuration is that a standard \(\mu\)PIV is used, with a single camera. Along the intersection of the two orthogonal planes, all three velocity components are simultaneously acquired. In principle, by letting the intersection line span the measurement volume, the entire three-dimensional field can be reconstructed. After validation in a simple straight channel, the new approach is used in a T-junction to show how the flow field around the bubble and the bubble interface can be extracted during generation and break-up phases by phase averaging the combined planar acquisitions. The new set-up is based on the idea of looking at the field from two orthogonal planes. The two views are conveyed to the camera and each one is captured on one half of the sensor producing a compound image of the two sights. A standard PIV processing of the image allows to extract the velocity. The availability of the two orthogonal views may also be used to estimate the total curvature of the bubble/droplet, providing access to the Laplace pressure.

The paper is organised as follows. The experimental set-up is described in Sect. 2 where a detailed description of the new device is provided, including manufacturing, measurement technique and validation. The main results are presented in Sect. 3 where velocity field and bubble configuration are discussed. Finally, Sect. 4 is devoted to conclusions and possible perspectives. The three appendices complement the discussion with a detailed description of the fabrication procedure and a theoretical model of the measurement process exploited to assess accuracy and main sources of error.

## 2 Experimental set-up

*D*. Under the present conditions, the correlation depth is \(\ell _\mathrm{{c}} = 90 \, \upmu \mathrm{m}\). The interrogation window for \(\mu\)PIV analysis is \(24 \times 24\) px with an overlap factor of \(50 \, \%\) where \(1 \, {\mathrm{px}}\) corresponds to \(1.1 \, \upmu \mathrm{m}\). For the present case, the polystyrene fluorescent particles (microparticles GmbH) are provided as a suspension in water with mass ratio \(r_\mathrm{{m}} = m_\mathrm{{p}}/m_\mathrm{{s}} = 2.5 \, \%\) where \(m_\mathrm{{p}}\) and \(m_\mathrm{{s}}\) are the mass of the particles and the mass of solution, respectively. Given the mass density of polystyrene, \(\rho _\mathrm{{p}} = 1.050\, {\mathrm{g/cm}}^3\), \(r_\mathrm{{m}}\) corresponds to the volume ratio \(r_\mathrm{{v}} \simeq 2.5 \times 10^{-2}\). Before using the particles as \(\mu\)PIV tracers, the suspension is diluted in 2-propanol in the ratio 1:133. This corresponds to a volume fraction of polystyrene particles in the flowing solution of 2-propanol (plus water in traces) of \(\phi \simeq 1.9 \times 10^{-4}\), resulting in a probability, occupancy fraction, \(f_\mathrm{{o}} = 0.21\) of finding a particle in the interrogation volume. In other words, one out of (almost) five acquired images contains a velocity signal per interrogation volume. On the other hand, the probability of finding more than one particle per interrogation volume is negligible (\(\sim 0.04\)) thereby considerably simplifying the error analysis. It should be mentioned that such a low particle concentration also enhances particle visibility (Olsen and Adrian 2000), a parameter of general relevance in \(\mu\)PIV which is even more crucial in the present application where, as explained in the following section, two views with different optical paths need to be imaged.

### 2.1 Device description and manufacturing

The double optical access through orthogonal planes allows to visualize the bubble formation and break-up in the two planar views, (*x*–*y*) and (*z*–*x*), respectively, (see the sketch in Fig. 2 for the definition of the coordinate system). The new chip allows for simultaneously capturing both images with a single inverted microscope. This is achieved by integrating a \(45^\circ\) inclined mirror on the side slide as shown in Fig. 4. In the present arrangement the (*x*–*y*) view, hereafter called direct view, is directly captured by the objective. The (*z*–*x*) view is instead first reflected on the mirror, reflected view. To simultaneously focus both views, the two optical paths should be identical. This requires the interposition of an optical adapter, here a simple calibrated glass spacer. From the geometry of the optical system, the refraction indices of the materials and the desired positions of the focal planes as well as the thickness of the glass spacer can be easily evaluated, see Appendix A for details.

