20th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 11 – 14, 2022

Stereoscopic MicroPIV Measurements in A Labyrinth-Channel Dripper
Used in Micro-Irrigation Systems

Gökhan Ergin1,*, Muriel Amielh2, Severine Tomas3, Jafar Al-Muhammad2,3, Jean-Jacques Lasserre4, Fabien Anselmet2
1: Dantec Dynamics, Skovlunde, Denmark
2: IRPHE, Marseille, France
3: IRSTEA, UMR G-EAU, Montpellier, France
4: Dantec Dynamics, Marseille, France* Correspondent author: gokhan.ergin@dantecdynamics.com
Keywords: Micromixing, Drip irrigation, Stereoscopic Micro PIV, Microfluidics, Passive micromixer

ABSTRACT
Small serpentine-shaped channels used in drip irrigation is an efficient irrigation technique in order to spare water.
Eventual clogging in such micro channels should be avoided to extend the lifetime of these irrigation systems.
Clogging often occurs when sedimentation takes place in low or zero velocity regions in steady laminar flow
conditions. For this reason, labyrinth dripper designs are used to enhance mixing and / or induce unsteady flow
conditions inside the channel. The aim of the present study is to investigate the flow inside such millimetric complex
channel geometry with Stereoscopic MicroPIV measurements. Current three-component (3C) velocity measurements
are compared with previous two-component (2C) velocity measurements. Results indicate that the u and v
components of the 3C measurements are in good agreement with the previous 2C measurements, identifying andconfirming the previously measured low- and zero-velocity regions. Furthermore, the out-of-plane (w) velocity
component adds new information about the flow field revealing three-dimensional (3D) flow structures, what appears
to be oblique vortices emanating from the baffle tips. In conclusion, both enhanced mixing due to 3D vortices andinduced unsteady flow field seems to be responsible for clogging suppression.

1. Introduction
There is a growing trend in agriculture towards more efficient irrigation systems, as water isbecoming a scarce resource for human survival. According to the world resource institute(www.wri.org), the water stress is expected to increase substantially by 2040, due to increasing
population, global warming, and increasing food demand (Figure 1). Today, agriculture accounts
for 70% of freshwater withdrawals on average, with up to 90% in some developing countries.
Unfortunately, 80% of irrigation is still performed using furrow irrigation, which is the oldest andleast efficient irrigation technique. Sprinkler irrigation is more efficient with 17% and micro
irrigation is the most efficient irrigation technique with only 3% usage worldwide. Despite theircost, there is a shift towards more efficient micro-irrigation techniques like drip irrigation.

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Fig. 1. Projected water stress in 2040. Source: World Resources Institute, www.wri.org
Low-cost drip irrigation nozzles are passive micromixer devices (Figure 2) which rely entirely on
the fluid pumping energy with the least number of moving parts. In these devices, the channel
geometry is the main design parameter that affects the durability. Often the irrigation nozzles havea channel topology (Figure 2) that introduces a large pressure drop to maintain the flow in an
irrigation network. Choosing a small exit cross section could be one solution but, this approach
often leads to clogging problems in the long term. This reduces the useful lifetime of the irrigation
nozzle, which produces more plastic waste over time, and this has a negative impact both on theenvironment and on the farming cost.
The nominal flow rates and dimensions used in drip irrigation nozzles result in Reynolds numbers
around 500, therefore clogging is promoted in regions with low or zero velocity for extended
periods of time where particles get a chance for deposition on the channel walls. Extensive
MicroPIV measurements have been performed to characterize the two-dimensional (2D) flow field
for this microchannel (2,3), but the 3D flow field characterization was not considered. In Ref (3),some regions were identified as shear motion zone and vortex zones based on the 2D velocity data,
i.e. only the mean vorticity in the z-direction was studied. However, serpentine micromixers withsharp turns are found to induce oblique vortices (4,5), and these could be responsible for enhanced
mixing and reduced clogging in the irrigation nozzle. Furthermore, in Ref (2) and (3) the unsteady
movement of the low- or zero-velocity regions were not considered. If these low- or zero-velocity
zones move within the serpentine, i.e. if their position is not steady, the particles may not havesufficient time to settle in one position, which may be responsible for the delay of clogging. The
aim of this study is :

