DROPLET AND/OR BUBBLE GENERATOR

Abstract

A device for generating bubbles or droplets may include a cavity comprising a first pressurized phase, at least one input capillary of a second phase, and an output capillary coaxially aligned with the at least one input capillary. The opening of the tip of the at least one input capillary has an internal diameter of less than half the internal diameter of the output capillary. The cross section of the cavity may be selected so that, in use, the average speed field in the cavity is quasi-static.

Claims

1. A device for generating bubbles or droplets, the device comprising: a cavity comprising a first pressurized phase; at least one input capillary of a second phase; and an output capillary coaxially aligned with the at least one input capillary; wherein an opening of a tip of the at least one input capillary has an internal diameter of less than half the internal diameter of the output capillary; and wherein all dimensions of the cavity are larger than 3 mm, and the output capillary has a hydraulic diameter smaller than 500 μm.

2. The device according to claim 1, further comprising a first phase input tubing connected to a first phase reservoir, the pressure in the reservoir being regulated by a first pressure regulator.

3. The device according to claim 2, wherein the first phase input tubing comprises means for measuring flow.

4. The device according to claim 1, further comprising a second phase input tubing connected to a second phase reservoir, the pressure in the reservoir being regulated by a second pressure regulator.

5. The device according to claim 4 wherein the second phase input tubing comprises means for measuring flow.

6. The device according to claim 1, further comprising means for observing the droplets produced, in use, by the device in the output capillary.

7. The device according to claim 6, further comprising a control unit connected to the means for observing the droplets, the control unit being configured to determine a diameter of the droplets, and controlling the pressure of the first and second phase to regulate the diameter of the droplets according to a predetermined value.

8. The device according to claim 1, wherein the cavity comprises thermoregulation means.

9. (canceled)

10. The device according to claim 1, wherein the input capillary comprises at least two coaxial capillaries for producing complex emulsion of the type ABC.

11. A method for generating bubbles or droplets, the method comprising: generating bubbles or droplets using a device comprising a cavity comprising a first pressurized phase, at least one input capillary of a second phase, and an output capillary coaxially aligned with the at least one input capillary, wherein an opening of a tip of the at least one input capillary has an internal diameter of less than half the internal diameter of the output capillary, and wherein all dimensions of the cavity are larger than 3 mm, and the output capillary has a hydraulic diameter smaller than 500 μm; observing the bubbles or droplets using a control unit connected to a means for observing the bubbles or droplets in the output capillary, determining a diameter of the bubbles or droplets using the control unit; and controlling the pressure of the first and second phase to regulate the diameter of the droplets according to a predetermined value, wherein the diameter of the droplets is at least two times bigger than the output diameter of the tip of the at least one input capillary.

12. The method of claim 11, wherein a flowrate Q.sub.d of the at least one input capillary, and a flowrate Q.sub.c of the first pressurized phase are configured so that the system operates in a dripping regime.

13. A method of manufacturing a device for generating bubbles or droplets, the method comprising: providing a device including a cavity having a first pressurized phase, at least one input capillary of a second phase, and an output capillary coaxially aligned with the at least one input capillary; and producing a nozzle of a tip of the at least one input capillary by micromachining or 3D microprinting; wherein an opening of a tip of the at least one input capillary has an internal diameter of less than half the internal diameter of the output capillary, and wherein all dimensions of the cavity are larger than 3 mm, and the output capillary has a hydraulic diameter smaller than 500 μm.

Description

SHORT DESCRIPTION OF THE DRAWINGS

[0038] FIG. 1 represents prior art setup.

[0039] FIG. 2 represents a microscope picture of an experiment according to the invention.

[0040] FIG. 3 represents a schematic view of the device of the invention.

[0041] FIG. 4 represents a typical nozzle geometry according to the invention.

[0042] FIG. 5 represents a picture of an example of device of the invention showing the metallic body of the system with the different input and output.

[0043] FIG. 6 shows an enlarged picture of the input and output capillaries through the window of the device of FIG. 5.

[0044] FIG. 7 represents the different parameters of the model developed in the invention.

[0045] FIG. 8 represents a diagram of experimental data (*) and lines corresponding to several α. γ=50 mNm−1, μc=5 mPas. Dispersed phase: water. Continuous phase:

[0046] mineral oil without surfactant.

