Antoine Ducoin
email: antoine.ducoin@laposte.net

Jacques Andre Astolfi

Jean-Francois Sigrist

Jacques André Astolfi

Jean-François Sigrist

An experimental analysis

Keywords:

Introduction

The knowledge of the hydroelastic behavior of flexible lifting bodies is fundamental for the design and sizing of recent naval systems such as the new concepts of propulsion systems based on composite marine propellers [START_REF] Young | Fluid-structure interaction analysis of flexible composite marine propellers[END_REF], active control surfaces like rudders [START_REF] Turnock | Directly coupled fluid structural model of a ship rudder behind a propeller[END_REF] or innovative tidal turbine blades [START_REF] Nicholls-Lee | Development of high performance composite bend-twist coupled blades for a horizontal axis tidal turbine[END_REF][START_REF] Young | Hydroelastic response of wind or tidal turbines[END_REF]. For a flexible body working in a steady flow, an equilibrium state is obtained between the deformed shape and the steady hydrodynamic loading [START_REF] Ducoin | Numerical and experimental investigation of hydrodynamic characteristics of deformable hydrofoils[END_REF]. However under specific or extreme operating conditions, a sudden change of incidence or inflow velocity can lead to transient regimes that may induce strong unsteady hydrodynamic loadings. This is often coupled with boundary layer unsteady characteristics like partial or large boundary layer detachment, sudden laminar to turbulent transition or unsteady cavitation. In that case, the high amplitude fluctuations of the hydrodynamic loading interacting with a flexible body can induce strong fluid structure interactions and possible occurrence of hydro-elastic instabilities. Several experiments have been performed to study the flow over pitching foils. The major part of the studies are related to oscillating rigid airfoils.

Particularly, the knowledge of the wall pressure field distribution and time evolution on the body brought new elements in the understanding of dynamic loading induced by pitching motions [START_REF] Jumper | Lift-curve characteristics for an airfoil pitching at constant rate[END_REF][START_REF] Hamdani | Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number[END_REF]. Jumper et al. [START_REF] Jumper | Lift-curve characteristics for an airfoil pitching at constant rate[END_REF] performed wall pressure measurements on a rigid hydrofoil for different pitching velocities α and upstream velocities V ∞ . They showed that the unsteady nature of the hydrodynamic loading is related to the similarity parameter α * = αc/V ∞ , where c is the chord length. This parameter gives the foil rotation, during the time of a particle that moves from the leading edge to the trailing edge. Moreover, the stall was clearly delayed when α increases.

It was shown that the unsteady nature of the flow influences the hydrodynamic loading [START_REF] Triantafyllou | Optimal thrust development in oscillating foils with application to fish propulsion[END_REF]. Lee and Gerontakos [START_REF] Lee | Investigation of flow over an oscillating airfoil[END_REF] focused on the effect of the laminar to turbulent transition downstream a Laminar Separation Bubble (LSB) for an oscillating airfoil at various pitching velocities at Re = 1.35 × 10 5 . For small values of the pitching velocity, they showed that the LSB induced variations in lift, drag and moment coefficients. As well, boundary layer transition was delayed and promoted when the pitching velocity increased. This conducted to the modification of lift coefficients and lift-curve slope. However, it was shown that the Laminar Separation Bubble characteristics are insensitive to pitching velocity. Similar conclusions are drawn for a transient pitching hydrofoil [START_REF] Ducoin | Computational and experimental investigation of flow over a transientpitching hydrofoil[END_REF].

On the other hand, cavitation is of primary importance for marine structure design [START_REF] Kuiper | Cavitation research and ship propeller design[END_REF]. Depending on the flow conditions, different kind of cavitation can occur [START_REF] Astolfi | An experimental investigation of cavitation inception and development on a twodimensional hydrofoil[END_REF]. It is known that under Poisson ratio unfavorable conditions, the vaporized area becomes unstable, with cavity break-off and periodical shedding of large bubble clusters. This configuration, usually called ''cloud cavitation'', generates pressure fluctuations downstream of the cavity [START_REF] Leroux | A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil[END_REF] and could have strong impacts when developing on flexible structures.

Cavitation have also been considered for pitching hydrofoils. In [START_REF] Stern | Comparison of computational and experimental unsteady cavitation on a pitching foil[END_REF], numerical results of a pitching Joukowski hydrofoil with sheet-cloud are compared to experiments. The numerical method is based on potential flow. For low reduced frequency k, large cavity oscillations are observed whereas higher reduced frequency leads to a progressive cavity response and a rapid collapse. In that case, k appears to be close to the cavity natural shedding frequency ω n . In [START_REF] Hart | Observations of cavitation on a threedimensional oscillating hydrofoil[END_REF], the effect of pitching velocity on cavitation was observed experimentally on a NACA64 hydrofoil. A phase lag was found between the extending of the cavity and the oscillation that increases with k. A strong interaction between k and ω n was observed and the cavitation behavior becomes random when k ≈ ω n . For the highest k, a loud pounding sound resulting from the collapse of the cavity and a strong hysteresis between cavitation inception and desinence was observed.

Recent efforts were made in order to approach through simulations both the fluid and the structure dynamics. This comes from the recent development of numerical methods and models which allow us to compute complex flows together with coupled simulation with reasonable CPU time [START_REF] Young | Time-dependent hydroelastic analysis of cavitating propulsors[END_REF]. For aerodynamic applications, studies have highlighted that structural deformation under static or dynamic loads may be of primary importance in the evaluation of aerodynamic performances [START_REF] Engel | Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems[END_REF]. Bhardwaj [START_REF] Bhardwaj | A CFD/CSD interaction methodology for aircraft wings[END_REF] developed a CSD/CFD coupling procedure where the importance of the computation initialization from a CFD steady-state solution was emphasized. Send [START_REF] Send | Coupling of fluid and structure for transport aircraft wings[END_REF] and Patil and Hodges [START_REF] Patil | On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ratio wings[END_REF] investigated the correlation between the wing deformation (mainly twist) and variation of the aerodynamic coefficients such as lift and wall pressure coefficients. On the other hand, few works show concern for hydro-elasticity applications. In [START_REF] Kuo | Propeller blade dynamic stress[END_REF] developed a coupled procedure solved in the frequency domain for blade stress analysis on propellers. Non linear hydroelastic behavior of propellers has also been investigated by Lin and Lin [START_REF] Lin | Nonlinear hydroelastic behavior of propellers using a finiteelement method and lifting surface theory[END_REF] using lifting surface theory. Amromin and Kovinskaya [START_REF] Amromin | Vibration of cavitating elastic wing in a periodically perturbed flow: excitation of subharmonics[END_REF] analyzed theoretically the vibration of an elastic wing with an attached cavity in a periodically perturbed flow. Wing vibration was described by means of a simple beam equation. As a result, two frequency bands were found. A high-frequency band associated mainly with the elastic resonant natural frequencies of the foil and a low-frequency band associated with cavity-volume oscillations. Ausoni et al. [START_REF] Ausoni | Cavitation influence on von Karman vortex shedding and induced hydrofoil vibrations[END_REF] have studied experimentally the interaction between cavitating Von Karman vortices in the wake of a NACA009 hydrofoil and its vibrations. In lock in conditions (resonance), the cavitation inception is enhanced and in fully developed cavitating condition, the vibrations of the first tortionnal mode increase the strouhal cavity shedding frequency. Reese [START_REF] Reese | Vibration and damping of hydrofoils in uniform flow[END_REF] have examined vibrations and damping of a NACA66 hydrofoil in uniform flow. He showed that the structural damping decreases when the vortex frequency gets close to a natural frequency, whereas the added stiffness and hydrodynamic damping becomes significant at high speeds. Recently, Young [START_REF] Young | Time-dependent hydroelastic analysis of cavitating propulsors[END_REF] presented a new approach applied to a cavitating propeller which takes into account the modification of fluid pressure field induced by the blade displacement. In [START_REF] Young | Numerical and experimental investigations of composite marine propellers[END_REF][START_REF] Young | Fluid-structure interaction analysis of flexible composite marine propellers[END_REF][START_REF] Motley | Utilizing fluid-structure interactions to improve energy efficiency of composite marine propellers in spatially varying wake[END_REF], the fluid structure interaction is used to increase the efficiency of marine propellers. Composite material is used to control the deformation of the blade in order to reduce the cavitation and to increase the efficiency. This has been recently applied for the design and optimization of adaptive marine propellers [START_REF] Young | Reliability-based design and optimization of adaptive marine structures[END_REF] and tidal turbines blades [START_REF] Nicholls-Lee | Development of high performance composite bend-twist coupled blades for a horizontal axis tidal turbine[END_REF].

The numerical works are very interesting and bring new results, however it appears that there are very few experimental data in fluid structure interaction applied to lifting bodies in hydrodynamic applications. The aim of the paper is to get a better understanding of fluid structure interaction in hydrodynamic applications and to provide experimental data for the development of high fidelity fluid structure interaction models. A previous study concerning the investigation of the flow over a flexible hydrofoil in uniform flow was performed (see [START_REF] Ducoin | Numerical and experimental investigation of hydrodynamic characteristics of deformable hydrofoils[END_REF]). The present paper gives extended experimental results by including stationnary hydrofoil and transient pitching motions. The system was modified in order to obtain transient pitching motion at low, medium and high pitching velocities and to measure the structural dynamics. Cavitation-Structure Interaction is also shown, for both stationary and pitching hydrofoils. The vibrations and displacements of the tip are measured together with the cavitation observed at the suction side of the hydrofoil. The comparison with subcavitating flow highlights the possible effects of cavitation on hydroelastic response.

