works on the T-junction. However it also includes in the intercept the dependence of ¯V on Ca at fixed φ, firstly observed experimentally by Christopher et al. [1].
An additional information from this empirical law is that the dependence on Ca relies only on the first term which refers to the volume gained by the droplet before it is almost completely filling the main channel. That means the ratio between viscous and capillary forces is fundamental in the very first stage of droplet formation and affects markedly the droplet volume at very low values of Ca. To the best of the author’s knowledge this result has not previously reported and could stand for a starting point towards an extension of existing theoretical models to low capillary numbers.
5.6 Device Reproducibility
In order to test the reproducibility of the whole fabrication process a reduced set of meas- urements were performed on a second device with the same characteristics of that employed in the analysis discussed in this chapter. All steps from the laser ablation to the sealing and the functionalization were repeated at the same conditions for both devices so that they represent two copies of the same microfluidic chip. The measurements of the dimensions of the channels were wc= 125.1 ± 0.8µm, h = 99.5 ± 0.7µm for the T-junction used in the
previous analysis (TJ2) and wc= 126.3 ± 0.6µm, h = 90 ± 2µm for the other (TJ1).
The length of the produced droplets was measured for both devices using hexadecane with 1%(w/w) SPAN R80 surfactant added as the continuous phase and DI water as the dispersed phase at Qc = 10µl/min and 30µl/min, varying the dispersed phase flow rate
Qd from 0.1×Qc to 1.0×Qc. The results are shown in Fig.5.13: again the linear relation
between ¯L and φ is verified and as can be seen the devices show a perfectly matching re- sponse in the tested flow rate range. This is the proof of the reproducibility of fabrication steps as a whole.
96 5.6 Device Reproducibility
(a) φ = 0.1 (b) φ = 0.3
(c) φ = 0.5 (d) φ = 0.7
(e) φ = 1.0 (f ) φ = 1.5
(g) φ = 2.0
Figure 5.6: Analysis of droplet production frequency in the case of pure hexadecane as continuous phase (no surfactant added, σ = 41mN/m). The plots show the rescaled frequency ¯f = µcwc
σ f as a function of Ca at fixed flow rate ratios φ. The red line represents the linear fit of the experimental data performed excluding the points at Ca< 9.7 · 10−3 which are indicated with a cross (×).
5.6 Device Reproducibility 97
(a) φ = 0.1 (b) φ = 0.3
(c) φ = 0.5 (d) φ = 0.7
(e) φ = 1.0 (f ) φ = 1.5
(g) φ = 2.0
Figure 5.7: Analysis of droplet production frequency in the case of hexadecane with added 0.08%(w/w) SPAN R80 as continuous phase (σ = 15mN/m). The
plots show the rescaled frequency ¯f = µcwc
σ f as a func- tion of Ca at fixed flow rate ratios φ. The red line rep- resents the linear fit of the experimental data.
98 5.6 Device Reproducibility (a) (b) (c) Average CL with [1] Mutual CL no SPAN R80 1.29 ± 0.02 54% 86.4% with SPAN R80 1.29 ± 0.01 59% overall 1.29 ± 0.01 53% (d)
Figure 5.8: Details on the study of the exponent of the power law linking ¯f to Ca: (a) (1 − δ) determined from fits at different fixed φ for the case without (black points) or with (red points) SPAN R80 added
to the continuous phase, together with their averages. Dotted lines represent the calculated error on the average of (1 − δ); (b) comparison of all (1 − δ) determinations with the value found by Christopher et al. [1]; (c) comparison between the (1 − δ) averages obtained in the case without or with surfactant and the value found by Christopher et al. [1]; (d) averages with their confidence level with the value of Christopher et al. and between theirself.
5.6 Device Reproducibility 99
(a) Qc= 5µl/min (b) Qc = 7µl/min
(c) Qc= 10µl/min (d) Qc= 12µl/min
(e) Qc= 20µl/min (f ) Qc = 30µl/min
(g) Qc = 35µl/min (h) Qc= 40µl/min
Figure 5.9: Analysis of rescaled droplet length in the case of pure hexadecane as continuous phase (no surfactant added, σ = 41mN/m). The plots show the rescaled length ¯L = L
wc as a function of φ at
fixed continuous phase flow rate Qc. The red line represents the linear fit of the experimental data (data excluded by the fit are indicated with a cross (×)).
