Device forming a manometer intended for measuring biphase fluid pressure, associated method of manufacture and fluidic network

TECHNICAL AREA

0001The invention relates to a pressure gauge device for measuring the pressure of a two-phase fluid in a fluid network.

0002It relates to an improvement in the sensitivity of a pressure gauge by allowing a noticeable reduction in dimensions and its integration into a fluidic network.

0003The applications particularly targeted by the invention are heat exchangers with two-phase fluids, the fuel cell or other system involving the use of a two-phase mixture operating around atmospheric pressure.

PRIOR ART

0004In systems, such as a two-phase fluid heat exchanger or the fuel cell, the liquid and vapor phases of the same fluid are simultaneously present in the fluid network supporting heat and mass exchanges.

0005The fluid pressure, the mass flow ratio between the vapor and liquid phases (titer) of the two-phase fluid as well as their respective distribution in the fluid network are parameters revealing, at all times, the operating efficiency of the system.

0006Thus, precise knowledge of these parameters, in real time and at critical points in the fluidic network, such as hot spots, drying points, bottlenecks, could help prevent malfunction / deterioration or correct / adjust the operating regime of the systems.

0007In other words, it would be desirable to be able to integrate precise measurement devices for these parameters, more particularly pressure, directly into the fluidic networks of systems mentioned above, without affecting their operation or their compactness.

0008It is known to measure the pressure of a liquid using a pressure gauge.

0009In particular, it is known to measure the pressure of a liquid by measuring the displacement of a meniscus of the liquid in a capillary tube. A device according to the preamble of claim 1 is disclosed in the article "<nplcit id="ncit0001" npl-type="s"><text>Microfluidic pressure sensing using trapped air compression ", Lab on a chip 7 (2007), p. 633-637 by Srirastava and Burns</text></nplcit>.

0010The patent <patcit id="pcit0001" dnum="US4404855A"><text>US 4, 404, 855</text></patcit> proposes the measurement of a pressure differential by measuring the displacement of a meniscus of liquid at the interface with an air bubble injected by a syringe in order to increase by a factor of 10⁴ measurement sensitivity. The dimensions of the measurement device thus proposed are macroscopic and do not allow its integration into a fluid network of a compact system. In addition, the minimum displacement of the meniscus which can be observed is of the order of 0.1 mm and requires the use of optical means external to the sensitive element of the pressure gauge itself.

0011The object of the invention is therefore to propose a solution making it possible to integrate a device for precise measurement of the pressure of a two-phase fluid in a fluid network of a system, such as a heat exchanger or a fuel cell without harm its functioning or its compactness.

STATEMENT OF THE INVENTION

0012To do this, the invention relates to a device forming a pressure gauge, intended for measuring the pressure of a two-phase fluid in a fluid network, comprising:<ul id="ul0001" list-style="dash" compact="compact"><li>a first channel inside which a two-phase fluid is able to circulate,</li><li>a second channel leading to the first channel, the second channel being blind, with each of its dimensions less than the capillary length of the liquid phase of the fluid, and with its longitudinal wall having a decreasing surface energy gradient from its entry towards the bottom, the surface energy gradient making it possible to increase the wetting angle of the meniscus of the liquid phase of the fluid in the blind channel from its entry towards the bottom.</li></ul>

0013The capillary length is a characteristic dimension of a liquid on which the capillary forces and the gravitational forces are of the same magnitude. For water, the capillary length 1c and the capillary volume Vc have the value respectively:<maths id="math0001" num=""><math display="block"><mi>lc</mi><mo>∼</mo><msqrt><mfrac><mi mathvariant="normal">σ</mi><mrow><mi mathvariant="normal">ρ</mi><mo>⋅</mo><mi>g</mi></mrow></mfrac></msqrt><mo>∼</mo><mn>2.7</mn><mspace width="1em" /><mi>mm</mi></math><img file="EP2564176B1_D0001.tif" /></maths>and <maths id="math0002" num=""><math display="block"><mi>vc</mi><mo>∼</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mn>.</mn><mi mathvariant="normal">π</mi><mn>.</mn><msup><mfenced><mfrac><msub><mi>l</mi><mi>vs</mi></msub><mn>2</mn></mfrac></mfenced><mn>3</mn></msup><mo>∼</mo><mn>10</mn><mspace width="1em" /><mi mathvariant="normal">μL</mi><mn>.</mn></math><img file="EP2564176B1_D0002.tif" /></maths>

0014Thus, in the context of the invention, for a given liquid, each of the dimensions constituted by the hydraulic diameter and the length of the blind channel is less than the capillary length of the liquid.