[0047] FIG. 9 represents the droplet diameter 2R as a function of the continuous phase flow rate Q.sub.c. γ=50 mNm.sup.−1 and μ.sub.c=5 mPas. Dispersed phase: water. Continuous phase: mineral oil without surfactant.

[0048] FIG. 10 represents an electrical analogy for the microfluidic circuit of an example of the invention.

[0049] FIG. 11 represents a feedback loop for the continuous control and adjustment of the droplet diameter.

[0050] FIG. 12 represents a schematic view of the entire system for two phases emulsion.

[0051] FIG. 13 shows the droplet diameters as a function of phases flow rates.

LIST OF REFERENCE SYMBOLS

[0052] 1. output or collector capillary [0053] 2. Droplets of second (i.e. dispersed) phase [0054] 3. flow of first (i.e. continuous) continuous phase [0055] 4. nozzle at the tip of the input capillary [0056] 5. cavity wall [0057] 6. input capillary [0058] 7. cavity [0059] 9. Control unit [0060] 10. output capillary bulkhead [0061] 11. additional cavity access (generally closed bulkhead) [0062] 12. dispersed phase input capillary bulkhead [0063] 13. dispersed phase input flow resistance means [0064] 14. dispersed phase input flowmeter [0065] 15. dispersed phase input tubing [0066] 16. dispersed phase sealed container [0067] 17. pressure input tubing [0068] 18. pressure regulating unit for the dispersed phase [0069] 19. bulkhead for continuous phase input [0070] 20. continuous phase input tubing [0071] 21. continuous phase flow resistance means [0072] 22. continuous phase flowmeter [0073] 23. continuous phase container [0074] 24. Pressurizing tubing for the continuous phase [0075] 25. pressure regulating unit for the continuous phase [0076] 26. output tubing [0077] 27. emulsion [0078] 28. Window [0079] 29. Camera

DETAILED DESCRIPTION

[0080] The device of the present disclosure was initially developed for various microfluidic applications requiring high-throughput emulsification for which existing systems fail to fully comply. It allows the long term production of droplets in a very robust and reproducible way because of its technical specifications on the one hand, and on the other hand because of the physical mechanisms on which it relies. The device of the invention is therefore a very good starting point for the development of an integrated droplet production system for the chemical and pharmaceutical industry where, existing solutions failed to reach the production stage.

[0081] As compared to confined configurations (FIGS. 1a-d), the unconfined one illustrated in FIG. 1e allows for higher throughput as the pressure drop is only localized in the extraction tube. However, it exclusively works in the jetting regime, which is not in favor of monodispersity.

[0082] The general configuration of the invention is illustrated in FIGS. 2 and 3. The system of the invention is able to generate mono-dispersed droplets or bubbles at high-throughput. In this setup, the system is optimized to operate in dripping (or squeezing) mode. Interestingly, in this dripping regime, the size of the injection nozzle 4 is about twice smaller than the desired size of the droplets/bubbles 2; a requirement that is not necessary in the jetting regime explored by the group of Gordillo. For example, to produce 100 μm droplets, a 40 μm inner-diameter nozzle 4 was designed and placed in front of the extraction tube 1, as illustrated in FIG. 2.

[0083] According to the standards of the National Institute of Standards and Technology (NIST), a particle (in this case droplet or bubble) distribution may be considered monodisperse if at least 90% of the distribution lies within 5% of the median size (Particle Size Characterization, Special Publication 960-961, January 2001). This is equivalent, for a normal distribution, to a standard deviation to average diameter ratio of less than 2%.

[0084] In this configuration, the system operates in the so-called unconfined squeezed flow, the cavity 7 containing the continuous phase having a much larger cross section than the output capillary 1, so that the speed field in the cavity is close to zero at large distance of the collecting end of the output capillary 1. The speed difference of the continuous phase between the cavity and the output capillary inducing a large pressure drop according to Bernouilli's equation, as would produce a Venturi tube in the case of bubble generation without surfactant, or according to Stokes equation in the case of a droplet generation dominated by shear forces at the interface.

Example

3D-Printed Nozzle

[0085] The nozzle 4 showed in FIG. 2 has been printed using a 3D printer. The UV-polymerized material is a photosensitive resin similar to SU-8 widely used in electronics, assuring a very good resistance to most oils and solvents. The inside geometry of the nozzle has been designed so as to assure an easy introduction and then gluing of a capillary tubing, with neither leakage nor clogging during operation. For that purpose, a stepped geometry is used. The inside cross section decreases step by step from the nozzle entrance to the basis of the conical part. The capillary can thereby be easily introduced to the end of the cylindrical portion of the nozzle with a minimal gap between both parts at the cone basis. This ensures that no glue will reach the inside of the capillary during the gluing process on one hand, and on the other hand that the capillary will be perfectly aligned with the nozzle axis. Typical size and geometry of a 3D-printed single emulsion nozzle are shown in FIG. 4.