Experimental setup

Measurements were carried out at the cavitation tunnel of the Research Institute of the French Naval Academy. The test section is 0.192 m 2 and 1 m long. The velocity ranges between 3 and 15 m/s and the pressure in the test section ranges between 30 mbar and 3 bar. A flexible hydrofoil is mounted horizontally at mid height of the test section, see Fig. 1. It is clamped at the root section and free at the tip.

The hydrofoil has an NACA66312 section. It has a camber type line a = 0.8, a camber ratio of 2% and a relative thickness of 12% [START_REF] Leroux | A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil[END_REF]. The chord is c = 0.148 m and the span is b = 0.191 m. It corresponds to an aspect ratio b/c = 1.3 and a confinement parameter h/c = 1.28. These relatively small ratios can induce 3D effects, induced by the development of boundary layers of the vertical walls that interact with the foil surface in the vicinity of the tip and the root of the hydrofoil. It was observed that the wall boundary layer thickness was of about 0.009 m for a free stream velocity of 5 m/s corresponding to about 10% of the span. However flow visualizations based on cavitation inception and cavity development showed that the flow can be considered reasonably bidimensional on a major part of the foil span as shown in Fig. 2 (see also [START_REF] Leroux | An experimental study of unsteady partial cavitation[END_REF]). The gap between the hydrofoil tip and the vertical wall is about 1 mm, which is lower that the wall boundary layer thickness. As shown later in the paper, this can however induce development of tip vortex and tip leakage cavitation, which is seen to have negligible effects on the hydroelastic response.

The flexible hydrofoil has a Polyacetate (POM) material (E = 3000 MPa, ρ S = 1480 kg/m -3 , ν S = 0.35). The system is composed of the hydrofoil and a disc fabricated in one-piece to ensure a clamped condition at the root section. The disc is fixed with eight screws to a steel disc. The system is finally fixed to a cylinder that is linked to the motor housing to ensure the foil rotation. A video camera BASLER at a sampling frequency of 100 images per second is used in order to get a side view of the hydrofoil and to measure the instantaneous displacement of the tip section (see video camera 1 in Fig. 1).

The total displacement ⃗ δ M t (t) of a point M(x, y) about the origin O(x 0 , y 0 ) (center of rotation) of the foil tip section can be split in two parts:

⃗ δ M t (t) = ⃗ δ M o (t) + ⃗ δ M (t) (1)
where ⃗ δ M o (t) is the rigid solid displacement of an arbitrary point M at the hydrofoil tip due to the rigid foil rotation and ⃗ δ M (t) is the elastic displacement of the same arbitrary point due to the foil deformations induced by the hydrodynamic loading. From Eq. ( 1) we have:

⃗ δ M (t) = ⃗ δ M t (t) -⃗ δ M o (t).
(

) 2
Without flow, no foil elastic deformation occurs; the displacement is only due to solid rotation. Then, ⃗ δ M o (t) and ⃗ δ M t (t) can be easily determined experimentally for a given pitching velocity. The pictures with and without flow velocity are processed to calculate the displacements, as shown in Fig. 3. Moreover, in the plane of the foil tip section, the elastic displacement has two components:

⃗ δ M (t) = δ M x (t) ⃗ i + δ M y (t) ⃗ j. ( 3
)
It was observed that the elastic displacement is mainly due to the vertical displacement (i.e. bending), then we have:

⃗ δ M (t) ≈ δ M y (t) ⃗ j. ( 4
)
For simplicity, the vertical elastic displacement will be noted δ y (t).

Reading uncertainty is about ±1 pixel. Since 1 pixel equals 0.07 mm, the uncertainty on measured displacements is ∆(y) = ±0.07 mm. The corresponding non dimensional uncertainty is ∆(y)/b = ±0.00037, where b is the span of the hydrofoil equal to 191 mm. The analysis of structural vibrations is carried out on the hydrofoil pressure side using a Laser Doppler Vibrometer Polytech PSV-400 (Fig. 1). It is a class II He-Ne laser of wavelength λ = 632.8 nm. The vibrometer sensitivity ranges between 10 mm/s/V and 1 m/s/V. The system performs scanning measurements over a grid pre-defined on the structure surface (Fig. 4) by means of an internal camera. A mean vibration spectrum was obtained from an average of 32 spectrums obtained on one point of the grid. Then the spectrum could be averaged over the surface to obtain the average spatial vibration spectrum of the surface.

Finally, the cavitation is observed at the suction side with a high speed camera PHOTRON on the top of the test section (Fig. 1) at a sampling frequency of 2000 images per second. The cavitation condition is based on the cavitation number defined as σ =

(P 0 -P V )/(1/2ρ F V 2 ∞
) where P 0 is the pressure in the test section (measured at about two chords upstream of the hydrofoil) and P V is the vapor pressure at ambient temperature. The cavitation was controlled by decreasing P 0 progressively in the tunnel test section. The transient pitching motion was defined as a single upward-downward motion from α = 0°to the maximum incidence α max . The rotation axis is located at x/c = 0.5 from the leading edge. The mean angular velocity is α = 2α max /t f , where t f is the fi- the present measurements, which is just beyond the angle of static stall close to 13°. The major uncertainty on the foil angular position comes from the initial zero angle of incidence, corresponding to the chord line parallel to the upstream velocity V ∞ . It was first adjusted by aligning the foil chord line to the horizontal top wall of the test section using a micrometer. Then the chord line was compared to the horizontal free surface line when the tunnel test section was half fulfilled in the vicinity of the foil pressure side. The comparison was done by image processing of lateral pictures. If necessary, the zero angle of incidence was adjusted iteratively in such a way that the horizontal free surface line was parallel to the chord line on the picture. By several trials, with this method, the uncertainty on the angle of incidence was estimated to be α = ±0.15°.

The nominal free stream velocity V ∞ is 5 m/s, corresponding to a Reynolds number based on the foil chord length of Re = 750 000. Uncertainties for the free stream velocity is V ∞ = ±0.02 m/s. The pressure in the tunnel test section was set to P 0 = 1.4 bar with an uncertainty of P 0 = ±0.003 bar. Uncertainty of σ is about ±0.02.

Results and discussions

Non cavitating flow

Static case

It was shown in [START_REF] Ducoin | Computational and experimental investigation of flow over a transientpitching hydrofoil[END_REF] that the flow experienced different regimes when the angle of incidence is modified, leading to a relative complex flow. For low angles of incidences (α < 5°), the boundary layer was laminar over the hydrofoil surface up to x/c = 0.7-0.8 for which an LSB took place. For α > 5°, the LSB moved suddenly toward the leading edge and the boundary layer was turbulent over the major part of the hydrofoil surface. Moreover, a turbulent boundary layer detachment was formed at the trailing edge and developed as the angle of incidence increase. The static displacement of the tip section is shown in Fig. 6 for different angles of incidences before stall. As shown, the displacement increases linearly up to 5°, then the plateau behavior is observed up to 6.5°due to the laminar to turbulent transition. For higher angles of incidences, the displacements are affected by the trailing edge boundary layer detachment.

Fig. 7 presents the mean spatial velocity vibration spectrum for three angles of incidences. Peaks corresponding to the natural frequencies of the hydrofoil can be observed: f 1 = 43 Hz corresponds to the first bending mode, f 2 = 171 Hz is the first torsional mode, f 3 = 291 Hz is the second bending mode and f 4 = 560 Hz is the first mixed bending and torsional mode. For α = 4°, a frequency of 510 Hz is observed. It is linked to the LSB induced laminar to turbulent transition at the trailing of the hydrofoil, which generate a high level of fluctuations close to the natural frequency at f 4 = 560 Hz. For more details about the laminar to turbulent transition characteristics and induced vibrations, see [START_REF] Ducoin | An experimental study of boundary-layer transition induced vibrations on a hydrofoil[END_REF]. At α = 8°, no shedding process was observed in the flow and the amplitudes peaks are low, resulting from a low level of periodic fluctuations around the body. When stall occurs at α = 14°, the low frequency of the leading edge vortex shedding highly excite the first bending mode. The frequency peaks of modes 7 and 8 are also observed which are excited by smaller structures of the leading edge vortex shedding. A peak around f = 1900 Hz were observed on wallpressure fluctuations. The level of vibration is relatively high for low angles of incidences resulting from the LSB fluctuations. It decreases suddenly the transition move to the leading edge. The highest fluctuation level is observed when stall occurs.

Dynamic case

The tip section displacement was measured for the four pitching velocities. An example of a typical visualization is shown in Fig. 8 at a maximal angle of incidence equal to 15°. The non deformed tip section (zero flow velocity) is given by the dashed line on the picture. The hydrofoil displacement is clearly observable when comparing the non deformed tip section to the deformed one. It was observed that the elastic displacement is mainly vertical (flexion) and that twist is small. When comparing the quasi-static case on Fig. 8(a) to the faster angular velocity on Fig. 8(b), it is observed that the displacement increases as the pitching velocity increases.