0015Thus, according to the invention, the production of a blind channel connected directly to a channel (main channel) of a fluidic network and the addition of a surface energy gradient along its longitudinal wall makes it possible to locate precisely. a meniscus of liquid at the interface with the vapor phase.

0016The displacement of this meniscus is dependent on the pressure of the fluid entering the blind channel.

0017The inventors have in fact started from the observation that in a liquid manometer the displacement of the meniscus at the interface with an air bubble under the effect of pressure was influenced by the wetting of the liquid in contact with the walls of the tube. capillary.

0018They therefore sought to study this influence more precisely from a blind channel in which a fluid in the liquid phase and in the vapor phase are simultaneously present. Air may also be present in the gas phase.

0019This configuration is represented in <figref idref="f0001">figure 1</figref>.

0020The equilibrium relation of force can thus be written in the following way: <maths id="math0003" num="(1)"><math display="block"><msub><mi>P</mi><mi mathvariant="italic">liquid</mi></msub><mo>-</mo><msub><mi>P</mi><mi mathvariant="italic">gas</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>⁢</mo><mfenced separators=""><mi>H</mi><mo>+</mo><mi>W</mi></mfenced></mrow><mi mathvariant="italic">HW</mi></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mo>⁢</mo><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>e</mi></msub></math><img file="EP2564176B1_D0003.tif" /></maths>in which :<ul id="ul0002" list-style="none" compact="compact"><li>P_liquid is the pressure of the liquid;</li><li>P_gas is the gas pressure;</li><li>W the width of the blind channel;</li><li>H is the height of the blind channel;</li><li>σ is the surface tension constant of the water (∼72 mJ / m²) ;</li><li>θ_e is the wetting angle of the water on the longitudinal wall 11 of the blind channel 1.</li></ul>

0021This equation is written in a different way: <maths id="math0004" num="(2)"><math display="block"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>P</mi><mo>=</mo><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ cos</mi><mo>⁢</mo><msub><mi mathvariant="normal">θ</mi><mi>e</mi></msub></math><img file="EP2564176B1_D0004.tif" /></maths>or <i>ΔP</i> = P_liquid - P_gas and <i>D_h</i> is the hydraulic diameter which is defined by: <maths id="math0005" num="(3)"><math display="block"><msub><mi>D</mi><mi>h</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>⁢</mo><mi mathvariant="italic">HW</mi></mrow><mfenced separators=""><mi>H</mi><mo>+</mo><mi>W</mi></mfenced></mfrac></math><img file="EP2564176B1_D0005.tif" /></maths>

0022The pressure of the gas trapped in the cavity 10 can be determined by the equation of the ideal gases: <maths id="math0006" num="(4)"><math display="block"><msub><mi>P</mi><mi mathvariant="italic">gas</mi></msub><mo>=</mo><mfrac><msub><mi>L</mi><mn>1</mn></msub><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>-</mo><mi>y</mi></mrow></mfrac><mo>⁢</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub></math><img file="EP2564176B1_D0006.tif" /></maths>where Patm is atmospheric pressure, L1 is the distance between a flat meniscus (cosθ_e = 1) and the bottom of the cavity 10; and y the position of the meniscus of liquid (water) at the interface with the gas.

0023We can consider that the wetting effect is significant if the two terms of equation (2) are of the same order of magnitude.

