Marco Mancini

Elhadji Mama Guène

Jérôme Lambert
email: jerome.lambert@univ-rennes1.fr

Elhadji Mama Guène

Renaud Delannay

Using Surface Evolver to measure pressures and energies of real 2D foams submitted to quasi-static deformations

Keywords: 2D foam reconstruction, Surface Evolver, 2D foam rheology

may come

Using Surface Evolver to measure pressures and energies of real 2D foams submitted to quasi-static deformations

Introduction

Foams are usually considered as good model systems for the study of complex fluids, because both their intermediate structure, the bubble, and the events that are responsible for their plasticity are well identified: they consist in an exchange of neighbors between bubbles and are called T1s (2; 3). Foams that are placed between two parallel plane surfaces in order to obtain only one layer of bubbles are called 2D foams and offer the possibility to observe all their bubbles and T1s, which consist in this particular case in the exchange of neighbors between four bubbles. Many studies have been dedicated to 2D foams in the last 20 years because of the possibility they offer to compare numerical and actual experiments that show features which may occur in more complex, or less accessible, situations like, for example, 3D foams. For example, many authors have worked on 2D foam rheology for different kinds of set-ups and flow regimes, and have compared experiments with real foams and simulated foams (see [START_REF] Kabla | Quasi-static rheology of foams. part 1. oscillating strain[END_REF] and references therein).

Indeed, one of the reasons why 2D foams are particularly studied is the fact that their structure is visible and that it is possible to observe directly any change that occurs under strain. In addition, it is possible, in principle, to derive the energy of static foams from their structure up to a single factor that accounts for the physico-chemistry since their energy is proportional to the total surface area of their films, and one may thus obtain obtain informations about the local stress in static and moving foams. One may expect to extend this procedure to quasi-static foams where the films experience slow enough motion for the pressure drop induced by viscosity in the Plateau borders to be negligible compared to the Laplace pressure drop.

In principle, it is thus possible to measure precisely the total length of the films and their curvatures on high resolution images of 2D foams using standard image analysis tools. This will lead to the measurement of the pressure inside each bubble and to the measurement of the total energy of the foam. However this process may be tedious and difficult to achieve when imaging a foam containing a large number of bubbles and when one wishes to follow its dynamics. The experimental apparatus required for this kind of measurement is expensive and both the computation time needed to perform the image analysis and the storage of the images are costly. We show here that an excellent measurement of the characteristics of a 2D foams, as well as of their dynamics is easily achievable using standard res-olution images coupled with the Surface Evolver (SE) software [START_REF] Brakke | The surface evolver[END_REF]. Indeed a mere standard image analysis is not enough on standard size images: A normal image is 770×550 pixels large and contains around 2000 bubbles (for a foam filling the image). Hence the average length of a film is around 10 pixels. This is too small to obtain a good precision measurement of the film lengths and their curvatures using standard image analysis tools. One way of achieving the reconstruction of the structure of a 2D foam from a standard size optical image, hence of obtaining a precise measurement of its total energy and of the pressures inside the bubbles, is to measure accurately the positions of the vertices inside the foam and use them as inputs in the mechanical equilibrium equations that govern the curvature of the edges of bubbles. This eventually comes to solving iteratively a linear system for the films' curvatures inside the foam starting from straight films (3; 5). By successive refinements, one may adjust the curvatures of the films and deduce the pressure drop between neighboring bubbles. This method is centered on film curvatures, hence it deals with a large number of variables. An equivalent of this procedure can be achieved using the Surface Evolver (SE) software devised by Ken Brakke to compute stable structures based on surface minimization (1; 6): this software performs the total length's minimization of the structure of a 2D foam given some constraints: Usually the areas (2D foams) or volumes (3D foams) are fixed and the vertices moved in order to minimise the total length (2D) or area (3D) of the foam. This software has been widely used by several authors working on 2D foams (see e.g. (2; 3)) as well as on 3D foams (7; 8; 9) to simulate various aspects of foam behaviour, like coarsening and rheology (4) and compare them to experiments with liquid foams. Here we use SE to reconstruct the structure of foams starting from experimental images. The areas or volumes that are used as constraints are determined experimentally from the optical images or simply assuming that edges are straight or faces are pyramids. Hence, while SE provides a very accurate way of equilibrating a structure whose topology is known, the fact that the exact areas or volumes are not measurable induces a mismatch between the equilibrated numerical structure and the experimental image it reproduces. For example, in a 2D foam, the area of each bubble in the equilibrated structure will match the area of the inscribed polygon of the SE input file, but not the area of the bubble on the optical image. This limits the accuracy of the determination of the curvatures of the bubbles' edges and hence the accuracy of the pressure that can be measured.

The aim of this article is to propose here an improvement of the latter method that also uses SE. It consists in running SE several times while adjusting the usual constraint on fixed bubble areas for the area of the inscribed polygon to match its experimental measurement. Hence we apply a feedback loop on the length minimization procedure performed by SE in order to converge iteratively towards an accurate value of the areas of the bubbles, the "error" signal being related to the area of the inscribed polygon for each bubble. This method, that will be described hereafter, minimizes the number of parameters (one per bubble) that must be set in order for the structure of the foam to be approached starting from the position of its vertices and its topology. It is thus well adapted to large collections of images since it is not time or memory consuming: it is thus possible to follow the dynamics of a 2D foam in the quasi-static regime. In addition this method should be transposable to the reconstruction of 3D foams starting from a method like the one described in Davies et al [START_REF] Davies | Reconstruction of tomographic images of dry aqueous foams[END_REF].