100 5.6 Device Reproducibility
(a) Qc= 5µl/min (b) Qc = 7µl/min
(c) Qc= 10µl/min (d) Qc= 12µl/min
(e) Qc= 20µl/min (f ) Qc = 30µl/min
(g) Qc = 35µl/min (h) Qc= 40µl/min
Figure 5.10: Analysis of rescaled droplet length in the case of hexadecane with added 0.08%(w/w) SPAN R80 as continuous phase (σ = 15mN/m). The plots show the rescaled length ¯L = L
wc as a function
5.6 Device Reproducibility 101
Figure 5.11: Plot of ¯Vfill as a function of Ca. The red line represents the power law ¯Vfill = ¯V (0) fill Ca
δ
where δ = −0.29 is taken from the overall average in table of Fig.5.8d and the red dashed line represents the uncertainty due to σδ = 0.01. The other lines represent the theoretical models from the literature described in section 3.3.1.
Figure 5.12: Plot of αV as a function of Ca. The red line represents the average αV = 1.23 ± 0.07 of the experimental data and the red dashed line represents the uncertainty on the calculated average value. The other lines represent the theoretical models from the literature described in section 3.3.1.
102 5.6 Device Reproducibility
(a) Qc = 10µl/min (b) Qc= 30µl/min
Figure 5.13: Comparison of the rescaled length obtained at (a) Qc = 10µl/min and (b) Qc = 30µl/min of hexadecane with 1% SPAN R80 with two different devices fabricated by laser ablation and sealed with
6 Optofluidic Coupling
6.1 First tests
The first tests on the coupling of the light from the waveguides to the microfluidic channels were performed on small lithium niobate samples obtained from an x-cut commercial wafer. At first a series of z-propagating optical waveguides were realized by the process described in chapter 2 and the transmitted light was recorded with the near field setup.
A single microfluidic channel was engraved on the surface perpendicularly to the waveguide, dividing it into two facing parts, one injecting the light signal and the other one collecting the output. By this way the optimal alignment of the input and output waveguides was ensured. The same approach was used on a series of parallel waveguides.
Both laser ablation and mechanical dicing techniques were exploited to engrave different samples. The collecting objective employed in the near field setup was chosen with a working distance of 1cm. By this way it was posssible to pull the objective towards the sample and point its focus inside the crystal as far as the channel walls without knocking the sample surface.
The first test on the coupling of the signal across the microfluidic channels were performed on the open channels without any sealing, with the same configuration of the near-field setup employed for the characterization of the waveguides (see section 2.5).
The key parameter to be studied in this opto-fluidic system is the light transmitted across the microfluidic channel.
In the case of the laser ablated channels, the light injected in the input waveguide was efficiently confined and propagated till the lateral wall of the microfluidic channel. It was experimentally verified that a well defined image could be indeed recorded pointing the objective focus to the channel side surface. Nevertheless no intensity was measured exiting from the outer face of the sample indicating that no excitation of the outlet waveguide was possible.
104 6.1 First tests
(a) I/I0 = 100% (b) I/I0 = 38% (c) I/I0= 76%
(d) (e) (f )
Figure 6.1: Example of the near field images of a waveguide coupled to a 200µm wide microfluidic channel: on the top (a) TE single mode of a waveguide before the channel was engraved, (b) after the channel was engraved and filled with air, (c) after the channel was filled with hexadecane; on the bottom images of a TM single mode waveguide crossing a 200µm microfluidic channel (d) filled with air, (e) water and (f) hexadecane.
In order to reduce light diffraction at the exit from the inlet waveguide and favour the excitation of the collecting waveguide, a drop of hexadecane was placed on an extremity of the channel in order to fill it by capillarity and allow for a better index matching between the lithium niobate crystal and the fluid inside the channel (nhexa=1.434 at λ=632.8nm).
No changes on the output waveguide were observed.
Unfortunately the laser ablated channels absorb too much energy at the walls and are too rough to recollect the signal from the injecting waveguide making possible only the enlightenment of the fluid inside the channels but not the detection. This issue seems aligned to results discussed in literature for silica devices: to the author knowledge no examples of waveguides in the visible range, obtained by laser ablation, were reported to be able to collect the incoming signal with a configuration similar to that described here.
The case of the microfluidic channel obtained using the dicing saw was completely differ- ent. Even in the case of the open channel in air, the single mode of the output waveguide was recognizable at the near field image collected at the surface of the crystal. An example of the near-field image of a z-propagating waveguide crossing the microfluidic channel is shown in fig.6.1b. The collected intensity is the 38% of the intensity recorded before the