0024The <figref idref="f0001">figure 2</figref> shows the curve representative of the pressure difference as a function of the hydraulic diameter. The area above this curve is the area of ​​low sensitivity of the wetting, while the area below is of high sensitivity of the wetting. For example, at a hydraulic diameter of 2 µm, the effect of wetting is significant if the pressure difference is less than 1.1 bar.

0025The inventors then studied the influence of the contact angle (wetting angle) on the displacement y of the meniscus of liquid at the interface with the gas.

0026By considering that the contact angle is constant, that is to say by writing the relation <maths id="math0007" num="(5')"><math display="block"><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>e</mi></msub><mo>=</mo><mi>K</mi></math><img file="EP2564176B1_D0007.tif" /></maths>

0027We have the relation: <maths id="math0008" num="(5)"><math display="block"><mi>P</mi><mo>-</mo><mfrac><msub><mi>L</mi><mn>1</mn></msub><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>-</mo><mi>y</mi></mrow></mfrac><mo>⁢</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub><mo>=</mo><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><mi>K</mi></math><img file="EP2564176B1_D0008.tif" /></maths>From where : <maths id="math0009" num="(6)"><math display="block"><mi>y</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub><mo>⁢</mo><mfenced separators=""><mn>1</mn><mo>-</mo><mfrac><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub><mrow><mi>P</mi><mo>-</mo><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><mi>K</mi></mrow></mfrac></mfenced></math><img file="EP2564176B1_D0009.tif" /></maths>

0028We illustrated in <figref idref="f0002">Figures 3A to 3C</figref>, three different liquid contact angle configurations with values ​​of 20 °, 90 ° and 120 ° respectively and where the characteristic dimensions H, L1 and L2 are shown.

0029By considering a linear variation of the cosine of the contact angle along the longitudinal wall of the blind channel, we have <maths id="math0010" num="(7)"><math display="block"><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>e</mi></msub><mo>=</mo><msub><mi>K</mi><mn>1</mn></msub><mo>⁢</mo><mi>y</mi></math><img file="EP2564176B1_D0010.tif" /></maths>with <maths id="math0011" num="(8)"><math display="block"><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>max</mi></msub></mrow><msub><mi>L</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>min</mi></msub></mrow><msub><mi>L</mi><mn>2</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>max</mi></msub><mo>-</mo><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>min</mi></msub></mrow><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>+</mo><msub><mi>L</mi><mn>2</mn></msub></mrow></mfrac></math><img file="EP2564176B1_D0011.tif" /></maths>By replacing (2) and (3) in (1), we have the relation: <maths id="math0012" num="(9)"><math display="block"><mi>P</mi><mo>-</mo><mfrac><msub><mi>L</mi><mn>1</mn></msub><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>-</mo><mi>y</mi></mrow></mfrac><mo>⁢</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub><mo>=</mo><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><msub><mi>K</mi><mn>1</mn></msub><mo>⁢</mo><mi>y</mi></math><img file="EP2564176B1_D0012.tif" /></maths><maths id="math0013" num="(10)"><math display="block"><mi>P</mi><mo>⁢</mo><mfenced separators=""><msub><mi>L</mi><mn>1</mn></msub><mo>-</mo><mi>y</mi></mfenced><mo>-</mo><msub><mi>L</mi><mn>1</mn></msub><mo>⁢</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub><mo>=</mo><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mo>⁢</mo><msub><mi>K</mi><mn>1</mn></msub><mo>⁢</mo><mfenced separators=""><msub><mi>L</mi><mn>1</mn></msub><mo>⁢</mo><mi>y</mi><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup></mfenced></math><img file="EP2564176B1_D0013.tif" /></maths><maths id="math0014" num="(11)"><math display="block"><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mfenced separators=""><msub><mi>L</mi><mn>1</mn></msub><mo>+</mo><mfrac><mi>P</mi><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><msub><mi>K</mi><mn>1</mn></msub></mrow></mfrac></mfenced><mo>⁢</mo><mi>y</mi><mo>+</mo><mfrac><mrow><mfenced separators=""><mi>P</mi><mo>-</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub></mfenced><mo>⁢</mo><msub><mi>L</mi><mn>1</mn></msub></mrow><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><msub><mi>K</mi><mn>1</mn></msub></mrow></mfrac><mo>=</mo><mn>0</mn></math><img file="EP2564176B1_D0014.tif" /></maths><maths id="math0015" num="(12)"><math display="block"><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><msub><mi>G</mi><mn>1</mn></msub><mo>⁢</mo><mi>y</mi><mo>+</mo><msub><mi>G</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></math><img file="EP2564176B1_D0015.tif" /></maths>with <maths id="math0016" num="(13)"><math display="block"><msub><mi>G</mi><mn>1</mn></msub><mo>=</mo><mo>-</mo><mfenced separators=""><msub><mi>L</mi><mn>1</mn></msub><mo>+</mo><mfrac><mi>P</mi><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mo>⁢</mo><msub><mi>K</mi><mn>1</mn></msub></mrow></mfrac></mfenced></math><img file="EP2564176B1_D0016.tif" /></maths><maths id="math0017" num="(14)"><math display="block"><msub><mi>G</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mfenced separators=""><mi>P</mi><mo>-</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub></mfenced><mo>⁢</mo><msub><mi>L</mi><mn>1</mn></msub></mrow><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mspace width="1em" /><msub><mi>K</mi><mn>1</mn></msub></mrow></mfrac></math><img file="EP2564176B1_D0017.tif" /></maths><i>K</i>₁ &lt;0 So, we have the relation <maths id="math0018" num="(15)"><math display="block"><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>G</mi><mn>1</mn></msub><mo>+</mo><msqrt><msubsup><mi>G</mi><mn>1</mn><mn>2</mn></msubsup><mo>-</mo><mn>4</mn><mo>⁢</mo><msub><mi>G</mi><mn>2</mn></msub></msqrt></mrow><mn>2</mn></mfrac></math><img file="EP2564176B1_D0018.tif" /></maths>