The dynamic vertical displacement is shown on Fig. 9 for α = 0°t o α = 15°with an angular step of α = 0.5°for the four pitching velocities during the upward and downward motion. For clarity, the angle of incidence during upward motion (respectively downward) will be denoted α + (respectively α -). It is reminded that the angle of incidence is deduced from the pitching laws giving the angle of incidence versus time (see Fig. 5). Also plotted on Fig. 9 is the static displacement and the experimental suction side pressure loading (C + L ) on a rigid hydrofoil measured by means of a wall-pressure array for the same flow conditions. It is obtained by summing the instantaneous pressure coefficients of the wallpressure array over the suction side [START_REF] Ducoin | Computational and experimental investigation of flow over a transientpitching hydrofoil[END_REF]. From α + = 0°to 5°(upward motion), the hydrofoil displacement increases linearly with the instantaneous hydrodynamic loading. When α + is close to 5°, an inflection is observed and the displacement is relatively constant and slightly reduced (Fig. 9(a)).

It was shown that this is the consequence of the leading edge laminar to turbulent transition. As the pitching velocity increases, the inflection point is delayed and its intensity reduced, it is suppressed for the highest pitching velocity (Fig. 9(d)). This agrees with the flow loading that exhibits similar trends. Beyond the inflection point the displacement increases again together with the loading. It is higher as the pitching velocity increases. At 13°it is δ y /b = 0.017 for α * = 0.18 and δ y /b = 0.023 for α * = 1.89. Beyond 13°(static stall angle), strong displacement fluctuations are observed. Three peaks are observed for α * = 0.18: a high amplitude peak at α + = 14.5°followed by two lower peaks at respectively α - = 14.5°and α - = 13°(during the downward motion).

This agrees with the flow loading exhibiting high amplitude fluctuations resulting from vortex shedding and stall. For the highest pitching velocity, one peak is observed. During the backward motion, from α - = 13°up to 0°, an hysteresis effect is observed. It is amplified when the pitching velocity increases. The effect of upstream flow velocity is also be investigated by comparing two measurements with the same pitching velocity and two different flow velocities. The displacements are divided by the square of the upstream velocity, on which they are proportional to, if the viscous effects are neglected (i.e. potential flow). Fig. 10 shows the results obtained for α = 6 °/s, V ∞ = 5 m/s and 7 m/s, leading to respectively α * = 0.18 and α * = 0.12, which are both quasi-static cases. As shown, the displacement level is quite the same when divided by the square of the velocity. It is observed that the effect of transition on displacement (α ≈ 5°) is lower for the highest upstream velocity, suggesting an effect of Reynolds number on the displacements. This figure also demonstrates the accuracy of the present method to measure the tip section displacements.

Cavitation-structure interaction

An investigation of the fluid structure interaction in the case of cavitating flows was carried out experimentally for a static angle of incidence and for the pitching motions α * = 0.18 and α * = 1.89.

Static case

Maximum displacement is measured with the same method as for non cavitating flows. A video camera is placed on the top in order to observe the cavitation development through the span (Fig. 1). The cavitation is obtained by decreasing the pressure in the tunnel test section. The cavitation inception for σ = 3 is obtained at α + = 8°, as shown in Fig. 11. It is characterized by a thin band located downstream the laminar separation bubble at the leading edge of the hydrofoil. The tip section displacement for different cavitation number was measured. Fig. 12 shows the maximum displacement versus the maximum cavity length. The development of the cavity up to 10% (σ = 2.6) have a few effects on the displacement. A slight decrease is observed due to the inception of vapor at a higher pressure level than the minimal pressure present in subcavitating flow, which effectively reduced the hydrodynamic loading at inception (see [START_REF] Carlton | Marine Propellers and Propulsion[END_REF]). From a cavity length of about 20%, the development of cavitation increase the hydrofoil displacements. The maximum is found for σ = 2.05 where the maximum displacement has increased of about 14% compared to σ = 7. The Fig. 14 shows the vibration spectrum for three cavitation numbers at α = 8°. It is also observed that the hydrofoil vibrations increase globally with the cavitation development. For σ = 7 (no cavitation), the first modes of vibrations are observed. For σ = 2.6, the cavity length is about 10% and the excitation is clearly observed around f = 68 Hz, corresponding to the cavity oscillation. As a consequence, the natural frequencies are excited, in particular the fundamental bending mode (mode 1). Moreover, the value is modified to f = 47.5 Hz (against f = 42 Hz for the non cavitating case). For σ = 2, a pulsating cavity is observed at a main frequency of f = 27.5 Hz (Fig. 13). The cavity shedding is clearly shown in the spectrum, but induces also an harmonic at f = 55 Hz with a higher amplitude than the fundamental frequency of excitation. The response of the first bending mode and the first torsional mode are particularly increased.

The influence of the excitation frequency on the value of the two first modes are clearly shown. The other natural frequencies are submitted to the variation of the added mass due to the presence of cavitation. The Fig. 15 show an increase of the frequency of mode 4 of respectively 3% and 8% for σ = 2.6 and σ = 2. Indeed, the development of vapor at the hydrofoil surface decreases the fluid density on the foil surface resulting in a decrease of the added mass.

Dynamic case

The pitching motions defined for the non cavitating case are performed for σ = 3, close to the cavitation number of inception for α = 8°(Fig. 11). Fig. 16 shows the cavitation inception for the two pitching velocities α * = 0.18 and α * = 1.89. For the low pitching velocity, the cavitation pattern at inception is close to the static case shown in Fig. 11. However it is delayed by about 1°due to the influence of the transient pitching motion, which stay significant compared to the inception rate of cavitation that form at the leading edge. A similar delay is observed during the downward motion, where the inception had been observed for α - = 7°. For the highest pitching velocity α * = 1.89, the cavitation pattern is changed (see Fig. 16(b)) and cavitation inception is delayed by about 3°(α + = 11°). It is an attached cavity at the leading edge over approximately 10% of the chord. The delay and modification in cavitation inception can be related to the delay of the laminar to turbulent transition and laminar separation bubble at the leading edge when pitching velocity increases.

As the angle of attack increases, differences are visible in the cavitation patterns for the different pitching velocities. The lowest pitching velocity is characterized by small cavities, as show in Fig. 17 The same events occur when the hydrofoil goes back to α - = 0°.

For the highest pitching velocity, a relatively long sheet cavity which develops from the leading edge up to 0.6 c is observed (Fig. 18), together with 3D effects which appear along the span. For α +,- = 15°, the sheet cavity breaks down into a large vapor-filled structure (Fig. 18(f)) and generates a large pounding sound. This motion up to the cavitation inception, except from 6°to 8°where a difference can be seen after boundary layer transition. Cavities increase displacement between 10°≤ α 1 ≤ 13°, as also observed in Fig. 21(a) at t 1 (α + = 12°), which show samples of the corresponding tip section displacement. This effect disappears when vortex shedding occurs and displacements fluctuates. When the flow reattaches, a slight difference is observed between the two flow conditions considered. When cavitation disappears, the same evolution is observed to the return set to 0°. The displacements analysis for the highest pitching velocity α * = 1.89 in Fig. 20 shows that the sheet/cloud cavitation has more influence on the structure. Displacements are higher than the case α * = 0.18 in both flow conditions, but the cavity inception at the leading edge induces a global increase of displacements. When the cavity develops on the suction side, displacements stop to increase until the implosion. A peak is then visible on Fig. 20 at t 2 , α = 15°, which can be observed in Fig. 21(d).

Conclusion

Experiments on a flexible hydrofoil in static and transient regimes have been carried out with original measurements techniques based on image processing and Laser Vibrometry, for non cavitating and cavitating flows.

For the non cavitating flow, the interaction between the viscous flow and the structure response was observed. The vibrations of the hydrofoil are increased by the vortex structures resulting from shedding of Laminar Separation Bubble at low angles of incidence, and leading edge vortex shedding at higher angles of incidence.

When the hydrofoil pitches, it is shown that the structural response evolves linearly with the hydrodynamic loading and that it is governed by the effect of viscosity. For small values of pitching velocity, a deplacement inflection is observed due to the laminar to turbulent transition whereas the highest pitching velocity suppresses the effect. Low frequency fluctuating displacements have been observed when leading edge vortex shedding occurs during stall. For cavitating flow, the structure vibration was measured for a fixed angle of incidence and show that cavitation highly excite the natural frequencies of the hydrofoil, in particular for pulsating cavities. The excitation of the torsional mode have probably a significant impact on cavitation structure interaction.

Measurements were also carried out in the case of cavitating flows in transient regimes, for the lowest and the highest pitching velocities. Displacements were measured and the cavitation behavior was observed at the same time by a high speed video camera. For the lowest pitching velocity small leading edge cavities are observed, then a vortex cavitation occurs at higher angles of incidences. This cavitation have few effect on the structure displacements. For the highest pitching velocity, a relatively long sheet cavity develops from the leading edge up to 0.6 c then collapse. It has a strong impact on structure displacements. The difference of cavitation patterns between the two pitching velocities is mainly due to the pitching motion which globally suppress the viscous effects and increase the cavitation. However, the deformations can also have an influence on cavitation.