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to compare the current three-component (3C) measurements with the 2C measurements in
Ref (2),



to identify any oblique vortices emanating from the baffle tips,



to identify any low- and zero-velocity regions and investigate their steadiness,evaluate the results with respect to clogging considering the new information inferred fromthe Stereo MicroPIV measurements.

Fig. 2. Labyrinth channel flow geometry used in the experiments(1)2. Stereoscopic MicroPIV
Experiments are performed using the Stereoscopic MicroPIV technique (Fig. 3a) as it can provide
the necessary multiple-component velocity information in the investigated irrigation serpentinewith micron scale resolution. All three velocity components are measured in the center height ofthe microchannel, around the 3rd baffle (Figure 2). The experimental setup (Fig. 3b) includes a
Leica fluorescence stereomicroscope, 1× Plan Apochromatic common main objective, a custombuilt micro image calibration kit, laser and LED illumination, and a checkerboard calibration plate.
The selected microscope and objective configuration can produce a stereoscopic half-angle of ~11°in air (full angle 22°), and this means that the uncertainty of the out-of-plane velocity component,
𝑤, is expected as 5× that of the in-plane velocity components, 𝑢 and 𝑣 (6). Since uncertainty of thein-plane velocity components are on the order or 0.5% (assuming ~0.055 pixels in a 11 pixel
displacement in a 32×32 interrogation window) (7), the uncertainty of the out-of-plane velocity
component is expected to be on the order or 2,5%.

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(a)

(b)

Fig. 3 (a) 2D3CµPIV measurement in back-scatter illumination mode. (b) a 2D3CµPIV system
featuring a fluorescence stereo microscope, two PIV cameras, a calibration kit and syringe pump.
Stereoscopic image calibration in a microchannel is simply difficult, if not impossible. To achieve
an accurate representation of the object space in 3D, a dedicated image calibration kit (Fig. 4a) isused, which consists of a checkerboard calibration target (Fig. 4b), a calibration pool and a microstage to traverse the target in the calibration pool. The cover glasses of the calibration pool and of
the microchannel are the same material (2mm thick glass for the current experiment) simulating
similar optical conditions during calibration and measurements. Further details on Stereoscopic
MicroPIV measurements can be found in Ref. (8).

Fig. 4. (a) Stereoscopic image calibration kit for MicroPIV. (b) View of the checkerboard
calibration target, the coordinate system (red), metric calibration grid (green). Each square edge
is 500µm.
The calibration target features a checkerboard pattern for a 4.5 mm object size. Carefully placed
three circular markers within the squares allow an unambiguous definition of the planar
coordinate axes. During calibration, a pulsed monochromatic LED device is used for illumination,
which proves useful in obtaining calibration images with good contrast. The calibration is
performed (i) by imaging the checkerboard pattern in known positions within the depth of field(ii) by computing mapping function for the 3D space using a 3rd order polynomial function (9)20th LISBON Laser Symposium 2022