0030By considering a second order variation of the cosine of the contact angle along the longitudinal wall of the blind channel, we have <maths id="math0019" num="(16)"><math display="block"><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>e</mi></msub><mo>=</mo><msub><mi>K</mi><mn>2</mn></msub><mo>⁢</mo><msup><mi>y</mi><mn>2</mn></msup></math><img file="EP2564176B1_D0019.tif" /></maths>with <maths id="math0020" num="(17)"><math display="block"><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mi>cos</mi><msub><mi mathvariant="normal">θ</mi><mi>max</mi></msub></mrow><msubsup><mi>L</mi><mn>1</mn><mn>2</mn></msubsup></mfrac></math><img file="EP2564176B1_D0020.tif" /></maths>

0031Thus, for the position y of the meniscus we obtain the relation: <maths id="math0021" num="(18)"><math display="block"><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><msub><mi>L</mi><mn>1</mn></msub><mo>⁢</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mfrac><mi>P</mi><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mo>⁢</mo><msub><mi>K</mi><mn>2</mn></msub></mrow></mfrac><mo>⁢</mo><mi>y</mi><mo>+</mo><mfrac><mrow><mfenced separators=""><mi>P</mi><mo>-</mo><msub><mi>P</mi><mi mathvariant="italic">ATM</mi></msub></mfenced><mo>⁢</mo><msub><mi>L</mi><mn>1</mn></msub></mrow><mrow><mfrac><mn>4</mn><msub><mi>D</mi><mi>h</mi></msub></mfrac><mo>⁢</mo><mi mathvariant="normal">σ</mi><mo>⁢</mo><msub><mi>K</mi><mn>2</mn></msub></mrow></mfrac><mo>=</mo><mn>0</mn></math><img file="EP2564176B1_D0021.tif" /></maths>

0032The inventors then carried out a comparative study by choosing the following numerical example:<ul id="ul0003" list-style="dash" compact="compact"><li>study pressure range of 1 to 2 bar to have a high sensitivity of wetting,</li><li>L1 = L2 = 100 µm,</li><li>channel depth and width H = W = 1µm,</li><li>angle θ_e varying from 0 ° from the entrance to the blind channel to 90 ° along the length L2,</li><li>angle θ_e varying from 90 ° to 150 ° over the length L1 at the bottom of the blind channel.</li></ul>

0033The <figref idref="f0002">figure 4A</figref> shows the curve representing the cosine of the angle θe as a function of the position y of the liquid meniscus.