We first describe the experimental apparatus used to obtain optical images of a 2D foam experiencing an inhomogeneous quasi-static deformation together with measurements of the pressure inside its central bubble. The quasi-static deformation is a series of cycles of inflation and deflation of a bubble at the centre of the foam. We introduce an image analysis procedure to write a SE input file containing the precise position of the vertices of the foam on an image. We then describe a script that calls the SE software starting from this input file to reconstruct an equilibrated numerical foam using the minimum number of variables in order to obtain a fast convergence. We first check that the equilibrated structure obtained with Surface Evolver maps the optical image of the foam and we show that this mapping is not reliable in order to obtain precise values for the pressures inside the foam. A definitive validation is provided by comparing the dynamics of both numerical and real foams experiencing a quasi-static deformation. This is performed by measuring the pressure inside the inflated bubble for each recorded image and comparing these measurements to the pressure of the same bubble in the equilibrated SE structure. Both pressures differ by a factor that takes into account the contribution of the liquid fraction of the experimental foam. We check that this factor should not vary significantly from a bubble to the other in the foam since the variation of the total energy of the numerical foam that includes this factor is consistent with our estimate of the work done experimentally.

Experimental apparatus and method

A 3D monodisperse foam is obtained by bubbling air at constant rate (around 10 mL.min -1 ) at the base of a column containing a foaming solution. The foaming solution contains 4% volumic fraction of commercial dishwashing liquid "Palmolive" brand) and 10% glycerin. The surface tension of the solution is measured using the pendant droplet method: γ = 26.6 ± 0.5 mN.m -1 . It is possible to tune the liquid fraction by controlling the height of the foam at the top of the column. A few hundred bubbles are extracted from the top of the column by bringing a circular glass plate in contact with this foam. The foam is then squeezed between this plate and another one maintained at a constant distance of 1 mm to form a 2D foam in a glass-glass Hele-Shaw geometry. The typical bubble diameter is then around 5 mm. The bottom glass plate is pre-drilled in its center with a 1.5 mm diameter hole in order to inflate air inside the foam using a computer controlled syringe pump and to measure the pressure inside the bubble using a differential pressure sensor (precision around 0.2 Pa) as pictured on Fig. 1. Gas is injected inside the central bubble at a very slow rate (around 250 µL.min -1 ) in order for the structure of the foam to be equilibrated only by capillary pressures. This is an idealization since viscous drag may play a role even at slow speed. However, an estimate of the pressure drop induced by the viscous forces exerted on each moving film shows that the influence of viscous drag on their shape is not observable here, whereas the cumulated pressure drop between the central bubble and the atmosphere results in an offset on the pressure measured using a pressure sensor. We will estimate this offset in the validation section. An additional pressure loss will play a role in the offset : it is due to the Poiseuille air flow between the sensor and the bubble. The sign of this offset depends on whether the bubble is being inflated or deflated.

The central bubble is submitted to cycles of slow inflation-deflation. The maximum size of the inflated bubble ranges from 20 to 40 times the average bubble size. For example, Fig. 2 shows an experimental 2D foam (20% glycerol, 1097 bubbles, 15 cm diameter) at two different stages of the bubble inflation. In Fig. 2a, the central bubble is about the same size as all other bubbles, whereas in fig 2b it is about 23 times as large as the others. The inflating rate is slow enough for the deformation to be quasi-static. The whole sequence is filmed using a 550 × 770 pixels camera. The image acquisition rate is 8 images per second. Between 2000 and 4000 images are recorded for each experiment.

Foam reconstruction

Image analysis

In order to write a SE input file corresponding to a given optical image, one needs to identify each bubble, edge and vertex inside the foam. This is done using common image analysis tools. After converting the image to a binary image, one uses a watershed procedure to label bubbles. A thin-skeleton procedure provides the position of the edges and of the vertices inside the foam. An overlap between the three types of objects enables matching edges with vertices and bubbles with edges. Thus one determines the exact topology of the foam by determining which bubbles share the same edge. SE takes as input the exact position of each vertex. The latter is estimated by computing the position of the centre of mass of each vertex. On the binary images, the vertices all look alike: They are star-shaped sets of 3 to 5 pixels. This enables computing the position of their centre of mass with a precision of the order of a third of the pixel size in both x and y planar directions. A cycle of bubble inflating/deflating corresponds roughly to 1500 images. We automate the procedure described above in order to write a SE file corresponding to each image and pressure measurement. Let us underline that, at this point, the SE input file merely contains the coordinates of each vertex, which are the most reliable piece of information one can extract from an image, along with the exact topology of the real foam.

Equilibrating the numerical foam

A way to proceed with the numerical foam equilibration using SE should be to set the vertices to fixed positions and use the standard equilibration procedure under SE by maintaining the vertices fixed throughout the equilibration procedure. However this method may pose convergence problems when some films are very short (e.g. shortly before a T1) and the relative error due to the position of the center of mass of the vertices becomes too important for SE to give a reliable output on the pressures of the bubbles surrounding this short film. We choose to introduce an alternative way of equilibrating the structure by adding a feedback loop to the procedure based on constant surfaces constraint. We thus keep the advantages of the latter method by setting only one constraint for each bubble in the foam. But this constraint is fine-tuned after each SE equilibration in order for the area of the polygon whose vertices are the vertices of the bubbles to match with their value deduced from the optical image. Since the positions of the vertices are measured with a good precision on this optical image, the polygon areas are determined rather precisely. Around ten iterations of area adjustments are needed to obtain an equilibrated numerical structure as close as possible to the real structure as seen on optical images. We first describe the procedure in detail and then the way we compare the successive numerical structures with the real one.