and (iii) by performing calibration refinement. The depth of field is controlled by adjusting theaperture of the zoom optics of the stereomicroscope. A depth calibration is also performed for
accurate positioning of the measurement plane in the microchannel. The depth calibration,
stereoscopic calibration and experiments are performed at 5× total system magnification, which
produces a Field of View (FoV) of 3mm × 3mm. During depth calibration and measurements, theaperture was adjusted to produce a 31 µm field depth (important for depth calibration) and 385µm correlation depth (important for experiments). Five calibration images were used at h= ±200µm, ±100 µm and 0 µm (center height). The average reprojection error for left and right cameras
were found as ~1 pixel because of image calibration using a new marker detection algorithm.
3. Experiments
The flow rig is considerably different from the flow rig used in Ref (2,3), except the flow channel:
A water pump and 2 dampers were used in Ref (2,3), and a high precision syringe pump with alinear step resolution of 12 nm is used in this work. Rhodamine B fluorescent particles were used
for seeding in both experiments, with 1 µm diameter in in Ref (2,3) and with 1-20 µm-diameter inthe current study. The syringe pump’s flow rate accuracy and reproducibility are given as ±0.35%
and ±0.05% respectively, and therefore no dampers were necessary in the current experiments.
The syringe pump can drive two syringes simultaneously and the flow rate is adjustable between
1.6 pl/min to 300 ml/min using different syringe sizes. High quality airtight glass syringes areused to generate a smooth flow during the measurements. Two flow rate settings of 24ml/min
and 48ml/min induce Reynolds numbers of 345 and 690 respectively, in order to produce close
experimental conditions to those of Ref (2) and (3) where Reynolds numbers were 435, 642 and867. The flow rates are selected so that they can be compared with the 2D2C PIV results obtainedin Ref. (2) and (3). During measurements, pulsed illumination at 532nm from a 50 mJ/pulse dualcavity Nd:YAG laser is delivered to the microscope using a liquid light guide and imaging is
performed using two 12-bit FlowSenseEO 4Mpix (2048pix × 2048pix) PIV cameras. Planar threecomponent velocity measurements are computed by combining the 2D2C velocity field
information from each camera, and refined image calibration information. Contrast of raw particle
images was enhanced by performing a background subtraction using the minimum pixel value
found in the ensemble. An ensemble static masking technique is applied to perform static masking(10), and this static mask was used to improve PIV interrogation near the boundaries (11).
4. Results
Comparison of 2C flow field: we start with some comparisons in the 2D flow field to ensure
repeatability of the results. Figures 5 and 6 below shows such comparison for the mean 𝑢 velocity
field and mean 𝑣̅ velocity field, respectively. In Figure 5a and 5b the mean 𝑢 velocity field resultsof the current study using Stereoscopic MicroPIV system is shown for Re=345 and Re=690,
respectively. In Figure 5c, the mean 𝑢 velocity field results for Re=687 from Ref. 1 is shown withsimilar contour levels to Fig. 5b.

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Fig. 5. Mean 𝑢 velocity field (a) Re=345 using Stereo MicroPIV (-0.75 < 𝑢 < 0.25 m/s) N=1000 (b)for Re=690 using Stereo MicroPIV (-1.5 < 𝑢 < 0.5 m/s) N=1000 (c) Re=687 using 2D MicroPIV (-2< 𝑢 < 0.7 m/s) from Ref. (1) N=500.

Fig. 6. (a) Mean 𝑣̅ velocity field (a) for Re=345 using Stereo MicroPIV (-0.75 < 𝑣̅ < 0.75 m/s)
N=1000 (b) Re=690 using Stereo MicroPIV (-1.5 < 𝑣̅ < 1.5 m/s) N=1000 (c) Re = 687 using 2D
MicroPIV (-2 < 𝑣̅ < 1.5 m/s) from Ref. (1) N=500.