0034The <figref idref="f0003">figure 4B</figref> shows the curve representing the position of the meniscus y as a function of the pressure P.

0035The <figref idref="f0003">figure 4C</figref> shows the curve representing the sensitivity of displacement of the meniscus as a function of pressure P.

0036Thus, on the basis of this study, the inventors have come to the conclusion that by varying the wetting angle (contact angle) one could very greatly increase the measurement sensitivity of a pressure gauge whose principle of measurement is the position of a liquid meniscus.

0037In other words, the inventors have concluded that the use of a surface energy gradient makes it possible to increase the measurement sensitivity of a pressure gauge relative to a hydrophobic surface with constant surface energy. In addition, they concluded that this increase in measurement sensitivity is even greater with an angle cosine gradient of 2^th order compared to a linear cosine gradient.

0038Thus, a device according to the invention can be, due to its high measurement sensitivity, microscopic dimensions for relatively minimal pressure variations, typically of the order of 1 bar. It can therefore be integrated into a fluidics network without affecting its compactness or its operation.

0039To achieve the surface energy gradient on at least one of the longitudinal walls, one can play on several parameters such as the variation of the chemical composition of the material on the surface of the longitudinal wall (s) or the variation in the structuring of the longitudinal wall (s). Said variation in structure of micro or nanometric nature is due to a variation either of the shape (depth, width) of the cavities, or of the density of said cavities or of the shape and density of the cavities forming surface structuring of said walls. We can thus mainly consider three solutions as follows:<ul id="ul0004" list-style="dash" compact="compact"><li>a uniform chemical composition and a surface structure with increasing depth gradient from the entrance to the blind channel towards the bottom,</li><li>a chemical gradient composition from the entrance to the blind channel towards the bottom and a uniform surface structure,</li><li>a chemical gradient composition and a depth gradient surface structure from the entrance of the blind channel to the uniform bottom.</li></ul>

0040For a device with microscopic dimensions to be integrated in a fuel cell or two-phase fluid heat exchanger, the transverse dimensions (or hydraulic diameter) of the blind channel can be between 50 nm and 5 µm, to measure a pressure variation greater than 0.5 bar (<figref idref="f0001">Figure 2</figref>).

0041The length of the blind channel can be between 50 nm and 500 μm.

0042The blind channel may have a substantially rectangular cross section, that is to say a rectangular or similar shape, with / without an edge (polygonal / ovoid).

0043Advantageously, provision is made to partially integrate into the blind channel the means for measuring the position of the meniscus of liquid in the blind channel to determine the pressure of the fluid.

0044In an advantageous embodiment, these measuring means comprise two electrodes arranged on two parts of longitudinal walls facing each other and each extending from the inlet at the bottom of the blind channel, the electrodes forming with a two-phase fluid present in the blind channel a capacitor with variable capacitance.

0045The pressure measurement is determined by the position of the liquid meniscus at equilibrium in the blind canal. The meniscus defines a variable liquid / vapor volume ratio in the canal according to its position. This volume ratio, or its variation, can be appreciated by an electrical measurement of the average capacity of the two-phase fluid in the channel.

0046The use of the two opposite electrodes makes it possible to measure the capacitance of the fluid.

0047In <figref idref="f0004">figure 5</figref>, an implantation of two electrodes 20, 21 is shown, arranged in parallel with each other at the top and bottom of the blind channel 1.

0048The distance between the two electrodes is close to the depth of the hydraulic diameter of the pressure gauge.