[0086] At the nozzle tip, two conditions must be fulfilled to promote the formation of small droplets. First, the edge width has to be as small as possible so that the exiting liquid wets the minimum resin area, and secondly, the angle of the cone tip has to be steep enough so that the liquid wetting the edge will not spread on the cone lateral surface (FIG. 5b).

Capillary Tubing

[0087] As mentioned before, two capillaries 1,6 are part of the device of the invention, one supporting a nozzle 4 at its end and carrying the dispersed phase and another one 1 for the droplet collection, as showed in FIG. 3. They are preferably made of fused silica coated with a 20 μm polyimide transparent film what makes the droplet visible for eye or camera observation.

[0088] Other materials, such as stainless steel or tungsten carbide, could possibly be used for the input and output capillaries 1,6 when transparency is not required.

Stainless Steel Body

[0089] FIG. 5 shows a general view of the mechanical parts of the device of the example.

[0090] A stainless steel reservoir filled with the continuous phase and containing the two aligned capillaries allows for the non-confined dripping configuration of the invention. It comprises a main body on which two windows 28 and two connection system 10,12 for the capillaries introduction are assembled. On the other lateral sides, two connections 11,19 are intended for the connection of the continuous phase supply and purge.

[0091] Windows 28 are preferably made of 1 mm width glass disc pressed onto an O-ring seal inserted into a groove. Quartz windows are also available for applications where UV or IR light transmission is needed. This system allows for a very easy access to the cavity 7 for cleaning purpose. The thickness of the windows 28 can be adapted to particular size or operating pressure.

Predictive Model for the Droplet Size

[0092] This model, aims to establish a relationship between the flow rates in the system and the droplet diameter. It is used as a predictive tool to determine the initial working parameters for the generation of calibrated droplets (or bubbles) in the device. This model is advantageously used to regulate the drop size, by using a closed loop regulation system wherein a controller unit 9 connected to a camera 29 determines the drop diameter and modifies the pressures applied to the phases by pressure controllers 18,25 connected to the controller unit 9.

[0093] The model is based on the assumption that the droplet will detach from the nozzle tip when the viscous force F.sub.μ applied on the droplet becomes greater than the surface tension force F.sub.γ keeping the droplet attached to the nozzle tip. This viscous force is approximated by using a modified Stokes law for a spherical particle in a flowing solution as

F.sub.μ=6ρμ.sub.c(R−a)(v.sub.c−v.sub.d)  (1)

where R is the droplet radius, a is the radius at the nozzle tip, μ.sub.c is the viscosity of the continuous phase, v.sub.c is the speed of the continuous phase and v.sub.d is the speed of the dispersed phase (see FIG. 7). The R−a term reflects the fact that the cross section of the nozzle tip works to shield part of the growing droplet from the viscous force. The velocities v.sub.c and v.sub.d are estimated from the flow rates and their associated cross-sectional areas in the system. Notice that the cross-sectional areas for both phases are variable because of the growing droplet radius R. Taking this into account, velocities are expressed as

[00002]$v_C=\frac{Q_c}{\pi \left(R_2^2-R^2\right)}.Math..Math.\mathrm{and}.Math..Math.v_d=\frac{Q_d}{\pi .Math.R^2}$

where R.sub.2 is the internal radius at the tip of the output capillary.

[0094] In the case of dominant inertial forces

[00003]$\left(\frac{{\mu }_c}{{\mu }_d}1\right),$

the dominant term acting against the surface tension is the Bernouilli force F.sub.ρ due to the pressure difference between the cavity (section Σ.sub.1) and the output capillary (section Σ.sub.2).

[00004]$\begin{array}{cc}{F}_{\rho }=\frac{{\rho }_c}{2}.Math.\left(v_{c,{\Sigma }_2}^2-v_{c,{\Sigma }_1}^2\right).Math.\pi \left(R_2^2-R^2\right)& (1’)\end{array}$

where ρ.sub.c is the density of the continuous phase and Σ.sub.1 and Σ.sub.2 are the cross sections far in the cavity and at the entrance of the output capillary, respectively. The droplet generation better works for Σ.sub.1>>Σ.sub.2 such as the velocity in the cavity v.sub.c,Σ.sub.1 is negligible as compared to the velocity in the output capillary v.sub.c,Σ.sub.2. The R.sub.2−R term reflects the fact that the cross section of the droplet works to shield part of the cross section of the output capillary.