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Fig. 7. The 𝑢′ ⁄𝑣′ ratio in the third baffle (a) Re=690 using Stereo MicroPIV (0 < 𝑢′ ⁄𝑣′ < 2.8)
N=1000 (b) Re=800 using 2D MicroPIV (0 < 𝑢′ ⁄𝑣′ < 2.8) from Ref. (12) N=250
Please note that the contour range of Fig. 5a is half of that of Fig. 5b. The three-way comparison
suggests that (i) the flow topology is very similar if the mean 𝑢 velocity field is normalized by the
Reynolds number, and (ii) the current measurement results using Stereo MicroPIV system have agood agreement with the results obtained using the 2D MicroPIV system. A similar conclusion isreached when the mean 𝑣̅ velocity field is considered (Fig. 6). It should be noted that the numberof images in the ensemble is, N=1000 for the current experiments, and N=500 for the 2D MicroPIV
experiments of Ref. (1).
As the mean flow velocity components, 𝑢 and 𝑣̅ provide a good comparison with the previous
results, we attempted to make a comparison of previously reported fluctuating velocity results.
Fig. 7 makes such a comparison using the ratio of mean squared velocity components, 𝑢′ ⁄𝑣′ , inthe third baffle. Whereas Fig 7a. shows the 𝑢′ ⁄𝑣′ ratio field in the third baffle for Re=690 using
Stereo MicroPIV, Fig 7b. shows the same ratio in the same baffle for a slightly higher Re=800 using
2D MicroPIV as reported in Fig. 23 of Ref. (12). Although there is a general good agreement in Fig.
7, there are also noticeable differences. The major difference is the presence of very high values of
the 𝑢′ ⁄𝑣′ ratio near the top and bottom walls of the channel (Fig 7b). These high values are notvisible in the current study (Fig 7a). There can be several reasons why this may be happening, as
everything except the flow channel is different in the current study, compared to the rig describedin Ref. (12). For example, a pump and 2 damper mechanisms were used in Ref (12), and a precisionsyringe pump is used in this study. Furthermore, an automated static masking technique is usedin this study in combination with interrogation window masking near the walls and these are notused in Ref (12). It is quite possible that the 𝑢′ ⁄𝑣′ ratio could yield large values due to undamped
oscillations originating from the pump in Ref (12), and these may have gone unnoticed due to lackof wall treatment in data analysis. However, the current study captures the main topology of𝑢′ ⁄𝑣′ field quite well away from the walls. Once again, it should be noted that the number ofensembles is N=1000 for the current experiments, and N=250 for the 2D MicroPIV experiments ofRef (12). All in all, it is quite encouraging that the current Stereo MicroPIV results are in good

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agreement with the previously reported 2D MicroPIV results, both in terms of the mean flow andin terms of fluctuating components.
𝒘 Results: The mean out-of-plane velocity component, 𝑤 fields for Re=345 and Re=690 cases areshown in Figure 8a and 8b, respectively. The negative values indicate vectors going into the page
and the positive values indicate vectors going out of the page. One immediate observation is thatthe flow topology is very similar if the mean 𝑤 velocity field is normalized by the Reynolds
number, as the contour range for Re=345 case is half of the same for Re=690 case. Anotherobservation is that there is a concentration of negative 𝑤 from baffle tips (in purple color),
elongated towards the left, in the flow direction. Regions of positive 𝑤 areas (in red colour) parallelto the purple regions may suggest the existence of a vortex tilted ~45° with the 𝑥-axis. These
locations are marked with black dashed lines in Fig. 8 (1,2,3,4). As mentioned before, serpentine
micromixers with sharp turns may induce oblique vortices (4,5), and these can be responsible forenhanced mixing and reduced clogging in the nozzle. To identify such vortices, the 3D viewshould be used (Fig. 9).

Fig. 8. The mean 𝑤 fields for (a) Re=345 (-0.3 < 𝑤 < 0.3 m/s) and (b) Re=690 (-0.6 < 𝑤 < 0.6 m/s)