0049The length and width of the electrodes are those of the pressure gauge. The total capacitance is the sum of the capacitance of the vapor phase and the liquid phase of the two-phase fluid<maths id="math0022" num="(20)"><math display="block"><msub><mi>VS</mi><mi>t</mi></msub><mo>=</mo><msub><mi>VS</mi><mi>l</mi></msub><mo>+</mo><mi mathvariant="italic">CV</mi></math><img file="EP2564176B1_D0022.tif" /></maths>with <maths id="math0023" num="(21)"><math display="block"><msub><mi>VS</mi><mi>l</mi></msub><mo>=</mo><msub><mi mathvariant="normal">ε</mi><mn>0</mn></msub><mo>⁢</mo><msub><mi mathvariant="normal">ε</mi><mi>l</mi></msub><mo>⁢</mo><mfrac><mrow><mi>W</mi><mo>⁢</mo><mfenced separators=""><mmultiscripts><msub><mo>/</mo><mn>2</mn></msub><mprescripts /><none /><mi>L</mi></mmultiscripts><mo>+</mo><mi>y</mi></mfenced></mrow><mi>H</mi></mfrac></math><img file="EP2564176B1_D0023.tif" /></maths><maths id="math0024" num="(22)"><math display="block"><mi mathvariant="italic">CV</mi><mo>=</mo><msub><mi mathvariant="normal">ε</mi><mn>0</mn></msub><mo>⁢</mo><mi mathvariant="normal">ε</mi><mo>⁢</mo><mi>v</mi><mo>⁢</mo><mfrac><mrow><mi>W</mi><mo>⁢</mo><mfenced separators=""><mmultiscripts><msub><mo>/</mo><mn>2</mn></msub><mprescripts /><none /><mi>L</mi></mmultiscripts><mo>-</mo><mi>y</mi></mfenced></mrow><mi>H</mi></mfrac></math><img file="EP2564176B1_D0024.tif" /></maths> relationships in which ε₀ is the absolute permittivity of the vacuum, ε₀ =8,854×10^-12 F / m; ε<i>_l</i> and εν are respectively the relative permittivity in water and in air.

0050Thus, the total capacitance is given by the relation: <maths id="math0025" num="(19)"><math display="block"><msub><mi>VS</mi><mi>t</mi></msub><mo>=</mo><mfrac><mi>W</mi><mi>H</mi></mfrac><mo>⁢</mo><msub><mi mathvariant="normal">ε</mi><mn>0</mn></msub><mo>⁢</mo><mfenced separators=""><msub><mi mathvariant="normal">ε</mi><mi>l</mi></msub><mo>+</mo><msub><mi mathvariant="normal">ε</mi><mi>at</mi></msub></mfenced><mo>⁢</mo><mfrac><mi>L</mi><mn>2</mn></mfrac><mo>+</mo><mfrac><mi>W</mi><mi>H</mi></mfrac><mo>⁢</mo><msub><mi mathvariant="normal">ε</mi><mn>0</mn></msub><mo>⁢</mo><mfenced separators=""><msub><mi mathvariant="normal">ε</mi><mi>l</mi></msub><mo>-</mo><msub><mi mathvariant="normal">ε</mi><mi>at</mi></msub></mfenced><mo>⁢</mo><mi>y</mi></math><img file="EP2564176B1_D0025.tif" /></maths>

0051The total capacitance, as a function of the ratio between the transverse dimensions (W / H) of the blind channel, is shown on the <figref idref="f0006">Figures 12A and 12B</figref>. The<figref idref="f0007">Figures 12C and 12D</figref> show that the greater the measurement sensitivity, the greater this ratio. In the practical case, this ratio is greater than 1.

0052Obviously, those skilled in the art will take into account the evolution of the relative permittivity of the liquid phase, such as water as a function of temperature.