For each bubble i of the SE input file we compute a i * the area of the polygon the vertices of whose are the bubble's vertices. The goal of the procedure is for each bubble to be mechanically equilibrated whilst its corresponding polygon reaches the target area a i * that is measured on the initial structure built from the optical image. Let us write A i p the area of bubble i before a p-th equilibration by SE. At step 0 of the procedure, A i 0 = a i * for each bubble since the structure of the foam has not been equilibrated yet and since the films are straight lines. Running an equilibration with SE at constant A i p , releases the vertices and leads to a new structure and new values for the polygon areas a i p+1 . This structure is mechanically equilibrated. The feedback procedure consists in adjusting the constraints A i p+1 of the next equilibration to reduce the difference between a i p+2 and a i * . To do so, we choose to use a bisection method.

A first step of the bisection method procedure consists in determining a lower A im and an upper boundary for A iM for each bubble i. For each bubble, these two areas lead to values of a i that bracket a i * . Once A im and A iM are set for each bubble (we give an example for doing so further in the text), the second step consists in using a bisection method to find the experimental areas using the following algorithm for each bubble i (p = 0 designates the initial non-equilibrated structure):

A i p = 1 2 (A iM + A im ) SE equilibration at constant A i p leads to new a i p+1 if a i p+1 -a i * ≥ 0 then A iM = A i p else A im = A i p
After p iterations, the relative uncertainty on the value of the areas is indeed of the order of < ∆A/A >=< (A iM -A im )/A i >≈ |δA|/2 p+1 / < A > (where < • > designates an average over all the bubbles) as pictured on Fig4a. In the same time, SE ensures that the bubbles' pressures converge as pictured on Fig4b where < ∆P/P >=< (P (A iM ) -P (A im ))/P i >. Thus, 10 iterations are enough to reach a 10 -4 relative precision on the values of A i , and a 0.2% relative precision on the pressures P i . The whole procedure is quite fast since it requires ≈ 200 s to run on a 800 bubbles foam with a 1.6 GHz CPU. The structures that are obtained using this procedure are thus mechanically equilibrated and seem to be similar to the structures of the foam from which they were originally deduced. We show in the following paragraph that the measurement made on the numerical structures are indeed very similar to experimental measurement that are made independently.

Let us end this description by making two remarks :

• We use a fast way of determining the lower and upper bounds of A i by deliberately trying to "overshoot" the convergence. A few equilibrations with SE are run after setting the new constraints on A i as :

A i q+1 = A i q -s q (a i q -a i * )
where s q is an increasing set of positive numbers, that is chosen to force (a i q -a i * ) to change signs as q increases. We use q rather than p here to stress the difference between this initiation stage, which is only but an example of method to obtain the initial values for A M and A m , and the bisection procedure. We set s q = q, which leads to a quick convergence: We obtain values bracketing āi for each bubble with 2 successive iterations, although not in the same order for each bubble. This procedure is run until we obtain for each bubble two successive values of A i for which the areas of inscribed polygons bracket a i * . The lower and larger areas are named A im and A iM . Let us notice that the number of iterations needed to reach this result for each bubble is observed to be always smaller than 5.

• It may look surprising that the bisection method works so well as if there were only one A i matching a a i for each bubble, or that A i might be an increasing function of a i , independently of the value of A j for neighboring bubbles. The authors are aware of this problem, but it seems that the films in the structures that are studied in this article are close enough to straight films for this approximation to hold. We nevertheless tested this procedure on a more polydisperse foam structure (∆A/ < A >= 3) where the films were clearly distinct from straight lines. Further work on more complex structures, like very polydisperse foams, might set a limit to the efficiency of the procedure we describe here. Nevertheless, even with the huge size polydispersity that we have here (one very large bubble among small ones), the method works very well.

Validation

Image correlation

A first -although very crude -way to check the validity of the method is to compare the foam structure on both optical and SE images. One may build the latter from the SE file by discretizing the edges with a large number of points, i.e. a number larger than the ratio of the maximum edge length to the size of a pixel. Of course this procedure results in a loss of information. Figure 3(a) shows an optical image of a 2D foam containing 1097 bubbles. One may build an image using the SE input file obtained by image analysis, as shown in figure 3(b). After 11 iterations, the reconstructed structure (figure 3(c), obtained using the same procedure) is very close to the original one. A superposition of the three images merged in a RGB image provides a crude means to check this observation, as is shown on figure 5a. A quantitative analysis of the image matching is performed by measuring the overlap ration between the binary original image after it has been slightly blurred and the successive images built from the SE files (also slightly blurred). In order to do so, we compute the average of the pixel by pixel multiplication of both images. Thus this overlap ratio appears to be the value of the correlation function between both images at frequency zero. The result is pictured on figure 5b. One may understand this result as a way to estimate the accuracy of measurements based on image analysis only: Two SE steps are enough to get the same estimate of the energy as the one that could be obtained by merely counting the number of pixels of edges on an optical image after it has been converted to a binary image. This shows that, whereas the correlation reaches a steady value at the third iteration (this value depending on the pretreatment of the images, it is of no particular interest), one needs to run more iterations to obtain a good precision in the determination of the areas and pressure.