A good quality micro-mirror is fabricated by evaporating a reflective metal on the surface obtained by cutting a \(150\, \upmu \mathrm{m}\)-thickness glass slide. A Bulzers evaporator was used to deposit, under vacuum, a 300 Å Aluminium layer on top of a first 150 Å Chrome layer to promote adhesion. In the practical design of the microchip in its basic configuration proposed here, a critical aspect is combining the two conflicting requirements of wide field to include the views in the two orthogonal planes in a single image and sufficient magnification to allow for a precise \(\mu\)PIV measurement. To this purpose, it is instrumental to minimize the thickness (\(150\, \upmu \mathrm{m}\) in the present realization) of the side slide (Fig. 4) that is imaged in the composite view capturing the two orthogonal planes, Fig. 5.

### 2.2 Flow calibration

To be certain of the operating conditions under which velocity measurements and bubble break-up visualisations are carried out, one should certify the viscosity of the liquid stream and the surface tension at the interface between the two phases that could, in principle, be altered by the fluorescent particles needed for \(\mu\)PIV. Given the high dilution of the suspension, the viscosity can be estimated by Einstein’s relation \(\mu _{\phi }=\mu (1+5/2 \times \phi )\) where \(\mu _{\phi }\) is the viscosity of the suspension and \(\phi\) is the volume fraction of the suspended particles. As expected, this leads to a negligible change in the viscosity. Surface tension modifications were instead directly quantified exploiting Yurin’s law (Jurin 1718), by measuring the height of the meniscus in a capillary tube partially immersed in the suspension, and were also found to be negligible at the present particle concentration, as expected.

## 3 Results

As a benchmark, results concerning a simple, straight microchannel featuring the same double view with length \(L = 30 \, \mathrm{mm}\) and square cross-section with side \(w = h = 800\, \upmu \mathrm{m}\) are illustrated first. Ideally, the \(\mu\)PIV tracer particles should be as small as possible to allow a fast relaxation to the local fluid velocity. In the specific case, assuming a typical flow velocity \(U_{\mathrm{{bulk}}} = Q/A = 52\, \mathrm{mm/s}\), the Stokes number of the fluorescent tracers is \(St = \rho _\mathrm{{p}} D^2 U_{\mathrm{{bulk}}}/(18 \, \nu h) = 3 \times 10^{-5}\) showing that inertial effects are negligible. Velocity measurements at the microscale may be affected by significant fluctuations due to the Brownian motion of the probing particles. For a colloid of mass \(m_\mathrm{{c}}\) the classical theory of Brownian motion predicts the rms (root mean square) fluctuation of a velocity component, say \(V_x^{\mathrm{{rms}}}\), to be \(V_x^{\mathrm{{rms}}} = \sqrt{k_\mathrm{{B}} T/m_\mathrm{{c}}}\). In the present case, assuming a nominal particle diameter of \(4.47 \, \upmu \mathrm{m}\) and a density comparable with water, random fluctuations of intensity \(V_x^{\mathrm{{rms}}} = 0.29 \,\mathrm{mm/s}\) are superimposed to the average particle velocity which is the proxy used to estimate the fluid velocity. The particle random motion can be removed from the data by averaging over a collection of samples, under the assumption that the background velocity field is purely deterministic and repeatable, as expected given the low Reynolds number of the flow, in the present case \(Re = Q/(h \nu ) = 13\), where *Q* is the flow rate and \(\nu\) the kinematic viscosity of the fluid (2-propanol). The maximum number of acquired samples is \(N_{\mathrm{{sample}}} = 450\), which gives a confidence interval on the estimated fluid velocity given by \({\bar{\sigma }^{\mathrm{{Brownian}}}_x} = V_x^{\mathrm{{rms}}}/\sqrt{N_{\mathrm{{sample}}}}\). The resulting figure should be compared with the bulk velocity \(U_{\mathrm{{bulk}}} = 52 \, \mathrm{mm/s}\) to give \({\bar{\sigma }_x^{\mathrm{{Brownian}}}}/U_{\mathrm{{bulk}}} \simeq 2.6 \times 10^{-4}\). The consequent inaccuracy due to Brownian fluctuations is found one order of magnitude smaller than those due to other error sources to be discussed below.