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Fig. 9. The mean velocity field, where 𝑢 and 𝑣̅ are drawn as vectors, and 𝑤 is depicted in colours.
(a) Re=345 (-0.3 < 𝑤 < 0.3 m/s) and (b) Re=690 (-0.6 < 𝑤 < 0.6 m/s)
Figure 9 shows the mean velocity field for the experiments, where 𝑢 and 𝑣̅ are drawn as vectors,
and 𝑤 is depicted in colours. The advantage of 3D view is that one can rotate the view freely in
any arbitrary axis to visualise potential oblique vortices in the flow field (Figs. 10 and 11). Fig. 10shows the 3D view for Re=345 case: On the left (Fig 10a) a counter-clockwise (CCW) vortex is
identified originating from the baffle on the left in Fig. 8a (dashed line 1), whereas on the right(Fig. 10b) a clockwise (CW) vortex is identified originating from the baffle on the right in Fig. 8a(dashed line 2). Figure 11 shows similar results for the Re=690 case with twice the vortex strengthcompared to the Re=345 case: On the left (Fig 11a) a counterclockwise (CCW) vortex is identified
originating from the baffle on the left in Fig. 8b (dashed line 3), whereas on the right (Fig. 11b) aclockwise (CW) vortex is identified originating from the baffle on the right in Fig. 8b (dashed line
4).

Fig. 10. 3D view for Re=345 (a) CCW vortex on axis 1 in Fig 8a (b) CW vortex on axis 2 in Fig 8a

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Fig. 11. 3D view for Re=690 (a) CCW vortex on axis 3 in Fig 8b (b) CW vortex on axis 4 in Fig 8b
Mean total velocity: As zero-velocity or low-velocity regions favor sediment deposition whichleads to eventual clogging, the mean velocity modulus must be investigated to identify stagnant
and recirculation zones in the microchannel. Previous 2D MicroPIV experiments in Ref.s (1–3,12)
only measured 𝑢 and 𝑣, so the modulus was computed as 𝑉 , = √𝑢 + 𝑣 , but here it can becomputed as 𝑉 , , = √𝑢 + 𝑣 + 𝑤 , with the availability of 𝑤 thanks to the Stereo MicroPIV
system. Fig. 12 compares the mean total velocity fields, 𝑉 , , , for Re=345 and Re=690 cases for thecurrent study and the 𝑉 , from Fig. 12 of Ref. (2) using similar colormaps.
First, a general comparison of current mean total velocity results to previous results shows thatthe general flow magnitude topology is captured quite well with subtle differences. This isencouraging since we expect the Stereo MicroPIV measurements to have good agreement with theprevious 2D MicroPIV experiments, but also reveal new information by the additional
measurement of 𝑤, which was not available before. Second, we can identify several recirculationand stagnation zones in the microchannel, marked with red and black colors, respectively (Fig.
12a and 12b). These zones are in good agreement with Ref. (2) (Fig. 12c and 12d): The recirculation
zones R1 and R2 are slightly larger for the Re=345 case (Fig. 12a), when compared with the Re=690
case (Fig. 12b); and the stagnation zone S1 is smaller for the Re=345 case (Fig. 12a), when comparedwith S2 in the Re=690 case (Fig. 12b). Finally, a new stagnation zone S3 (Fig. 12b) is visible close to
the lower wall only for the Re=690 case and was not visible for the Re=345 case (Fig. 12a). In short,
it seems like the recirculation zones are shrinking and stagnation zones expanding with increasing
Re number.

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S1

R2

S2
R4

R3

R1

S3

Fig. 12. The mean velocity modulus in the 3rd baffle. (Left) Re=345 (Right) Re=690 (Top) 𝑉 , , ofthis study (Bottom) 𝑉 , from Fig. 12 of Ref. (2). (a and b) Black marks stagnation zones, redmarks recirculation zones.
Fluctuating velocity field: The mean 𝑤 fields have shown that an oblique CCW vortex is producedon the lee side of baffles located on the top wall and an oblique CW vortex is produced on the leeside of baffles located on the bottom wall. These vortices could not be observed previously as theout-of-plane velocity component was not measured. Furthermore, the mean total velocity fields
show several recirculating and stagnant zones in the microchannel. To draw some conclusions
about clogging in the channel, the fluctuating velocity components (Figure 13) should be
investigated, together with the mean flow field to check the steadiness of the low- or zero-velocity
zones identified earlier in Figure 12.
Figure 13 shows the fluctuating velocity components 𝑢’ (top row), 𝑣’ (middle row) and 𝑤’ (bottomrow), for two cases: for Re=345 (left column) and for Re=690 (right column). The contour map
ranges for the right column (Re=690 case) are always twice of those on the left column (Re=345