Much work has still to be done for a good understanding of flow and cavitation structure interaction applied to lifting bodies. Specific numerical coupled procedures need to be developed and can be useful in the understanding of this interaction. In this context, the experimental results exposed in this paper can be useful in the understanding of complex flow features and for the validation of these new methods.

Fig. 1 .

 1 Fig. 1. Experimental set up.

Fig. 2 .

 2 Fig. 2. Typical cavitation pattern obtained from the high speed camera (top view), α = 8°.

  (a) V ∞ = 0 m/s. (b) V ∞ = 7 m/s.

Fig. 3 .

 3 Fig. 3. Measurement of the free tip section.

Fig. 4 .

 4 Fig. 4. Mesh grid on the foil surface for the vibration measurements.

  nal time of the transient motion. Four pitching velocities were considered, from a slow mean angular velocity of 6 °/s (quasi-static) to a high mean angular velocity of 63 °/s. The pitching laws giving the angle of incidence versus time are shown on Fig.5. Two phases of acceleration and deceleration are observed for the highest pitching velocity (Fig.5(d)). The non-dimensional angular velocity based on the chord length c and the upstream velocity V ∞ can be introduced as α * = α × c/V ∞ . The values of α * are also given on Fig.5for V ∞ = 5 m/s. The maximum angle of α max was set to 15°in

  (a) α = 6 °/s, α * = 0.18. (b) α = 20.6 °/s, α * = 0.618. (c) α = 35 °/s, α * = 1.05. (d) α = 63 °/s, α * = 1.89.

Fig. 5 .

 5 Fig. 5. Pitching velocities, angle of incidence versus time, V ∞ = 5 m/s.

Fig. 6 .

 6 Fig. 6. Static displacement for various angles of incidence, V ∞ = 5 m/s.

Fig. 7 .

 7 Fig. 7. Velocity spectrum for various angles of incidence, static case, Re = 750 000, V ∞ = 5 m/s.

  (a) α * = 0.12. (b) α * = 0.44. (c) α * = 0.75. (d) α * = 1.35.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Tip section measurement for 4 pitching velocities at α +,- = 15°, V ∞ = 7 m/s.

Fig. 10 .

 10 Fig. 10. Flow velocity effect: maximum displacement for 2 upstream velocities, α * = 0.18.

Fig. 11 .

 11 Fig. 11. Cavitation at inception at the leading edge for a fixed angle of incidence, α = 8°, σ = 3, Re = 750 000, V ∞ = 5 m/s.

Fig. 12 .

 12 Fig. 12. Maximum displacement versus maximum cavity length along the chord, α = 8°, Re = 750 000, V ∞ = 5 m/s.

Fig. 13 .

 13 Fig. 13. Instantaneous cavity length, σ = 2, α = 8°, Re = 750 000, V ∞ = 5 m/s.

Fig. 14 .

 14 Fig. 14. Velocity spectrum of the hydrofoil for various number of cavitations, α = 8°, Re = 750 000, V ∞ = 5 m/s. σ = 7 has subcavitating flow.

17

 17

  (e) and (f).

Fig. 15 .

 15 Fig. 15. Modification of the natural frequency during cavitation development, mode 4, α = 8°, Re = 750 000, V ∞ = 5 m/s.

  (a) α * = 0.18, α = 9.5°. (b) α * = 1.89, α = 11°.

Fig. 16 .

 16 Fig. 16. Effects of pitching velocity on cavitation inception at the leading edge, and σ = 3, Re = 750 000, V ∞ = 5 m/s.

Fig. 17 .

 17 Fig. 17. Cavitation development during the pitching motion, α * = 0.18, Re = 750 000, σ = 3.

Fig. 18 .Fig. 19 .Fig. 20 .

 181920 Fig. 18. Cavitation development during the pitching motion, α * = 1.89, Re = 750 000, σ = 3.

  (a) α * = 0.18, t 1 , α + = 12°. (b) α * = 1.89, t 1 , α + = 14°. (c) α * = 0.18, t 2 , α +,- = 15°. (d) α * = 1.89, t 2 , α +,- = 15°.

Fig. 21 .

 21 Fig. 21. Tip section measurement for 2 pitching velocities, α * = 0.18 and α * = 1.89, Re = 750 000, V ∞ = 5 m/s. σ = 3.

Acknowledgment

The authors gratefully acknowledge the technical staff of IRENav for its contribution to the experimental set up.


Mohammed Kechadi

Lila Chaal

Bernard Tribollet

Jean Gamby

Dynamic of BSA adsorption onto photoablated polymer surface in dielectric microchip

come

Dynamics of BSA adsorption onto a photoablated

polymer surface in a dielectric microchip.

Introduction

Direct immunosensor can detect interactions between ligands by measuring changes in capacitance [1], [2] , mass [3], [4] , or fluorescence [5], [6] . Optical biosensors measure the variation in the intrinsic optical property of a surface onto which a dielectric material is loaded [7], [START_REF] Schuck | Measuring Protein Interactions by Optical Biosensors[END_REF] . They are widely used and allow obtaining dynamic interaction data between ligands. One of the most used instruments is one that takes advantage of the surface plasmon resonance (SPR) [START_REF] Lee | [END_REF] . For this, the metal/ dielectric interface is excited by a beam of monochromatic light, in conditions of total reflection leading to the famous resonance. The intensity of the reflected light at a specific angle has a depth in which the intensity is operable. Several factors influence the position of the resonance angle, which is a refractive index of the medium close to the face of the non-excited metal thin film. The concentration of dissolved species is thus determined in the medium as it is directly related to the refractive index [START_REF] Lee | [END_REF], [10] . As shown, a conventional SPR cell biosensor has two parts: the channel flow and the region in which the interactions between ligands take place. The ligand is immobilized on the sensor surface while the analyte continuously flows over the entire surface. The main advantage of SPR methodology is to detect in label-free and real-time processes of association and dissociation of ligands. However, its disadvantage is the absolute necessity to immobilize the ligand to drastically increase the amount of analyte bound. This has resulted in a successful research development in surface chemistry functionalization to immobilize ligands, such as antibodies, in a functional and controlled orientation in order to increase the sensitivity of SPR immunoassays. Detection of the recognition elements on the SPR sensor are performed using intermediate chains such as alkanethiols, silanes, or polypeptides grafted on the sensor surface. However, the use of soft hydrogel matrix composed of carboxylmethylated dextran chains remains the most common strategy. The porous three dimentional matrix hydrogel is attached to the sensor surface and increases the length of the plasmon arising from thin the gold film (100 nm). Thus, a protein adsorbed or bound to the matrix induces a radical change in the activity of the latter. The hydrogel acts as a tertiary structure of the protein at or near the active site, where the 55 binding of interest may be modified by the immobilization step, thereby changing its properties. The steric hindrance encountered by the analyte in the hydrogel constitutes another drawback [11], [12], [13] .

In recent years, a new kind of electrical biosensor has been 60 developed. It is based on the capacitive coupling between microelectrodes galvanically isolated in a dielectric polymer such as polyethylene terephthalate (PET). Over the PET, a flow microchannel is fabricated by laser photoablation procedure [14], [15] . Briefly, the principle is to sandwich a thin dielectric PET 65 layer (5 µm) between the two microelectrodes (electronic charges) and a flow microchannel (ionic charges). More recently a detailed methodology for non contact impedance in such dielectric microdevice has been published [16] . This method eliminates the contribution of the impedance of the thin 120 µm-70 PET layer which separates the two embedded microelectrodes (see Figure 1A). This procedure enables a clear observation of the microchannel impedance associated in series with the interfacial impedance, Z int , together with the impedance of the 5 µm-PET non contact layer from the microelectrode to the microchannel 75 bottom. Indeed, eliminating the contribution of the impedance of the polymer between the two microelectrodes enables new applications for high frequencies [15] . This article is a direct and practical application to monitor at low frequencies the interfacial impedance where correction is not needed. The PET surface can be of various kinds, depending on the modification of the polymer. In this way the state of the surface on the activity of the biomolecules can be investigated. It will be shown here that the described methodology using dielectric measurement is more practical and less time-consuming 20 than other techniques. In comparison to SPR principle, the diffusion of species is not hindered since hydrogel is not necessary. Indeed, the amount of data collected leading to a correct interpretation of the adsorption dynamic under flow conditions constitutes a paramount importance for investigating 25 the association dynamics of ligands on a material support.

Materials and methods

Chemicals

The NaCl solution (10 mM) was fixed at pH 9 with solutions of NaOH and HCl. Bovine serum albumine was purchased from 30 VWR International (96%). A 10 -4 M stock solution was obtained after dilution in 0.01 M NaCl.

BSA adsorption under flow conditions

Solutions of BSA with concentrations ranging from 1 pM to 500 35 pM in 0.01 M NaCl were pumped in a 2 cm long microchannel (50 x 100 µm in cross section, as shown in Figure 1 B) by a syringe pump at a rate of 7.2 µL/min. The samples were adsorbed onto the photoablated PET surface and the variation in the differential impedance was recorded with time at fixed low 40 frequency (200 Hz).