*x*–

*y*) in the channel symmetry plane, \(z = h/2\). The three curves correspond to different flow rates, \(Q = 1, \, 2,\) and \(3\, \mathrm{ml/min}\) and are normalised by the corresponding bulk velocity. On the right panel, Fig. 7 shows the profiles in the orthogonal view (

*x*–

*z*, reflected image), now in the symmetry plane \(y = w/2\). The profiles, estimated by averaging the velocity over different samples, collapse within the provided confidence interval. For each flow rate, Fig. 8 shows the behaviour of the confidence interval, \({\bar{\sigma }}_x(N_{\mathrm{{sample}}}) = V_x^{\mathrm{{rms}}}/\sqrt{N_{\mathrm{{sample}}}}\), as a function of the number of samples, where \(V_x^{\mathrm{{rms}}}\) is the velocity rms obtained from \(N_{\mathrm{{sample}}}\) data. The error bars reported on the velocity profiles of Fig. 7 corresponds to \(N_{\mathrm{{sample}}} = 450\). The effective number of samples follow from the acquisition of \(N_{\mathrm{{frame}}} \simeq 1500\) acquired image couples with occupancy fraction of each interrogation window \(f_\mathrm{{o}} = 0.21\). The value of \(f_\mathrm{{o}}\) was estimated as explained in Sect. 2 and is confirmed by analysing the raw images from the acquisition system. The inset of the figure shows in green an example of the confidence interval distribution in the transversal direction. The red curve is a theoretical prediction based on a model of the measurement process to be illustrated below.

The positions of the two orthogonal planes can be independently varied by changing the objective focus and the thickness of the optical path adapter with an accuracy related to the correlation depth. Since, in principle, the coordinates \(y_0, \, z_0\) of the intersection line can span the entire channel section, the full three-dimensional field can be, in principle, reconstructed.

*x*along the intersection line of the two views, illustrating the possibility to simultaneously measure all three velocity components.

*x*–

*y*plane at nominal spanwise location \(z_0\) involves the slab \(z_0 - \ell _\mathrm{{c}}/2 \le z \le z_0 + \ell _\mathrm{{c}}/2\). Since tracer particles randomly reach the sensitive region (i.e., they are independently and uniformly distributed across the correlation depth), the estimated velocity is in fact the spatial average of the probe velocities across the slab. Apart from Brownian fluctuations, the probe velocity fluctuations are basically a function of the probe position and may be explicitly determined from the analytical velocity and the statistical model reported in Appendix C, see Lima et al. (2006) for a related procedure. Figure 11 illustrates the results of the model. The left panel is the axial velocity distribution across the channel section normalised by the bulk velocity. The right panel shows three profiles at three different spanwise positions. For each case two curves are shown, the (modelled) experimental estimate of the velocity together with the corresponding statistical error bars and the exact velocity at the nominal position. As the model suggests, the main source of error in the conditions of the experiment are due to the averaging of the velocity across the correlation depth. This systematic error component dominates over the statistical error incurred in evaluating the average with a finite sample. As already discussed, the Brownian fluctuation is even smaller, showing that the depth of correlation is the crucial parameter determining the accuracy. As apparent in Fig. 11, the profile taken in the middle of the channel is perfectly captured by the model, see the red curves in the right panel. Both accurately correspond to the actual measurement as shown in the right panel of Fig. 10. Moving towards the side of the channel, the systematic component of the error tends to grow, due to the steeper change of velocity with the position of the probing particle which makes the average across the slab significantly different from the nominal local value.

Let us now focus on the T-junction configuration described in Sect. 2. The left panel of Fig. 12 shows the velocity field in the two orthogonal views corresponding to the planes \(y_0 = 0.16 \, \mathrm{{w}}\) and \(z_0 = 0.75 \, \mathrm{{h}}\). In both planes, the intersection of the plane with the bubble meniscus can be readily figured out. The fields are reconstructed by phase averaging the \(\mu\)PIV frames corresponding to the same configuration of the bubble. Along the common intersection line, all the three velocity components are measured, providing a time-dependent (depending on the bubble position), three-component reconstruction. As for the case of the straight channel, by changing objective focus and thickness of the optical adapter the entire flow domain can, in principle, be spanned for a complete three-dimensional reconstruction.

The right panel of Fig. 12 consists of the superposition of a raw image taken from the \(\mu\)PIV system with three axial velocity profiles at selected stations, one before the bubble (red curve), one on the middle of the bubble (green curve) and the third (blue) behind the bubble. The top/bottom part of the image corresponds to the reflected/direct view, respectively. The axial velocity distribution along the common intersection line is plotted in the left panel of Fig. 13, where the red curve denotes data from the direct (*x*–*y*) view and the blue one corresponds to the reflected (*z*–*x*) view. As for the case of the rectilinear channel, the confidence interval is \({\bar{\sigma }}_x = V_x^{\mathrm{{rms}}}/\sqrt{N_{\mathrm{{sample}}}}\), where \(V_x^{\mathrm{{rms}}}\) is the variance of the velocity signal and \(N_{\mathrm{{sample}}} \simeq 100\) is the number of samples, related to the total number of acquired frame couples by \(N_{\mathrm{{sample}}} = f_0 \, N_{\mathrm{{frame}}}\). The values measured at corresponding positions from the two views are consistent with the expected statistical error, now significantly larger than in the straight channel case due to the reduced number of frames available for a given bubble configuration. The right panel of the figure shows the transverse velocity components along the intersection, with the red line showing \(U_y\) from the direct (*x*–*y*) view and the blue line providing \(U_z\) from the reflected (*z*–*x*) view.