Accuracy

In order to obtain an evidence that our procedure may indeed provide quantitative information about the foam, i.e. good estimates of pressures or areas of the bubbles, let us first examine the accuracy of the pressures and areas that are measured and then compare them to experimental measurements. It is easy to check when an error occurs in determining the topology and to correct it. Thus, the only source of inaccuracy is the error on the position of the vertices. Errors may occur in the initial position of the vertices as a result of the image analysis process: indeed the latter provides the positions of the vertices with a 0.33 pixel precision in both directions. This error in the input file of course modifies the final areas and pressures after the SE equilibration process. Let us estimate the errors on pressure P i and area A i of bubble i by moving randomly each vertex in the SE input file of ±0.33 pixel in x and y directions and measuring the resulting ∆A i and ∆P i for each bubble after equilibration. The size of the range in which A variations are very small for both quantities as shown on figure 6 after averaging over all the bubbles for a foam containing 1104 bubbles. The maximum relative error induced by the random displacement of vertices on pressures and areas are 2% and 5% respectively. This can be understood by noticing that, for an average edge length of 10 pixels, the area corresponding to the uncertainty on the position of a vertex is much smaller that the average area of a polygon. A few vertices may experience a 1 pixel displacement but most of them move inside the margin defined by the image analysis step as can be seen on figure 7: the average displacement is around half the margin induced by image analysis. Thus the accuracy on the measurement of the pressures and areas of the procedure is excellent.

Comparison with experimental measurements

The errors discussed above are relative errors, insensitive to the absolute values of pressure and areas. One must therefore calibrate the scales of pressures and areas. The process is straightforward for areas : the pixel area is easily measurable on optical images using a ruler. As for the pressures, the pressure sensor provides a good estimate of the pressure P Sensor inside the central bubble (CB), but with an offset the sign of which depends on the direction of the gas flow inside the pipe. This offset is induced by the air flow in the tube : P CB = P Sensor -∆P flow . Considering the air flow as a Poiseuille flow, one gets :

∆P flow = 8ηQL πR 4 ≈ 0.7 Pa
where η = 17.1 10 -6 Pa.s is the air viscosity, Q = 250 µL.min -1 the flow rate fixed by the syringe pump (positive for the inflating stage, negative for the deflating stage), L = 120 cm and R = 0.75 mm the length and radius of the tube. As for the air flow in the gap between the two glass plates, it induces a pressure drop that is proportional to h -3 in a plane geometry. Since h = 1 mm is of the same order of magnitude as R, the pressure drop per unit length inside the cell is approximately 1000 smaller than in the pipe. Thus one can neglect it.

In addition, the relation between the dimensionless numerical pressure P num computed using SE and P CB should be P CB = a P num + ∆P visc.

where the offset is now due to the viscous drag exerted on the films and a is a constant pressure. Let us estimate the order of magnitude of ∆P visc. : Cantat et al. [START_REF] Cantat | Dissipation in foam flowing through narrow channels[END_REF] show that the pressure drop depends on the orientation of the film with respect to its velocity. Only films perpendicular to the flow will experience a pressure drop. For a typical flow rate of 250 µL.min -1 , the speed of a film at a typical distance r = 1.5 cm of the injection tube is v ≈ 5.10 -3 cm.s -1 (for a 20% volumic glycerin solution, this corresponds to a Capillary number Ca ≈ 2.10 -6 ). The resulting pressure drop is then of order 3.10 -2 Pa (see [START_REF] Cantat | Dissipation in foam flowing through narrow channels[END_REF]), which is less than the resolution we can expect from our equilibration procedure. Hence we won't see any difference between the structure we image and a static one. However this drop may cumulate across the foam to give a measurable pressure drop between the central bubble and the atmosphere. We image foams that are approximately organized as 10 to 20 rings of bubbles around the central bubble. Assuming for sake of simplicity that all the films move at the same speed, this may lead to an average pressure drop of ∆P visc. = ±0.3 Pa depending on the sign of the gas flow rate. This offset in large enough to modify slightly the value of the pressure inside the central bubble.

The a factor has pressure dimensions and depends on the geometry of the foam and on the surface tension. It might depend as well on the bubble that is under scrutiny. To compute this factor, let us introduce b, the length scale enabling linking SE structures to real ones. The dimensionalized film lengths and bubble areas are :

ij(d) = b ij and A i(d) = b 2 A i
where ij is the length of the film that is common to bubbles i and j, and where the (d) subscript stands for a dimensionalized quantity. One may write the relation between the pressure in bubble i and its area in SE :

P i = ∂E ∂A i
where E = ij is the energy of the foam. Let g be a geometrical factor that describes the shape of a film along its height (we will derive it further). Then the dimensionalized energy and pressures are respectively :

E (d) = 2γ films {ij} h g ij(d) = 2γhgb E and P i(d) = ∂E (d) h ∂A i(d) = 2γg b ∂E ∂A i
Comparing the latter equation in the case of the central bubble leads to

a = 2γg b
One can use a crude model of film shape in order to derive g : Fig. 8 shows a naive shape of a 3D film compared with the idealization of a 2D film. The 3D film is itself idealized for two reasons : first the liquid phase is evenly shared between the top and the bottom ends of the film. This assumption is justified by the fact that the height of the foam is slightly less than the capillary length. The second reason is that we neglect the second curvature radius of the film by considering a straight segment between the two glass plates. Whilst this is true for a static film, a moving film may possess a second curvature radius to balance the drag force exerted on both its upper and lower ends (see e.g. ( 11)). However we estimated above that the added pressure increase induced by the drag force on one film is around 0.03 Pa, which is much less than the pressure variations we observe during both inflating and deflating stages. Thus we choose to neglect this second curvature: Films may be considered as static as for their shape. This simple model leads to

g = (π -2)r + h h (1)
where r and h are the radius of the Plateau border and the height of the foam respectively. Thus the relation between the numerical pressure and the pressure recorded by the sensor is :

P Sensor = a P num ± ∆P = 2γg b P num ± ∆P
where ∆P ≈ 1.0 Pa takes into account both sources of pressure drop. The plus or minus sign depends on whether the bubble is inflated or deflated. To determine g (the only unknown quantity in the factor) and ∆P experimentally we compare the dynamics of P Sensor and 2γ b P num for a set of 1500 successive images during the central bubble inflation.