0053The invention also relates to a method for producing a pressure gauge device described above, according to which the following steps are carried out:<ol id="ol0001" compact="compact" ol-style=""><li>a / production of a first longitudinal part of a blind channel in a substrate plate comprising a first portion of a main channel inside which a two-phase fluid is able to circulate,</li><li>b / realization of a surface energy gradient on the first part of the blind channel,</li><li>c / production of a second longitudinal part of the blind channel in another substrate plate comprising a second portion of a main channel inside which a two-phase fluid is able to circulate, the first and second longitudinal parts of the blind channel being of identical length,</li><li>d / transfer of one substrate plate onto the other with alignment of the two longitudinal parts of the blind channel and of the two portions of the main channel,</li><li>e / closing the two substrate plates together.</li></ol>

0054To achieve a chemical gradient composition according to steps b / and d /, it can be done by a process called SAM process (self-assembly process of molecules, in English "SELF-ALIGNED-MOLECULES") and deposit any first a layer of hydrophobic molecules on the surface of the channel. The hydrophobic layer is then partially removed by a plasma or a laser ablation in order to locally discover a hydrophilic substrate. The reverse is also possible: a layer of hydrophilic molecule on a hydrophobic substrate.

0055Controlling the etching / ablation design thus makes it possible to produce a surface chemical gradient. The gradient can also be obtained by evaporation of a functionalized molecule.

0056According to an alternative embodiment, before step d /, a same surface energy gradient is produced on the second longitudinal part of the blind channel.

0057To integrate the electrodes as measurement means, before each of the steps b / and d /, a thin metal layer is advantageously deposited constituting an electrode in each longitudinal part of the blind channel. The electrode can be deposited in a thin layer by a PVD type vacuum deposition technique of a metal such as Ti, Cu, etc.

0058In the case where the plate is conductive, the element for electrical connection with the electrodes can be made on the rear face. Otherwise, a contact path can be made at the same time and according to the same process as the electrode.

0059Depending on the configurations of conductive plates or not, it is also possible to provide one or more electronically insulating layers (Ex. SiO2, TiO2, ...) in order to electrically isolate the capacitor constituted by the electrodes and the two-phase fluid.

0060The invention also relates to a fluid network integrating one or more devices forming pressure gauges described above.

0061The invention also relates to a fuel cell comprising such a fluid network, at least one of the manometers being adapted to measure the pressure of the water produced at the cathode or at the anode.

0062The invention finally relates to a two-phase fluid heat exchanger capable of passing from a liquid phase to a vapor phase comprising such a fluid network, at least one of the manometers being suitable for measuring the pressure of the fluid.

BRIEF DESCRIPTION OF THE DRAWINGS

0063Other advantages and characteristics of the invention will emerge more clearly on reading the detailed description given by way of illustration and without limitation, with reference to the following figures among which:<ul id="ul0005" list-style="dash" compact="compact"><li>the <figref idref="f0001">figure 1</figref> shows in longitudinal schematic sectional view a blind channel 1 of a device according to the invention,</li><li>the <figref idref="f0001">figure 2</figref> shows the curve representing the evolution of pressure variations as a function of the hydraulic diameter of a blind channel of a device according to the invention,</li></ul><ul id="ul0006" list-style="dash" compact="compact"><li>the <figref idref="f0002">Figures 3A to 3C</figref> show in longitudinal section view of a blind channel of a device according to the invention, three different contact angle configurations,</li><li>the <figref idref="f0002">figure 4A</figref> shows the curve representing the cosine of the angle θ_e depending on the position y of the liquid meniscus in the blind canal,</li><li>the <figref idref="f0003">figure 4B</figref> shows the curve representing the position of the meniscus y as a function of the pressure P,</li><li>the <figref idref="f0003">figure 4C</figref> shows the curve representative of the meniscus displacement sensitivity as a function of the pressure P,</li><li>the <figref idref="f0004">figure 5</figref> shows the implantation of two electrodes as means for measuring the position of the liquid meniscus in the blind channel of a device according to the invention,</li><li>the <figref idref="f0004">figure 6</figref> is a schematic representation of a device according to the invention,</li><li>the <figref idref="f0004 f0005">figures 7 to 11B</figref> show different stages of producing a blind channel of a device according to the invention,</li><li>the <figref idref="f0006 f0007">Figures 12A to 12D</figref> show the various curves representative of the evolution of the capacitance of a two-phase fluid as a function of the pressure and of the position of the liquid meniscus respectively in a blind channel of the device according to the invention and according to the value of the ratio between dimensions of the channel one-eyed.</li></ul>

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

0064The <figref idref="f0001 f0002 f0003 f0004">Figures 1 to 5</figref> have been commented on in the preamble, so they are not commented on here.