20th LISBON Laser Symposium 2022case). This immediately suggests that the components 𝑢’, 𝑣’ and 𝑤’ information scales with Re, as
the topology is quite similar on the left and right column within each row. Also marked on Fig. 13
are the stagnation and recirculation zones identified previously in Figure 12a and 12b (marked

S1

R2

S2
R4

u’
R3

R1

S3

S1

R2

S2
R4

v’
R3

R1

S3

S1

R2

S2
R4

w’
R1

R3
S3

Re=345

Re=690Fig. 13. Fluctuating velocity fields (m/s). (Top) 𝑢’ (Middle) 𝑣’ (Bottom) 𝑤’. (Left) Re=345 (Right)
Re=690.

(a) (0 < 𝑢′ < 0.135), (b) (0 < 𝑢′ < 0.270), (c) (0 < 𝑣′ < 0.2) (d) (0 < 𝑣′ < 0.4), (e) (0 < 𝑤′ <0.5) (f) (0 < 𝑤′ < 1)

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again with black and red, respectively). The basic idea is to search for some non-zero values in thefluctuating fields for the low-velocity zones in the mean flow field. If non-zero fluctuating values
indeed exist in these zones, this means that the low- or zero-mean-velocity zones suspected of
sediment deposition are in fact non-steady, and the particles may not have enough time to settle
in these zones. When Fig. 13 is carefully examined in zones R1, R2, R3, R4 and S1, S2, S3; not only
the values are non-zero but also they are significantly large within each range. This may explain
why the dripper geometry used in the current study and in the previous experiments (1–3,12) isless susceptible for clogging: Using the estimated Kolmogorov time scales from the Reynolds
Stress Model numerical simulation of Ref(1) in the range 0.045-0.13 ms for Reynolds numbers
between 800 and 400, the Stokes number will be around 0.1 only for sand particles above 10
microns which could begin to be entrapped into the water vortices.
4. Summary and Conclusions
Stereoscopic MicroPIV measurements are performed on a serpentine microchannel geometry
which is known to suppress clogging when used in agricultural drip irrigation systems. In short,
all 4 aims of this study were fully achieved: Comparison of the current three-component (3C) measurements with the 2C measurements
in Ref (2), reveals that the flow topology is quite similar, and 3C results are in good
agreement with the 2C results, yet adding more information to the existing knowledge on
the flow field.
 Oblique vortices emanating from the baffle tips were identified thanks to the measurementof 𝑤 component. These vortices are rotating in CCW and CW directions per baffle, one after
the other. These are better visible using 3D viewers, as the flow field in the channel is quite
complex. These oblique vortices are very likely to have a contribution to the mixing process
in the microchannel and thereby have an influence on clogging suppression.
 The low- and zero-velocity regions, i.e. stagnation and recirculation regions were identified
and their steadiness were investigated. It was found that although several stagnation andrecirculation zones were identified from the steady flow field results, the unsteady flow
fields showed that the fluctuating velocity components are all non-zero.
 Results were evaluated with respect to clogging considering the new information using theStereo MicroPIV measurements: Following point 3, the fluctuations are thought to be themain contributor for clogging suppression as the particles do not get a chance to settle inthese low- and zero-velocity regions due to fluctuations.
The fluctuating 𝑤 fields were observed to have a suspiciously large amplitude and this may be
attributed to the larger uncertainty associated with the shallow stereo angle. Another reason could
be due to the large correlation depth (385µm) during the experiments. Future work will focus on
improving the out-of-plane component accuracy using a thinner correlation depth or using 3D
particle tracking in the existing correlation depth. The larger than expected out-of-planefluctuations do not change the last conclusion above, since the in-plane fluctuations are still nonzero and may be responsible for clogging suppression.

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