Figure 9 shows the variations of both quantities where P num is now dimensioned : we write P Evolver,wet = 2γg b P num + ∆P and P Evolver,dry = 2γ b P num + ∆P . Both factors g and ∆P are détermined by the least squares method. One finds that g = 1.407 and ∆P = .91 Pa give the best accord between SE and pressure sensor data. Wet Evolver data and pressure sensor data are well correlated except at the beginning of the inflation sequence (from t=0s to t=50s) and at the beginning of the deflation sequence (from t=255s and 305s) during ∆t ≈ 55 s when we suppose that the experimental set-up slowly adapts to the new flow regime. We discuss only the intervals outside this adaptation period in the following paragraphs.

One may see both experimental and numerical pressures vary continuously except when plastic events (T1) occur. These T1 look instantaneous on this figure but a close look at the few points that come immediately after the T1 show that the only discrepancies between the two pressure sets (apart from the initial stage and noise on the Sensor measurements) occur in the half second following the event. This is due to the fact that most T1 occur near the central bubble and that the structure is not mechanically equilibrated anymore. Thus an optical image cannot provide coherent data to build a mechanically equilibrated SE structure. T1 characterization using the method introduced here will be discussed in [START_REF] Guène | Cycles of deformation in a 2d foam[END_REF]. By comparing both numerical and experimental curves during inflation and deflation, the value of ∆P is found to be around ±.9 Pa, with a mere sign change between both phases. This value is close to the theoretical prediction taking into account the Poiseuille pressure drop and the viscous drag on films.

In order to prove that g is indeed a constant throughout the foam, and may be considered as a manifestation of the liquid fraction, we compare the experimental work done to change the shape of the foam with its energy ∆E(t) computed by SE and and dimensioned with the constants introduced before. In the quasi-static regime and in the absence of T 1 events, both quantities must be equal. This writes

∆W (t) = t 0 (P CB -P ext )dA CB = ∆E(t)
While the work depends only on the area of the central bubble and on the difference P CB -P ext , the energy is influenced by the whole structure of the foam. If a and thus g were to vary in the foam, this would reflect on the energy, but not on the work. Figure 10 shows that the average values of ∆E and δW are indeed equal when g = 1.4. This validates the hypothesis that g is a geometrical factor accounting for the shape of the films. From the expression (1) of g written above, it is then possible to derive the liquid fraction of the foam (assuming the bubbles are circles of radius ≈ 2.5 mm): one finds φ ≈ 5%, which is a credible value given the way the foam was made.

Conclusion

In this paper we show a new way of measuring the total energy along with each bubble's pressure of a 2D foam experiencing quasi-static deformation by combining image analysis tools with the SE software. The method relies on a determination of the position of the vertices and of the topology of a foam on the one hand, and on the use of SE to build an equilibrated structure starting with these data on the other hand. Other means of equilibrating the structure using SE can be employed but the method introduced here favors the least number of variables. This was useful in this study because of the great number of images to be analyzed. But it should also be useful for future studies on 3D foams. Optical tomography tools have been used first by Monnereau et al to observe a few tens of bubbles in the bulk of a coarsening foam [START_REF] Monnereau | Dynamics of 3d real foam coarsening[END_REF]. The same authors were able to rebuild the same mechanically equilibrated structure using SE to characterize the coarsening process [START_REF] Monnereau | Coarsening of a three-dimensional reconstructed foam under surface evolver[END_REF]. Xray tomography now makes it possible to observe larger numbers of bubbles in quasi-static liquid foams (e.g. see ( 13)). But the reconstruction of such structures under SE requires an automated procedure. Davies et al [START_REF] Davies | Reconstruction of tomographic images of dry aqueous foams[END_REF] have recently demonstrated a way to build the latter and to obtain an SE equilibrated structure close to the experimental foam structure. The procedure described in the current paper could be applied to 3D structures to obtain a better description of the pressures inside the bubbles by including a feedback control parameter to better adjust the volume of the SE reconstructed bubbles to the experimental ones. This might be especially interesting since most of the imaging methods in 3D produce images where only the vertices are clearly visible, and where the films are often faint or even invisible. Such a method would certainly greatly improve the analysis of 3D foam structures since it would not rely on a precise observation of the films. The current paper opens the possibility to analyze a great number of quasistatic experiments and to measure the distribution of pressures inside 2D foams since the film curvatures could hardly be measured using standard image analysis tool. In future studies, we will analyse the global behavior of a foam under many cycle of inflation and deflation of the central bubble as well as the energy and range of a T 1, which has been numerically analyzed by Cox et al. [START_REF] Cox | Screening in dry two-dimensional foams[END_REF].

Foam

Pressure Sensor

Syringe pump

P CB ∆P

Figure 1 :

 1 Figure 1: Hele-Shaw cell and pressure circuit involving the syringe pump, the central bubble and the pressure sensor.

Figure 2 :

 2 Figure 2: Experimental 2D foam (f2) at two different stages of the bubble inflation. a) Initial stage before inflation. b) Central bubble is about 23 times as large as the average bubble size.

Figure 3 :Figure 4 :

 34 Figure 3: a) Optical image of a 1097 bubbles 2D foam. b) Image built from SE input datas obtained by analysing (a). Notice the edges are straight lines. c) Image built from SE output file after 11 iterations of area adjustments.