Microchip Network

The microchip device used in this work was described elsewhere [17] . Impedance measurements were carried out through a 45 polyethylene terephthalate (PET) microchannel photoablated having a trapezoidal cross-section shape with a depth of 45 µm, a top width of 100 µm and a length of 1.4 cm. The distance separation between both microchannels is 200 µm center to center (see Figure 1B). The electrode fabrication is achieved 50 using a carbon ink loaded with gold nanoparticles, thermally laminated at 135°C and a pressure of 2 bar by a polyethylene (10 µm)/polyethylene terephthalate (25 µm) (PE/PET) layer with a total thickness of 35 µm. The distance separation in the PET band between the two planar microelectrodes and the main 55 microchannel is equal to 5 µm and the detection surface area per microelectrode is 80 µm x 100 µm.

Apparatus

Electrochemical impedance spectroscopy measurements have 60 been performed by applying an AC voltage with constant amplitude (0.1 V) through the microelectrodes with a fixed frequency at 200 Hz. The current measured is thus related to the total impedance of the sensor. These measurements are performed using a frequency response analyzer (FRA 1255B, 65 Solartron U.K.) together with a dielectric interface 1296 (Solartron, U.K.) which extends the frequency range from 1 Hz to 10 MHz. Data is performed using the company-made software SMaRT. To analyze these results, a physical model is used as described on Figure 1A.

Results and discussion

Methodology for realtime adsorption in microchannel

The characteristics of this kind of interface with an insulated layer sandwiched between two galvanic isolated microelectrodes can be represented by a dielectric system with, on one part of the 75 thin polymer layer, electronic charges on microelectrodes and, on the other part, ionic charges in the microchannel. An electrical equivalent circuit can be drafted, considering impedances for each part of the microdevice as displayed in Figure 1A. The global impedance, Z G , through the microdevice using free contact 80 microelectrodes configuration, is given by the sum:

) ( ) ( ) ( 1 2 1 1 1         Z Z Z G (1)
wherein ω is the angular frequency (rad s -1 ), defined by ω = 2 π f, where f is the frequency (Hz). As explained in a previous paper [16], [18] the electrical impedance 85 through the microchannel/polymer interface is defined as Z 1 and the impedance between the two galvanically isolated microelectrodes as Z 2 : Impedances through the 5 µm-PET layer or the 120 µm-PET layer are defined as a capacitances C PET,1 and C PET,2 , respectively. The PET/ microchannel interface behaves as a non ideal capacitor and is defined by a constant phase element CPE with Q int and α int being the CPE element and the CPE exponent, respectively. The CPE exponent α int takes into account the role of the photoablated PET surface at the microchannel bottom. In previous work alpha α int was found equal to 0.5 [16] . In the microchannel, the impedance is represented by an R S //C S circuit. The resistance, R S , is characteristic to the electrolyte resistance and C S is the cell capacitance.

S S S PET R C j R Q j C j Z          1 ) ( 1 1 ) ( int 1 , 1 int (2) 2 , 2 1 ) ( PET C j Z    (
To make a sweep in frequency and record the electrical impedance of this filled device, the experimental set up was built by connecting the microchip to a dielectric interface apparatus dedicated for insulated material (Solartron ID1296). All the experimental set-up was computer-controlled through commercial software (Smart, Solartron Analytical). A 100 mV alternating signal was applied in a 1 MHz to 20 Hz frequency range. For the following bioanalytical application at a fixed frequency, low frequency window were preferred because the main information contained in the imaginary part of impedance is the interfacial impedance, Q int .

BSA adsorption under flow conditions

In a first step, 10 -2 M NaCl was pumped at 7.2 µL/min in the microchannel to obtain the baseline, Z NaCl , for 360 s. The corresponding impedance module, Z NaCl , in the y-axis was taken as the signal given by the NaCl solution. In a second step a diluted solution of BSA in 10 -2 M NaCl was introduced and adsorption occurred over 600 s. After a short period of BSA incubation, a net increase of the impedance module was noted until reaching a plateau value, Z NaCl,BSA , as displayed in Figure 2.

In the last step, the buffer was pumped again during 1100 s to ensure an efficient washing procedure. In order to have the same incubation time on the x-axis, all samples were introduced following the same procedure. The impedance module with time was normalised by the buffer response baseline because, as explained previously, we assume that the differential sensor response is directly related to the interfacial impedance which is itself linked to the interfacial impedance. For that purpose, the obtained experimental plateau for the BSA adsorbed was defined as an equilibrium value: Z BSA,eq = Z NaCl,BSA -Z NaCl . The maximum impedance module value obtained for Z BSA,eq for higher BSA concentration was taken as the experimental plateau which corresponds to the theoretical maximum, Z BSA,max . In the fitting procedure of the experimental data, the kinetic isotherm was normalized by Z BSA,max , (see right axis in Figure 3A). Linearization of the adsorption isotherm was performed as illustrated in Figure 3 B.

Indeed, in the case of monolayer assumption, the biosensor response measured with time, Z(t), increases proportionally with the surface concentration until the equilibrium is reached, while the quantity, Z BSA,max -Z(t), decreases proportionally with the adsorbed surface concentration maximum. In our case, the traditional Langmuir isotherm [19] adsorption does not fit well with the experimental data. We use the Langmuir-Freundlich combined equation [20], [21] in order to approximate BSA adsorption onto PET photoablated surface which can be viewed as an heterogeneous surface with different ionised groups 60 generated on the PET surface by phoablation process [22] . Taking into account, the Langmuir-Freundlich combined equation, the adsorbed surface concentration can be expressed as follows:

        1 1 max , , m m BSA eq BSA KC KC Z Z (4)
65 where m exponent is the power term of Freundlich isotherm and the parameter  can be viewed as the capacity of the system to reach the maximum coverage. When  <<1 (small coverage of the adsorbent, i.e. Z BSA,eq << Z BSA,max ) this parameter can be neglected in the denominator of 70 Equation ( 4).

Values of K= 5×10 4 M -0.43 and m=0.43 were found after the fitting procedure with equation (4) (see Figure 3A) taking into account the measured experimental value of Z BSA,max equal to 4 MΩ.

75

A useful test traditionaly used for Langmuir adsorption validation can be also extended to the Langmuir-Freundlich equation under a linear form as written in equation ( 5) below:

max , max , , 1 BSA m BSA eq BSA m Z C Z K Z C      (5)
Linearisation using equation ( 5) in Figure 3B is in a good Step 1: the 10 -2 M NaCl buffer was introduced for 360 s.

Step 2: the diluted 5 pM BSA was introduced for 600 s for incubation.

Step 3: the NaCl buffer was introduced again for the washing procedure for 1100 s. The value of the K constant is in a good agreement with those found in the literature. As an example, the experimental value obtained by James et al. [20] for BSA adsorbed in anion exchanger (DEAE-Sepharose Fast Flow) medium at pH 9 and 0.012 M NaCl was equal to K=6.64 10 4 M -0.86 . This confirms our choice using the power law equation for the adsorption fit procedure which is generally applied for heterogeneous surface. In this device, the semi-crystalline surface of the photoablated PET can act as a heterogeneous surface due to the different functional groups existing on its surface, even after the photoabaltion process [22] . 20

Methodology for interfacial impedance in microchannel

In the microchannel, the impedance is represented by an R S //C S circuit. The resistance, R S , is characteristic to the electrolyte resistance and C S is the cell capacitance. This capacitance is observed in very high frequencies mainly in dielectric media.

The study of the dielectrical response of the microchip shows that at low frequencies, the impedance contribution (Z 2 ) of the PET thickness (120 µm) between the microelectrodes can be neglected. The correction of the global impedance (Z G ) 30 performed in previous work [15] is not necessary, which indicates that at 200 Hz the global impedance (Z G ) is assimilated to the impedance measured through microchannel (Z 1 ). The contribution of the interfacial impedance can be expressed as follows:

35 int int int int int int 2 sin 2 cos ) ( 1 Q j Q j                       (6)
The expression of the impedance Z 1 can be further written as:

         int int int 2 1 , 2 1 , 2 1 , 1 , 2 1 , 1
int 2 sin 2 cos 1 ) ( Q j C C R C C j C R C C C R j Z PET S S PET PET S S PET PET S S                                 (7)
After development, we obtain the following expression of the 40 impedance Z 1 where one can clearly identify the real part, Re (Z 1 (ω), and the imaginary part, Im (Z 1 (ω)).