## 4 Conclusions

An important issue in microfluidics is accessing the three-dimensional structure of the velocity field. For the specific case of a T-junction, the three-dimensional field can be reconstructed using stereo \(\mu\)PIV as shown in Lindken et al. (2006). Here we provided a proof of principle of a simpler approach which is able to reconstruct the three-dimensional, three-component velocity using a standard \(\mu\)PIV set-up. A microdevice has been conceived to allow the simultaneous visualisation of the flow in a T-junction along two orthogonal planes. As a specific feature, the novel device allows for capturing both views in a single camera sensor. Half the image corresponds to the direct view, (*x*–*y*) plane. The other half captures the orthogonal view in the (*z*–*x*) plane which is conveyed to the camera objective through an inclined mirror and a suitable optical adapter. The device is used together with a traditional, single camera, \(\mu\)PIV system able to measure the planar velocity components on the two planes. Beside providing simultaneous views and related velocity components in the two orthogonal planes, all three velocity components are measured along the common intersection line. By adjusting the objective focus and the thickness of the optical adapter, the intersection line can span the three-dimensional flow volume, allowing, in principle, to reconstruct the entire 3D field.

The analysed data were obtained for channels with typical size of \(800 \, \upmu \mathrm{m}\) using \(4.47 \, \upmu \mathrm{m}\)-sized seeding fluorescent particles. In these conditions, the thermally induced Brownian motion of the probes is negligible. The main source of error is found to be related to the \(\mu\)PIV correlation depth. The adopted fabrication technique allows to reduce the size of the channels down to \(100 \, \upmu \mathrm{m}\), due to limit in the assembly precision.

For a \(100 \, \upmu \mathrm{m}\) channel, an increased magnification should be used together with smaller tracer particles, e.g., \(M = 20 \times\) with \(1 \,\upmu \mathrm{m}\) tracer particle diameter. In these conditions, the correlation depth is \(\ell _\mathrm{{c}} = 10 \, \upmu \mathrm{m}\), such that \(\ell _\mathrm{{c}}/h\) is almost the same as the case of the \(800 \, \upmu \mathrm{m}\) channel, explicitly studied here. Assuming the same supply pressure, the expected velocity in the small channel is of the order of \(1 \, \mathrm{mm/s}\). On the other hand, the Brownian fluctuations of \(1\, \upmu \mathrm{m}\)-particles at the same ambient temperature turn out to be \(2.7 \, \mathrm{mm/s}\), which is comparable with the fluid velocity. As a consequence, the number of samples needs to be substantially increased to maintain the same statistical accuracy. In any case, like for the larger channel, the main source of error is associated with the correlation depth. In these conditions, a possible strategy to increase the measurement accuracy would be to resort to confocal microscopy (Oishi et al. 2009) which allows for reaching correlation depths of the order of \(\ell _\mathrm{{c}} \simeq 5 \, \upmu \mathrm{m}\). One of the interesting aspects of the present device is that it can be easily used in conjunction with confocal \(\mu \mathrm{PIV}\), substantially increasing the potentiality of this powerful technique. A second interesting perspective emerges in the opposite limit of a (relatively) large depth of focus in the context of particle tracking. In this case, the two orthogonal views would allow to track the seeding particles in their three-dimensional motion through the measurement volume (Yoon and Kim 2006). A third field of possible application is for benchmarking of other less direct methods to obtain the third velocity component like, e.g., Barnkob et al. (2015), in defocusing \(\mu \mathrm{PIV}\). Finally, using image analysis techniques, the present set-up can be used to directly measure the curvature radii of the bubbles, simultaneously with the acquisition of the velocity field.

## Notes

### Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. [339446]. Useful discussion with Prof. Giancarlo Ruocco on the optical set-up is acknowledged.

## Supplementary material

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