Figure 5 :

 5 Figure 5: (a) :RGB image obtained by merging different reconstructions of the same foam. Red: Optical image. Green: SE input file. Blue: SE output file after 11 iterations. The insert pictures a detail of the image after zooming in. (b): Overlap ratio between the optical gray-level image and successive images built after n iterations. Iteration 0 stands for the input SE file built using image analysis.

Figure 6 :

 6 Figure 6: Left : histogram of the relative error on the final value of A i induced by a random displacement of the vertices in the SE input file. Right : same for p i .

Figure 7 :Figure 8 :Figure 9 :Figure 10 :

 78910 Figure 7: histogram of displacements r i of vertices induced by the SE equilibration process after 11 iterations.

Acknowledgements

The authors thank the "Region Bretagne" for awarding a ARED grant to this project. They also gratefully thank Isabelle Cantat, Simon Cox, Benjamin Dollet and François Graner for numerous and useful discussions, Janine Émile and Alain Faisant for their kind technical assistance at different stages of the experiment.


Sheer Difference, or, Mining Mental Prospects in Lyrical Ballads (1798) Thomas Dutoit, Université de Lille 3 For Marc Porée Or. And? No. Or. Or includes and. And/or. Sheering already. Mind this "or." Mine this "ore." Mine, this "or"? No, "or" never belongs. "Or" does not pertain. The pertinence of "or" is that it shares: it divides. "Or" is the "sheer difference" we share and that shears us, sheering us off course. Of course. Whose course? Mine, or his? Which his? Teachers of a course. Lyrical Ballads, de Wordsworth et Coleridge. La difference en partage, this breath-taking book, is also the course written by Denis Bonnecase and Marc Porée. Porous difference, that they share, that shore them as each wrote from his respective shore. [START_REF] Bonnecase | Lyrical Ballads de Wordsworth et Coleridge. La différence en partage[END_REF] Explore only the veins of this course rich in wordly, and mental, prospects.

Or.

Or. Or. Wordsworth has two. Only two? Is "or" only two? How many "or's" in Wordsworth, in Lyrical Ballads, to begin? Inexhaustible vein.

The destination is the mine. To mine the mine. Mined. Mind. Mental. I'm taking "mental prospects" as of the mind, as in the mind, as to be mined in the mind, the mind as a mine, but that does not mean as my mind, as mine, but as something to be prospected, foraged.

I translate La différence en partage less as Shared Difference than as Sheer Difference. In sheer as partage, as participation, there is, certainly, "share," which obviously denotes the scissors, the "shear" or "shearing" requisite for "sharing." Share. Shear. Sheer warp? "Sheer" already means a lot: "sheer" is a synonym for "perpendicular," "steep," and "to sheer" is to rise or descend vertically, very steeply, from the shore. We are therefore sheer with, smack in front of, all those cliffs in Wordsworth, for example in the boat stealing episode of The Prelude when "I dipped my oars." [START_REF] Wordsworth | The Prelude (1805 version) Book 1[END_REF] Must try to avoid a crash landing in this attempted flight, this vol, I hope I will be "sheer," in its sense of "not guilty"; "sheer" also means "absolutely" (used especially with verbs denoting cleavage and separation); "sheer" is used of a blow, as in a sheer blow; of immaterial things, as in sheer mind; "sheer" is transparent, as in sheer textiles. As verb, "sheer" also means "to turn aside, alter its direction, swerve to one side or another"; to "sheer" is to curve, and as a noun, it is a nautical term: "sheer" denotes the curvature of a deck or bulwarks of a vessel. It is the curvature, for example, of a rowboat. A "sheer" in sailing is a "swerve," and as verb, is to change one's course, to depart, go away, into a new direction: to change tack. In trying to mine -to undermine, to exploit, to explore by burrowing through; but also to make mine, to appropriate -La différence en partage, their reading of Lyrical Ballads, there will be a constant risk of "sheering-off": breaking from one's course. After all, their book is the template for all courses in France on Lyrical Ballads. "Sheering" is, basically, bad steering, for it is when one is unable to hold or walk or sail on a line.

"Sheer difference," then, is to bend difference, to take it off line, to turn difference into something other than itself, other than being other. If two people were related by sheer difference, then they'd be identical. Because absolute difference would mean to share absolutely nothing in common, but then, if each is radically incomparable, then both are equal in that incommensurable measure. All pleasure is the experience of this impossible measure. 51). Through a reading of parts of their book, but also of Lyrical Ballads, we wish to show how a Mallarmean poetics is, avant la lettre, operating in these poems.

Confounding the temporality of literary history, this poetics requires a reading memory that is able to conceive of the mind, and of the text, as thoroughly syntactical, paratactical, hypotactical. In other words, a tactic of remembering and reading that eschews the semantic in preference to a literary reference: a network of words and letters that in this paper will be constructed, in poems such as "The Idiot Boy," "The Female Vagrant," "Anecdote for Fathers," and "Tintern Abbey," through galleries such as "mine," "mined," and "mind"; "or," "ore," and "oar"; "now" and "own"; "woe" and "owe," "vain," "vane," and "vein." Yet this reading-as-memory of (reading) a text shall also give special attention to the writing of the present as complex imbrication of movements to the past and to the to-come (avenir), privileging for this purpose "Lines written near Richmond, upon the Thames, at Evening." [START_REF] Nor Stephen | Dramatic Technique in the Lyrical Ballads." 4 Quotations from Lyrical Ballads are referenced according to William Wordsworth and Samuel Taylor Coleridge, Lyrical Ballads, the 1798[END_REF]

Flowereason

Floraison, in French, means "flowing," "flowering." Yet it contains the letters of the word "reason" (raison). To talk about it imposes a mode that mimes it.