                                               2 1 , 2 1 , 2 1 , 1 , 2 1 , 3 int int int int 2 1 , 2 1 , 2 2 1 , 2 1
int int 2 sin 2 cos ) ( PET S S PET PET PET S S S PET PET S S PET S PET C C R C C C C C R C Q j Q C C R C R C Z               (8) with 45         int int 2 1 , 2 1 , 2 2 1 , 2 1
int 2 cos ) ( Re Q C C R C R C Z PET S S PET S PET                 (9) and                                    2 1 , 2 1 , 2 1 , 1 , 2 1 , 3
int int 1 int 2 sin ) ( Im PET S S PET PET PET S S S PET C C R C C C C C R C Q Z         (10)
Wherein the target application is the real-time monitoring of the 50 interfacial impedance in the microchannel, the imaginary part only of the impedance which contains the contribution of the interfacial is taken into account at 200 Hz. Finally the interfacial impedance is defined as follows:

                               1 , 2 1 , 3 1 , 2 2 1 int int 1 ) ( Im ) ( 2 sin int PET S S PET PET S S S C R C C C C C R Z Q        (11)
It will be more convenient to have an expression, as presented by equation (11), which gives a quick estimation of free contact microchannel interfacial impedance from a read value of the imaginary part of impedance at fixed low frequency. By recording imaginary part variation against time at a given frequency, it will be possible to deduce the interfacial impedance Q int in microchannel using the previous equation.

The numerical values of C S , R S , C PET,1 , α int were considered as being fixed and obtained in previous studies by fitting of the Nyquist plot [16] . We obtained the same parameters values in this study: C S =2×10 -13 F, R S =3.5×10 7  C PET,1 = 14×10 -11 F, α int =0.5. This can finally lead to an analytical expression for the interfacial impedance from the realtime monitoring of the experimental imaginary values of the impedance Z 1 at a fixed frequency in time. By replacing the parameter values of C S , R S , C PET,1 , α int in equation ( 11) at f = 200 (Hz) we obtained the following analytical equation for Q int :

    6 1 int 10 6 ) ( Im 44 . 35 707 . 0      Z Q (12)
From this equation, at the selected frequency that is 200 Hz, the value of 6×10 6 in the denominator is negligible compared to the values of the imaginary part which are in the order of 6×10 8 . As a consequence, the impedance measurement at a fixed frequency can be exploited to calculate the values of the interfacial impedance, which is related to the adsorbed BSA concentration. The plot of Q int according to the BSA concentration at 1 pM is illustrated in Figure 4. By following the same procedure described above, Q int change with time is normalised with the buffer response as baseline. The obtained experimental plateau for the BSA adsorbed was defined as an equilibrium value: Q int,BSA,eq = Q int,NaCl -Q int,NaCl,BSA . Theoretically, the maximum of the value Q int,BSA,max must be obtained for higher BSA concentration. However, the application of equation (12) for concentration above 100 pM does not permit obtaining consistent values. The plot Q int,BSA,eq estimated for low BSA concentration (1 pM to 100 pM) is presented in Figure 5. A linear variation between the BSA concentration in the microchannel and the value of the interfacial impedance is obtained only for ultralow concentration. This representation can be used as a calibration curve in the following concentration range : from 1 pM to 100 pM.

Conclusions

Previous articles have demonstrated the feasibility of monitoring temporally adsorption and desorption of lactoglobulin on PET coated with gold nanoparticles [14] or antibodies on gold 60 nanowires as carpet on hybrid polycarbonate membrane [23] . However, this present study with the associated model underlines a direct procedure to monitor adsorption kinetics and detecting ultralow concentration of adsorbed protein onto photoablated PET without modification such as coating with gold nano-objets.

65

The experimental results show a very good reproducibility with negligible variation of the signal. As portrayed in Figure 5, the threshold of detection is close to the picomolar concentration. As expected, due to the tunability of the surface charge, the interfacial impedance increase with the BSA concentration. The 6 main process governing the electrical properties of the sensor is the adsorption of charged BSA onto photoablated PET surface. Indeed, BSA contains several amino acid functional groups in side chain, which are either positively or negatively charged. For example, Arg, His, Lys, are positively charged and Asp, Glu, Tyr, Cys, are negatively charged. These groups are in different proportions on the BSA. At pH 9, BSA is known as being negatively charged [24] and we suppose that its adsorption on the photoablated PET surface causes a change of the charged region in the Gouy-Chapman layer. The work in progress concerns the real time monitoring of biomolecular recognition of BSA adsorbed on PET by using the corresponding rabbit anti-BSA antibodies as an analyte in the flow microchannel.

Notes and references

Figure 1 A

 1 Figure 1 A. Representation of the microchip interfaces by an equivalent electrical circuit. C PET,2 represents the capacitance of the 120-µm PET layer between the two parallel microelectrodes. C PET,1 represents the capacitance of the non contact 5-µm PET layer. Q int represents the interfacial impedance through the active surface. R S and C S represent the solution microchannel resistance and the cell capacitance, respectively. B. Top view of the microchannel with the non detection area.

  70

Figure 2 :

 2 Figure 2: Sensorgrams showing the impedance module with time for 85

ZFigure 3 .

 3 Figure 3. Calibration for BSA detection on PET-microchannel. A Isotherm of BSA adsorption obtained from the experimental sensorgrams at various concentrations from 1 pM to 100 nM (Figure 2). The fit resulted in normalisation by experimental. Taking a value of ΔZ BSA,max = 4MΩ for normalization curves, values of K= 5×10 4 M -0.43 and m=0.43 were found after the fitting procedure with equation (4). B. Linearisation of the adsorption isotherm, following equation (5): regression coefficient = 0.999, slope = 2.48×10 -7 Ω -1 , intercept = 4.98×10 -12 (M m . Ω -1 ), from which ΔZ BSA,max = 4.05 M Ω and K = 4.98 10 4 M -0.43 were found.

Figure 5

 5 Figure5 Calibration curve of the normalised ΔQ int,BSA,eq versus BSA concentration for ultralow concentration from 1 pM to 100 pM at fixed 55

  CNRS, UMR 8235, Laboratoire Interface et Systèmes Electrochimiques, (LISE), F-75005 Paris, France .* Jean.gamby@upmc.fr b Sorbonne Universités, UPMC Univ Paris 06, UMR 8235, Laboratoire Interfaces et Systèmes Electrochimiques, (LISE), 4 Place Jussieu, F-75005, Paris, France.

a c Laboratoire d'Electrochimie, Corrosion et de Valorisation Energétique (LECVE), Faculté de Technologie, Université A. MIRA, Béjaia 06000, Algeria.


Mohammed Kechadi

Bruno Sotta

Lila Chaal

Bernard Tribollet

Jean Gamby

Real time affinity biosensor onto insulated polymer using electric impedance spectroscopy in dielectric microchip

come

A real time affinity biosensor on an insulated polymer using electric impedance spectroscopy in dielectric microchips.

Introduction

The last decades have seen the emergence of microfluidic devices with various tranducers for affinity biosensor development. The most used tranducers are electrochemical [1], [2] , electroacoustic [3], [4] , or optical [5], [6] for detecting interactions between ligands. Surface plasmon resonance (SPR) is one of the most used optical biosensors for the measurement of the refractive index changes [7], [START_REF] Tudos | Schasfoort in Chapter 1 Introduction to 75 Surface Plasmon Resonance[END_REF] . As illustrated in Figure 1A with Biacore SPR instrument scheme, the ligand (antigen, receptor…) is immobilised in the hydrogel, while the analyte (antibody, messenger…) flows in the channel and diffuses in the gel where the ligand is bound. The metal/ dielectric interface constituted to glass slide coated with hydrogel and gold is excited by a beam of monochromatic light, in conditions of total reflection leading to the resonance. The light beam probes the hydrogel and detects changes in the local refractive index due to the accumulation of analyte mass. The depth of the evanescent wave is 100 nm towards the hydrogel, i.e. the thickness of the hydrogel itself. In the last decades, several groups have focused on electrical signal transduction in microchip by using direct or indirect electrode configuration to measure the conductivity of the streaming electrolyte in microchannel. An original technique has been the development of measurements through capacitively coupled contactless conductivity detection (C 4 D) through two electrodes with a distance separation constituting the detector cell [9], [10], [11] . However, the high applied ac voltage 0.5-10 V amplitudes are much larger than conventionally used values, 5 ~ 100 mV. Such large amplitude generates a non-linear relationship between voltage and current which cause distortion of impedance results. It is for this reason that this transduction can be viewed as pseudoimpedance or transimpedance technique. In recent years, laser photoablation technique was used to defined a well-controlled microelectrodes position in polymer microchip. The feeble gap between the microelectrodes as well as with the thin layer of dielectric material that coated the microelectrode allowed to avoid the linearity problem [12] . As mentioned for SPR, the principle of the developed electric impedance in dielectric microchip is also based on the metal/ dielectric interface excitation by applying a modulated voltage of one hundred of 55 millivolts in frequency range through the dielectric layer. The output impedance through the device can thus be related to the interfacial impedance of the modified dielectric layer sandwiched between the microelectrodes and the flow microchannel (see Figure 1B). The crucial advantage of electric impedance 60 spectroscopy on insulated polymer sandwiched between two microelectrodes is the absence of direct contact between the microelectrodes and the flow microchannel [12], [13] . As a consequence the polymer microchannel layer sandwiched between the two planar microelectrodes can be considered as a 65 dielectric component [14] whose physical properties may change in response to an external electrical excitation. Based on this principle, in a previous paper, a flow sensor was developed to record at high fixed frequency the chemical conversion of enzymatic substrate like aminophenyl phosphate in PET 70 microchannel through the channel resistivity [15] . In this paper, we demonstrate for the first time the possibility to probe the interfacial electric impedance change when a biomolecular interaction takes place between a ligand in solution (analyte) with a ligand attached onto the polymer microchannel. This new 75 transduction for biosensing was demonstrated for the detection and quantification of bovine serum albumin (BSA) immobilized on the polymer microchannel surface using the corresponding rabbit anti-BSA antibodies (Ab-BSA) as an analyte, which is loaded in the flow microchannel at nanomolar range 80 concentration. Experimental studies are based on the real time monitoring of the measured impedance variation at a fixed frequency (400 Hz) by applying a small 100 mV alternating potential excitation through two microband electrodes, during the association/ dissociation rate between Ab-BSA loaded in flow 85 microchannel and BSA immobilized on PET.