0065The device forming a pressure gauge according to the invention is intended for measuring the pressure of a two-phase fluid-F.

0066It comprises a blind channel 1 opening onto a main channel 3 of a fluid network, open or closed, through which a two-phase fluid F circulates. This blind channel 1 thus forms an integral part of the network.

0067Each of the dimensions (length, depth, width) of the blind channel 1 is less than the capillary length of the liquid phase of the fluid.

0068At least one of the longitudinal walls 11 of the blind channel 1 has a decreasing surface energy gradient from its entry towards the bottom.

0069Thus, according to the invention, the surface energy gradient makes it possible to increase the wetting angle of the meniscus of the liquid phase of the fluid in the blind channel 1 from its entry towards the bottom.

0070We have represented in <figref idref="f0004 f0005">figures 7 to 11B</figref> different stages of making a device.

0071A first longitudinal portion 110 of a blind channel is produced in a substrate plate 4 comprising a first portion 30 of a main channel inside which a two-phase fluid is able to circulate.

0072A metal layer is deposited to produce an electrode 20 with its contact point 200 on the first part 110. Then, a surface energy gradient 112 is produced on the surface of the electrode layer 20 (top view of the <figref idref="f0004">figure 7</figref> and sectional views of <figref idref="f0005">Figures 8A to 11B</figref>).

0073A second longitudinal part 111 of the blind channel is likewise produced in another substrate plate 5 comprising a second portion of a main channel inside which a two-phase fluid is able to circulate. A metallic layer is likewise deposited to produce an electrode 21 with its contact point, then an identical surface energy gradient is produced on the second part 111 of the blind channel 1.

0074The first 111 and the second 110 longitudinal parts of the blind channel are of identical length.

0075A transfer of a substrate plate 5 onto the other 4 is then carried out with alignment of the two longitudinal parts 110, 111 of the blind channel and of the two portions of the main channel (<figref idref="f0005">figure 8A, 9A, 10A, 11A</figref>) .

0076Finally, the step of closing the two substrate plates 4, 5 together is carried out (<figref idref="f0005">figure 8B, 9B, 10B, 11B</figref>).

0077Regarding the realization of the energy gradient, different approaches can be envisaged such as two identical gradients facing each other (<figref idref="f0005">Figures 8A and 8B</figref>).

0078Alternatively, it is conceivable that one of the walls does not have a gradient but either constant surface energy or is hydrophilic or hydrophobic (<figref idref="f0005">Figures 9A, 9B</figref> in which the first part 110 of the blind channel is devoid of energy gradient and <figref idref="f0005">Figures 10A and 10B</figref> in which the second part 111 which is carried over is devoid of energy gradient).

0079It is also conceivable that one longitudinal wall has a given surface energy gradient and the other facing longitudinal wall has a different surface energy gradient (<figref idref="f0005">Figures 11A and 11B</figref> in which the first part 110 of the channel has a surface energy gradient 112 while the second 'part 111 has a different surface energy gradient 112').

0080The curves in <figref idref="f0006">Figures 12A and 12B</figref> show the variation of the total capacitance with the pressure and the position of the water meniscus (liquid phase) at the interface with air and water vapor (gas phase) respectively in a blind channel according to the ratio between dimensions between transverse dimensions (W / H).

0081Although described in relation to a two-phase fluid whose liquid phase is water and the vapor phase is air and water vapor, the invention can be applied to many other two-phase fluids.

0082Likewise, other production methods can be envisaged for producing the blind channel of the device according to the invention. It is thus possible to provide mechanical machining of an aluminum or steel substrate, a lithography and etching of a silicon substrate or a replication by injection or embossing of a polymer substrate.