In La différence en partage, the brilliant analysis of rustling noises (DP 202-09), in particular in "The Idiot Boy," with the stunning reading of "burr, burr" 4 ("Barbare [b°r; b°r en grec], parce que s'exprimant par borborygmes ['burr, burr']"

[DP 206]) --to which we'd only like to wedge in the question to which we'll return later: when they link this barbaric sound to the "hoot" (l. 114) and to the "curr" (l. 114) of owlet, why the "hoot" is not heard as who and cure, so important in the poem, the "hoot" returning in Johnny's last words "to-whoo, to-whoo" (l. 460) and the "curr" being the "as if my magic cure" (l. 436) by which Johnny's poetic voice heals the dying Susan Gale, the metalepses ("to-whoo" and "hoot" attesting two agencies, a doubled who [two who-o]) and the echoing ("curr," "cure") being the "intertexture" ("Preface," p. 305) or poetic language which Wordsworth is inventing in the Lyrical Ballads so as to create a poetic agency among citizens --this reading of the noise of "burr" flows out, flourishes, in a crescendo-like concatenation in which we readers hear the "burr" relative to the infant's oral stage, an orality intimately related to the oracle, but also to the aphorism, to a form of horizon, the horizon, almost an oraison or prayer (Porée does not mention oraison, but once he mentions "horizon," he's mimed and mined it 5 ), an oraison in all the irreducible intransivity of a prayer, prayer being, like poetry, its own object, the horizon of form itself, the horizon of oraison.

This horizontal form of the oral oracular oraison, an or-raison (an original reason, the vein or source of "or" as poetic language, or language as irreducibly poetic; the "or" is the "ur", the Ur of "burr" that is called, "tongue of pleasure before the Fall and sin, activated right on the lips of the infans stuck in the oral stage" [DP 208]) gives what Porée, frequently insisting on the profound "mimeticism" here (and Mallarme's or and "mime" are very close 6 ), calls a "savoir de la différence dans la ressemblance" "rejoignant en profondeur le 'savoir different' mis en oeuvre dans les Lyrical Ballads" ["a knowledge of difference in resemblance" "deeply rejoining the 'the different lore' [here, savoir différent, but at DP 198, "connaissance différente"] put into operation in Lyrical Ballads" (DP 209). In a wonderful moment of floraison, of flowereason and éclosion, Porée calls this "different lore" "éclatante sagesse": brilliant, shining, bursting wisdom. Difference in sharing, différence en partage, called by Porée the "perception of the similar [semblable] in objects that are distant," this sheer difference between, say, "ore" and "oar," or between "or" and "ore," is elsewhere in this book La différence en partage called "differance" (with an "a") (DP 239). Like Betty Foy, Poree has "o'er and o'er told" told us "what to follow," and it "o'er and o'er" is, like the final rime in "The Idiot Boy," the "glory" of his (Porée's) "story." To mime and to mine the narrator in the poem here, I (T.D.? 7 ) declare that "Whether" he (Porée) does (tell, write) "in cunning or in joy,/ I cannot tell" (ll. 388-9), for this "or" is "suspended," yet how now can we, now like Betty, not cry out, "Tell us," "mind you tell us true" (ll. 450-51)? But how to hear now this "mind," whose mine is this rich mine of flowereason, of pouring poetic reason, this oraison, how to hear the injunction "mind" when the very word that follows in the poem is the narrator's "Now," "Now Johnny all night long had heard" (l. 452), for "Now" activates, retro-activates all the instances in the poem, let alone in all the poems of Lyrical Ballads, of the word "now," this "now" that, in its working, in the working of its travels, unravels any ownership, this "now" that mines and undermines, releases from the mine the letters n, o, and w, with which the problem of what it is to "own" is so radically raised in Lyrical Ballads? We would read here the function of the word "now" in all of the Lyrical Ballads, as perhaps the key perlocutionary and percussive poetic word, a word that will not be won, because it is not one, "now" that is never simply "now" but always potentially destabilizing the ideology of "own," of "owning" that is everywhere in the Lyrical Ballads, but perhaps nowhere so insistently as in the poem "The Female Vagrant." 8 Mining mental prospects in Lyrical Ballads and in La différence en partage renders vain any making mine when it comes to poetic property. Wordsworth's poetic thinking undoes what is one's "own" by submitting it to the "now" of poetry.

Porée's beautiful reading of "Lines written near Richmond, upon the Thames, at Evening," (DP 199-202) concludes in the suspended still: "Preluding this meditation, this pensivity, an homage in the form of suspense, mixed with immobility and tranquillity (the two meanings of still) on the edge of silence: 'How calm! how still! the only sound,/ The dripping of the oar suspended'." Porée leaves the "oar" suspended, not mentioning the "or." The entire reading points to it, yet he hangs his cleats on an imaginary peg. Can we read in another's shoes, will they fit?

In "Lines written near Richmond, upon the Thames, at Evening," reading ends in suspension: the alternative of the "or" between death and life, between the ghost and presence, between memory and doing, between the past and the to-come.

This poem is about the illusion of presence in their between, the there in between. Yet the poem is constantly haunted by the trace, by the ghost. The poem is about the idea that there could be secured a pure presence, a continuous presence, now. However, the whole poem is shadowed by a kind of absent presence, a devilish mockery. The suspension of thought hangs upon an undecidable "or." This "or" in the "oar" refracts through the entire Lyrical Ballads, turning every occurrence of the sound /or/ into a mirror that is their mimesis.