Materials and methods

Chemicals

10 mM of Tris(hydroxymethyl)aminomethane (from Sigma Aldrich) was obtained after dilution in 10 mM HCl and 10 mM NaCl. The checked pH was at 9 and was used as the buffer solution. 1mM NaOH (from Sigma Aldrich) was used as washing buffer in a regenerating step. Bovine serum albumin (96%) was purchased from VWR International. The rabbit anti-bovine serum albumin antibodies (Ab-BSA) was received from Sigma-Aldrich. The antibody solutions were also diluted in the buffer solution from a 10 -5 M Ab-BSA stock solution in 50% glycerol. Tween 20 solution was used with the ratio: Tween 20/buffer solution = 0.2 ml.L -1 [16] .

Microchannel Networks

Photoablation procedure for the microchannel networks has been previously described [17], [12] . In brief, the microchip used in this work was realised by photoablation process which leads to the ablation of the material in contact with UV laser source. Before the photoablation step, the PET film thickness was measured at 100 µm. On the one side of the PET sheet two parallel microchannels (which will be transformed into microelectrodes) were drilled. The two microchannels depth into PET film was measured under microscope at 50 µm. On the other side of the PET sheet, a perpendicular microchannel for fluidic was drilled having a trapezoidal cross-section shape with a depth of 45 µm, a width of 100 µm and a length of 1.4 cm (See Figures 1B andC). Thus, a 5 μm thick PET layer separated the microchannel from the bottom of the two microelectrodes (See Figure 1B). The two parallels microchannels were transformed into microelectrodes by incorporation of a graphite carbon ink then dried afterward at 50°C. Finally the photo-ablated PET film was laminated using a 35 µm-PE/PET layer. As shown in Figures 1B andC, the distance separation between both microelectrodes is 120 µm edge to edge (200 µm center to center) and the detection surface area per microelectrode is 80 µm x 100 µm. Study was carried out by the electric impedance measurement in alternative mode (ac) through the two microelectrodes at frequency range from 1 MHz to 1 Hz with 0.1 V amplitude, in order to control the dielectrical behaviour of the overall microsystem and to extract the specific microchannel response from the background response [18] .

+ _

Flow channel

that for a more detailed view of the interface the dimensions are not to scale. C. The zoomed detection is taken under an inverted microscope.

Instrumentation

Impedance measurements are performed using Dielectric interface (Solartron, DI 1260) gain phase impedance analyzer coupled with a frequency response analyzer (Solartron, FRA 1255). Dielectric interface is characterised by the large frequency range, from 1 mHz to 20 MHz. Software Smart (Solartron Analytical) was used as the computer control of all experimental set-up. Dielectric interface is usually used for high impedance measurement on high insulated material that is the case with polyethylene terephthalate. Indeed, current measurement range of the system varies from 6 mA to 100 fA, thus enabling the measurement of very high impedance (100 to 100 T). In this study, impedance measurement is making at low fixed-frequency (here 400 Hz) which was appropriate for sensing the interfacial impedance through the dielectric microchip device connected to a dielectric interface apparatus.

Experimental procedure for electric impedance measurements in dielectric microchip

The microchip characteristics with an insulated PET layer sandwiched between two galvanic isolated microelectrodes can be assimilated to a dielectric interface with, on the one part of the 5 µm-PET thin polymer layer, electronic charges on 25 microelectrodes and, on the other part, ionic charges in the microchannel considering impedances for each part of the microchip (see Figure 1B). The global impedance Z G (ω) between the two microelectrodes with a filled microchannel depends on the different parts which constitute the microchip. In this configuration, Z G (ω) can be expressed as the combination between Z 1 (ω) (blue line in Figure 1B) and Z 2 (ω) (green line in Figure 1B) [18] , as expressed as follows,

1 2 1 1 1 ) ( ) ( ) (         Z Z Z G (1) 35
Firstly, acquisition and interpretation of electric impedance are performed with an empty microchannel through a 100 mV voltage excitation applied between the two carbon microelectrodes embedded in PET and separated to 200 µm center to center (120 µm edge to edge, Fig. 1B). The 120 µm-40 PET impedance layer, Z 2 (), which separated two electrodes behaves as a capacitor (see equation 2) and will be eliminated from the global impedance, Z G (), in further experiments when microchannel will be filled. The capacitance written in equation 2 was obtained at C PET,2 = 8×10 -13 F.

µm PET C j Z 120 , 2 1 ) (    (2)
where ω is the angular frequency (rad s -1 ), defined by ω = 2 π f, where f is the frequency. The target application is the real-time monitoring of the electric impedance module variation Z 1 () at low frequencies. The latter impedance as appears in Figure 1B corresponds to a serial combination of three impedances as written below:

  ) ( ) ( 2 ) ( 2 int , 1 1     el microchann PET Z Z Z Z    (3)
The first term in equation 3 is the 5µm-PET layer impedance from the top of one electrode to the channel bottom that behaves 55 also as C PET,120µm (see equation 2). The value of C PET,5µm equals 14×10 -11 F, is fixed and will be suppressed during the normalized procedure. The second term displayed in equation 3 is the microchannel solution impedance, Z S , that corresponds to a parallel association between the microchannel solution resistivity, 60 R S , and the cell capacitance, C C . The resistance R S only depends on the buffer concentration that is high in comparison with the analyte concentration. The capacitance, C C , is defined as a geometric capacitor that only depends on the chip dimension. This latter was equal to C C =3×10 -13 F. The last term represents 65 the interfacial impedance, Z int , at the photoablated PET/ solution interface. As obtained in previous paper [19] , this latter behaves as a non ideal capacitance represented by a constant phase element (CPE) where α int and Q int are the CPE exponent and the CPE element (see equation 4), respectively.

70

    int int int 1 Q j Z     (4)
To conclude, Z int is the only interesting parameter to monitor (see equation 3) which varies when a biomolecular interaction takes place on the photoablated PET surface throughout the course of 75 the experiment. As a consequence, the real time monitoring of Z int can be measured through the relative variation of Z 1 . Indeed, this latter at low frequencies mainly reflects the contribution of the interfacial impedance as written in equation 5.

Experimental procedure for adsorption monitoring

In the first step, PET microchannel was coated under a laminar flow contained 10 -7 M BSA for 1200 s in order to saturate the microchannel surface. The solutions were loaded into the 85 microchannel using high precise micropump with a flow rate equal to F v = 7.2 µL min -1 . Indeed this optimized BSA concentration was chosen because it corresponds to the experimental plateau for BSA adsorbed onto PET surface [20] . Before loading the antibody, Tween 20 solution was also 90 introduced over 1200 s to prevent the non specific adsorption of Ab-BSA in the molecular recognition step [16] . The molecular recognition step was the introduction of various Ab-BSA solution (from 10 -8 to 10 -7 M) in the same hydrodynamic conditions. The last step consisted in a washing procedure with 10 -3 M NaOH for 95 PET surface regeneration [20], [21], [22] . This procedure allows the start baseline recovering when water and the buffer solution were introduced again for a new started run experiment.

Results and discussion

Affinity reaction rate determination onto PET

microchannel

A typical variation of the interfacial impedance module when Ab-BSA solution is loaded on a prepared PET microchannel surface (BSA then Tween 20) is displayed in Figure 2. The initial value corresponds to the electric impedance module baseline obtained after BSA and Tween 20 samples were successively loaded in the microchannel (named Z BSA ). First, a control experiment was performed showing no significant changes on the measured interfacial impedance modulus when no rabbit anti-BSA antibodies are present in buffer solution (Figure 2, curve a). Secondly, the measured interfacial impedance modulus increases in the presence of Ab-BSA diluted with the buffer solution while the affinity reaction with BSA takes place. Then, the interfacial impedance signal response reaches a plateau value corresponding to a stationary signal (named Z Ab-BSA ). A statistical study about the changes on interfacial impedance modulus in presence of Ab-BSA is given in Table S1 (See the supplementary material). The difference between the two stationary signals leads to an equilibrium status named ΔZ Ab-BSA,eq which is equal to Z BSA -Z Ab-BSA . Plotting the equilibrium binding obtained from the difference values ΔZ Ab-BSA,eq against various loaded Ab-BSA concentrations leads to an isotherm behaviour displayed in Figure 3A. Indeed, as the reaction binding progresses, the rate decreases gradually until a state that corresponds to an equilibrium between association and dissociation rates. The maximum value obtained for ΔZ Ab-BSA,eq is more quickly reached while Ab-BSA concentration is high. We obtained a maximum value of ΔZ Ab- BSA,eq (named ΔZ Ab-BSA,max ) from a Ab-BSA concentration equals to 510 -8 M. This means that all the active sites of BSA molecules adsorbed onto PET microchannel are saturated after the biomolecular recognition with Ab-BSA.