[0095] The surface tension force is

F.sub.γ=2πaγ  (2)

where γ is the interfacial tension between continuous and dispersed phases that is assumed to apply in the longitudinal direction provided the elongated shape of the attached droplet.

[0096] Because these expressions for the two forces result from approximations, a corrective factor α is added in the equation for the force balance such as

F.sub.μ+F.sub.ρ=F.sub.γα  (3)

[0097] In the case of dominant viscous forces

[00005]$\left(\frac{{\mu }_c}{{\mu }_d}1\right),$

F.sub.ρ can be neglected, and by injecting the expressions 1 and 2 for the forces, equation 3 becomes

[00006]$\begin{array}{cc}3.Math.\mathrm{Ca}.Math.\frac{R-a}{\alpha .Math.a}.Math.\left(\frac{R_2^2}{R_2^2-R^2}-\frac{Q_d.Math.R_2^2}{Q_c.Math.R^2}\right)=1& \left(4\right)\end{array}$

Where

[0098] [00007]$C.Math.a=\frac{Q_c.Math.{\mu }_c}{\pi .Math.R_2^2.Math.\gamma }$

is a capillary number representing the relative effect of viscous force versus surface tension. By assuming Q.sub.d<<Q.sub.c, the latest equation simplifies as

[00008]$\begin{array}{cc}3.Math.\frac{C.Math.a}{\alpha }.Math.\left(\frac{R}{a}-1\right).Math.\left(\frac{1}{1-{\left(\frac{R}{R_2}\right)}^2}\right)=1& \left(5\right)\end{array}$

[0099] The droplet diameter at rupture becomes the solution of an algebraic second order equation whose the only physically meaningful solution is

[00009]$\begin{array}{cc}R=-\frac{3.Math.R_2^2.Math.C.Math.a}{2.Math.a}+R_2.Math.\sqrt{1+\frac{3.Math.C.Math.a}{\alpha }+\frac{9.Math.R_2^2.Math.C.Math.a^2}{2.Math.a^2.Math.{\alpha }^2}}& \left(6\right)\end{array}$

To determine α, equation 5 is written as

[00010]$\begin{array}{cc}\alpha =\frac{3}{a}.Math.\frac{R-a}{1-{\left(\frac{R}{R_2}\right)}^2}.Math.C.Math.a=A.Math.C.Math.a& \left(7\right)\end{array}$

Where the term A contains geometrical parameters. log(A) is then plotted versus log(Ca) using data coming from experiments. As shown on FIG. 8, experimental data are located between both lines corresponding to α=0.08 and α=0.2. Assuming a mean value for the critical capillary number, α=0.12, the droplet diameter 2R is then plotted in function of the continuous phase flow rate Q.sub.c (FIG. 9).

[0100] In the case of dominant inertial forces

[00011]$\left(\frac{{\mu }_c}{{\mu }_d}1\right),$

F.sub.μ can be neglected, and by injecting the expression (1′) and 2 for the forces, and using v.sub.c,Σ.sub.2=v.sub.c, equation 3 gives

[00012]$\frac{R}{R_2}=\sqrt{1-\frac{C.Math.a}{4.Math.\alpha }.Math.\mathrm{Re}.Math.\frac{R_2}{a}}$

with

[00013]$\mathrm{Re}=\frac{{\rho }_c.Math.Q_c}{\pi .Math.R_2.Math.{\mu }_C}$

is the Reynolds number based on the continuous phase.

Predictive Model for the Pressure

[0101] In this section, an electrical circuit analogy (or lumped model) is proposed to predict the applied pressure on the continuous phase so as to obtain the desired continuous phase flow rate. The model can also provide flow resistance values to be used in the circuit to avoid that the pressure modified on one channel will impact the flow rate on the other. In other words, using the right flow resistances results in independent flow rates in the two channels.