In order to find the model parameters corresponding to the binding reaction between Ab-BSA with BSA determined by impedance measurements, the relative equilibrium binding curve is plotted against Ab-BSA concentration after normalization of ΔZ Ab-BSA,eq values divided by ΔZ Ab-BSA,max (displayed in the rightaxis of Figure 3A). As described previously, for Ab-BSA concentrations lower than 510 -8 M, the equilibrium binding varies linearly. The Langmuir equation model [23] has been tested 45 to fit the experimental data synthetized in Figure 3 without good correlation. However, as yet known for heterogeneous sites for adsorption, the adapted Langmuir model named Langmuir-Freundlich model [20], [24], [25] was more adequate for the fitting procedure to determine the kinetics parameters. Briefly, in the described experiment, the impedance normalized in Figure 3b was assumed to be in linear correlation with the surface concentration of occupied sites. As a consequence, the Langmuir-Freundlich combined expression can be expressed as 60 follows in equation 6 :

    m BSA Ab app m BSA Ab app BSA Ab eq BSA Ab m BSA Ab C K C K Z Z C BSA aAb BSA BSA Ab BSA             / / 1 max , ,  (6)
where  (C m Ab-BSA ) can be viewed as the capacity of the microchannel to reach the maximum coverage, m exponent represents the power term of Freundlich, and the apparent equilibrium constant, K app BSA/Ab-BSA . As traditionally admitted for the Langmuir equation [23] , a linear expression of equation 6 is a useful test for the model validation as follows in equation 7:

max , max , , / 1 BSA Ab m BSA Ab BSA Ab app eq BSA Ab m BSA Ab Z C Z K Z C BSA Ab BSA            (7)
In order to obtain the traditional unit in M -1 for the equilibrium constant K BSA/Ab-BSA the following relation must be taking into account:

  BSA Ab K K BSA Ab BSA app BSA Ab BSA     / / (8)
As predicted, a better fit of experimental data is obtained with the Langmuir-Freundlich equation and the obtained parameters are equal to K app BSA/-Ab-BSA = 5×10 15 M -2 and m = 2. By replacing relation 8 in equations 6 and 7, we recover the typical Langmuir equation model with a power term corresponding to the unit (m= 1). The linearization step of the association isotherm using a linear fit as indicated in equation 7 leads to a straight line with a correlation coefficient R 2 equals to 0.996. Indeed, the curve fitting highlights a straight line characterized by a slope of 1.6510 -6 Ω -1 and an intercept of 1.5110 -21 M 2 .Ω -1 . From these values the parameters of equation 6 were obtained equal to m= 2, ΔZ Ab-BSA,max = 0.606 MΩ and K app BSA/-Ab-BSA = 1.110 15 M -2 .

kinetic model for affinity reaction onto polymer microchannel

The interaction model for the binding reaction between Ab-BSA and BSA can be defined in the reaction scheme 1 below:

      associated ads k k solution ads BSA Ab BSA BSA Ab BSA on off     
As demonstrated previously, results involve that the observed association rate, v obs , between Ab-BSA and BSA can be expressed as a second order reaction proportional to the square of Ab-BSA concentration, as follows:

  2 BSA Ab k obs obs    (9)
with v obs in M s -1 and k obs in M -1 s -1 represents the observed association kinetic rate constant. Taking into account the concentration influence in the observed second order, the association kinetic rate constant can be determined as follows:

  BSA Ab k k obs on
  (10) with k on in s -1 . The dissociation rate of BSA ads -(Ab-BSA) complex, v off , is proportional with the BSA ads -(Ab-BSA) concentration and it is considered as a zero order reaction since the amount of the adsorbed complex BSA ads -(Ab-BSA) onto PET microchannel can be considered as a constant:

off off k v  (11)
with k off in M s -1 represents the dissociation kinetic rate constant As a consequence the ratio (k on /k off ) is defined as the equilibrium 50 constant, K BSA/Ab-BSA which is defined in M -1 . The aim is now to determine by a full fitting procedure of the sensorgram impedance curve (see Figure 2), the kinetic parameters k on and k off leading to an estimation of the equilibrium constant of the complex BSA ads -(Ab-BSA). For that, a theoretical 55 expression of the impedance module Z(t) at fixed frequencies with time can be written taking into account that the initial amount BSA adsorbed is related to impedance Z BSA at the time t=0, as follows:

      t k C k k C k C k Z Z t Z off BSA Ab on off BSA Ab on BSA Ab on BSA Ab BSA                    exp 1 . ) ( max , 60 (12)
where Z(t) in  is the impedance module measured at fixed frequency 400 Hz. The result of the fitting procedure using equation 12 is illustrated in figure 4 with a working Ab-BSA concentration taken at 410 5B. This latter underlines that an average value for K BSA/Ab-BSA can be estimated at (5.151.45)10 7 M -1 , that is in a good agreement with the literature [26] . It is observed that the average value is very close to the one obtained with the higher Ab-BSA concentration i. e. 1.210 7 M 1 . 2 in the supplementary material).

3.5x10

2.0x10

Concluding Remarks

Electric impedance spectroscopy in microchip was applied for the first time to monitor the biomolecular recognition of two ligands on insulated polymer designed as a microchip. As shown, the presence of BSA molecules immobilized onto the microchannel detection zone increases the interfacial impedance module leading to a sensitive surface for biosensing in the nanomolar Experimental results obtained highlight the possibility for the monitoring at low fixed-frequency of the electric impedance changes provoked by the association of proteic ligands. Here it is illustrated for association reaction between rabbit anti-BSA 30 antibodies in solution and BSA adsorbed onto the PET surface. Thus, it was found that the kinetics of association reaction rate depend on a second order kinetic law with the anti-BSA antibodies concentration. The promising results obtained for the kinetic parameters and the equilibrium association constants 35 between ligands using the present methodology make it a competing method for biosensing. The dielectric PET microchip is also a low cost and flexible material which offers a multiuse chip possibility. It could be used to screen putative partners in biological fluids with regard to a specific protein. Also, the 40 minute volumes of solvent used make it suitable as a detector for a capillary electrophoresis apparatus or to be connected with mass spectrometer.

Figure 1 .

 1 Figure 1. A. Schematic representation of the BIACORE optical biosensor. The hydrogel is 100 nm high approximately; the flow channel for a standard instrument is 24 mm long, 50 µm high and 500 µm width. The50

Figure 2 .

 2 Figure 2. Sensorgrams showing the impedance module versus time. Curve a: A control experiment when no rabbit anti-BSA antibodies are present in buffer solution. Curve b: The association step between Ab-BSA as analyte and the adsorbed BSA on the microchannel sensor at a fixed frequency of 400 Hz and for a flow rate 7.2 μL.min -1 . Step 1: BSA and Tween 20 in buffer solution for microchannel coating. Step 2: Introduction of 4×10 -8 M Ab-BSA diluted in the buffer solution.

6 Figure 3 .

 63 Figure 3. Calibration curve obtained for various Ab-BSA concentration loaded on the coated PET surface with BSA. (A) An association isotherm of Ab-BSA on the adsorbed BSA obtained from various experimental sensorgrams from 12 nM to 120 nM concentration. (B). Linearization step 55

Figure 4 .

 4 Figure 4. Experimental and fitted sensorgram of interfacial impedance modulus for 4×10 -8 M of Ab-BSA loaded in the flow microchannel sensor showing the association reaction between Ab-BSA and the adsorbed BSA at a fixed frequency of 400 Hz and for a flow rate of 7.2 μL min -1 . The curve fit was performed with equation 12 leading k on , k off equal to 70

Figure 5 .

 5 Figure 5. Kinetic parameters obtained from the fitted sensorgrams of interfacial impedance modulus with several Ab-BSA (from 1.2×10 -8 to 1.2×10 -7 ) loaded in the flow microchannel sensor coated with BSA. A. The values obtained were from fitting procedure using equation 12 leading k on and k off parameters which appear on left-axis and right-axis, respectively. B. The equilibrium constant corresponding to each k on / k off 10

20 range

 20 concentration. The high sensitivity is found because this transduction takes advantage of the dielectric properties of the flow microchannel embedded in PET with two planar microband electrodes without contact with the solution, thus avoiding non specific adorption on microelectrodes and degradation of 25 biological samples through uncontrolled faradic reactions.

  -8 M -1 . The obtained values of k on and k off are 8.5610 4 s -1 and 310 - 3 M s -1 respectively. The same procedure was applied for various 75 Ab-BSA concentrations and values of k on and k off have been determined for each curve (see TableS2in the supplementary material). All the kinetic data obtained are synthetized in Figure5A. It can be noticed that the values of k on and k off are slightly dependent on the Ab-BSA concentration while the ratio, k on / k off ,

	80
	is as expected, less dependent with Ab-BSA concentration, as
	appear in Figure

Acknowledgments

45

The authors thank Prof Hubert Girault and Dr Philippe Flückiger for allowing them access to experimental facilities at the EPFL center of MicroNano Technology, Lausanne.

Notes and references