[0102] The electrical circuit analogy is based on the scheme of FIG. 10. P.sub.c and P.sub.d are the pressures applied on the continuous and dispersed phase, respectively, R.sub.c and R.sub.d are the flow resistances of the channels for the continuous and dispersed phase, respectively, upstream of the nozzle. Q is the sum of both flow rates and R.sub.s is the flow resistance of the channel downstream of the nozzle. Following the electrical analogy, the relation between P, Q and R is similar to the Ohm's law, such as

P=QR  (8)

[0103] This “Kirchoff law for fluidic circuit” is then applied to the entire circuit and Q is expressed as

[00014]$\begin{array}{cc}Q=\frac{P_c.Math.R_d+P_d.Math.R_c}{R_s.Math.R_d+R_s.Math.R_c+R_c.Math.R_d}& \left(9\right)\end{array}$

[0104] The resistance values are evaluated using the Hagen-Poiseuille equation

[00015]$\begin{array}{cc}\Delta .Math.P_i=\frac{1.Math.2.Math.8.Math.{\mu }_i.Math.L_i.Math.Q_i}{\pi .Math.d_i^4}=Q_i.Math.R_i,i=\left(d,c,s\right)& \left(10\right)\end{array}$

where L.sub.i is the tubing length, d.sub.i the tubing diameter, ΔP.sub.i the pressure drop across L.sub.i and is then defined as (ΔP at connectors is neglected in this model)

[00016]$\begin{array}{cc}{R}_i=\frac{1.Math.2.Math.8.Math.{\mu }_i.Math.L_i}{\pi .Math.d_i^4}.& \left(11\right)\end{array}$

[0105] The evaluation of R.sub.s in (9) assumes that the viscosity of the output stream is equal to the viscosity of the continuous phase. This is generally a good approximation if the continuous phase flow rate is higher than the droplet flow rate.

[0106] In conjunction with the results obtained to predict the size of the droplets in function of the continuous flow rate, the model presented allows the user of the device of the invention to use operational starting pressure values to generate the desired droplet size and flow-rate. The fine tuning of the pressure can then be continuously operated during the droplet generation process using a feed-back loop, as shown in FIG. 11. The measured diameter of the droplets is compared with the target value to, first, find the best a coefficient corresponding to the experimental working setup, and then to continuously adapt the pressure to meet the size requirement.

Experimental Results

[0107] The setup for the droplet generation of the example is shown in FIG. 12. A high-speed camera 29 and microscope system is typically used to view the droplet formation. Videos are recorded and later analyzed to estimate the droplet size and droplet production rates. The flow of each fluid is driven by pressure controllers 18,25 that use compressed air injected through tubing 17,24 to drive each fluid. In conjunction with flow-rate meters 14,22, the pressure controllers 18,25 allows fine tuning of both flow rates with a very low response time and a pulseless liquid flow, which is advantageous for achieving monodispersity. In each channel, the flow rate is proportional to the pressure and inversely proportional to the flow resistance. These resistances are designed using the predictive model developed before and are added in the setup to equalize the pressures at the nozzle tip, avoiding backflow and ensuring that there will be no interference between both channels. In others words, even if the flow rates of both phases are dramatically different, typically on a ratio 10:1, operating pressures must be similar. That requirement is met through the choice of resistances. Finally, resistances also lend a wider operating range so that the flow ratios can be adjusted with greater control.

[0108] In the tested design, the nozzle 4 output diameter was 40 μm, the distance d between the nozzle 4 and the collector 1 capillary: 40 μm, and, finally, the inside diameter of the collector capillary was 180 μm.

[0109] To ensure that a minimum of dust is introduced into the system, the fluid pumped to the system have previously been filtered through a 0.2 μm pore size filter and a ferrule with integrated filter is used as an in-line filter in the tubing leading to the nozzle 4.

[0110] Droplets of water and ethanol in aqueous solution have been generated in silicon or mineral oil. For example, water droplets of 125 μm diameter have been produced at a 1707 Hz production rate, at a flow rate of 100 μl/min. This value could certainly be increased by using lower flow resistances or a more powerful pump.

[0111] One of these tests is reported in FIG. 13, where it can be seen that at high continuous phase flow rate, the droplet size becomes independent of the dispersed flow rates.

[0112] It is worth to note that the maximum of 50 μl/min for the droplet flow rate reached in this experiment is higher than the transition dripping-jetting obtained using a glass chip under the same conditions. Furthermore, no wetting issues have been reported in long term operation, unlike glass chip with hydrophobic coating with which severe wetting issue is generally observed when used for the long term production of droplets of coating aggressive chemicals.