The poem is an allegory for the movement of the line of poetry and of the progression of the being-perception of the poet. The boat flowing on the river is the poet and the pen tracing their way across the page. (The passing of the river represents a past that is never past.) The drama of the poem depends also upon the "now" of the poem where we (readers or the protagonist) are between the "evening darkness" and the "virtue's holiest powers" (ll. 39-40, p. 147).

A tension, a contradiction, is inscribed at the outset by the line, "The boat her silent path pursues" (l. 4), where the verb of action is deferred, its place inverted with the predicate in which the idea of movement is annulled by its soundlessness. One has to imagine a rowboat, with the poet therefore facing the back of the boat, rowing with his back to the front of the boat cutting through the water. The opening forward creates the flow of a wake that fixes the poet-rower's gaze upon it. The tension is created by the immediate backlash, the reaction to this action, in the appearance of the wake: "And see how dark the backward stream!" (l. 5). The consequence of the forward movement is the backward stream, the trace made by the pursued path. The modality of the future opening is the uniquely backward glance. By being "dark" the backward has something ominous about it, as a word like "following gloom" (l. 10) will indicate, reinforced by its rime, "tomb" (l. 11). This backward movement is the creation of the past, "A little moment past" (l. 6). Indeed, this movement forward is haunted, or seconded, or shadowed, by a mysterious other presence, the "Some other loiterer " (l. 8). The creation of the past that is the receding result of the movement forward -the creation of what is behind us by our broaching, opening, the future -is alluring, enticing, seducing. Its smile ("so smiling!" l. 6) is deceitful, partaking of sorcery. It beguiles ("beguiling" l. 8): like the serpent in Genesis "beguiled me and I did eat." Adam and Eve are lured thus by the devil. The absence of faith ("faithless gleam" l. 7) reinforces the connotation of danger in this godlessness. The word "beguile," used in Genesis for the deceit into evil, is formed on the word "guile," the meaning of which is divination, sorcery: using black magic, evil means, to mimic divine power. Defying any single reading, "And still, perhaps, with faithless gleam,/ Some other loiterer beguiling" (ll. 7-8), the word "still" might be a verb, so that the smiling past, the backward movement of my moving in time (towards a to-come), calm or appease the mysterious "other loiterer"; or, "still" might be an adjective, characterizing the quietness of the lurking other, who is trying to draw back, to hold back, the stillness of those in the boat going forward; or "still" might mean there is yet something more, the "other loiterer" there with his "faithless" attraction or shine, his "gleam," his ever-continuing seducing and beguiling. All these readings of "still" concur, however, in placing behind the forward-moving boat an attraction that would make the person in the boat look back to the "backward stream," obsessed with the past: the idea is of a kind of melancholy or inability to move towards the to-come (save, perhaps, in the mode of retreat).

The "views" (l. 9) of the past "allure" the young poet into a kind of stasis: taking the twilight colours as if they were permanent: "heedless of the following gloom,/ He deems their colours shall endure" (ll. 10-11). The alliteration in "following gloom" and "faithless gleam" force an association of these two combinations. "Gloom," word often paired with doom, is not sufficiently "deem[ed]" by the young poet. The "youthful bard" likes his condition of being deceived ("fond deceit" l. 13). This deceit consists in thinking that the passing moment is static, stable, enduring. It consists in holding on to the immediate past as a form of permanent present, and therefore turning one's back on the necessity to move forward, even if what "may come to-morrow" be "grief and pain" (l. 16).

Nonetheless, the poem and its speaker advocate something else. The poem imagines a perpetual gliding, as if the present could become eternal: as if the course of the river were the course of a "history" that would not at all be historical, but rather a perpetual flow of sameness. This illusion of a permanent present is closely related, however, to a ghostliness. The verb "glide" used four times in the poem (twice in l. 17, l. 21, l. 33) has a strong association with the conventional description of the motion of a ghost. The word "glide" also, by alliteration, is linked to "faithless gleam" and "following gloom." In line 17, "glide" is used in proximity with "other bards" (l. 18), just as "gleam" was used with the shadowy "other loiterer" (8) and as "gloom" was used for "youthful bard" (9). The "glide" movement therefore has something ghostly about it, reinforced moreover by the fact that the poet William Collins mourns the dead poet James Thomson, as indicated by the note to the poem. Collins is of course dead when Wordsworth writes (no one escapes this process of substitution, writing: by writing, I become as Collins to Wordsworth, as Wordsworth to me, as me to you). The third stanza records an apostrophe to the river in the form of an imperative, a wish, a jussive mode practically. May the river glide forever so that visions always visit poets. The wish is for a transformation of the present into the future, but a future that would be an eternal repetition of the present, without (apparently) it seeming to be a repetition. 9 The word "glide" is itself the place for a sliding or gliding between supposedly different entities. The river is requested to "glide" (l. 17, l. 21) so that "our minds" "flow" "for ever" (l. 23) just as the river would "for ever glide" (l. 17), but this equation operating on the words "for ever" transfers the verb "flow," used for the humans but which had substituted for "glide" used for the river, back to the river ("thy deep waters now are flowing" l. 24). The conceit here is that both the flow of the river and the flow of "our minds" reduce to the same movement, sheer difference collapsing into sheer sameness. A transformation.

Strangely enough, no criticism to our knowledge has pointed out the sexual explicitness of this lubricious "gliding," the boat and the oar in the river as a description of vaginal penetration, recorded by the poet witnessing or poeticizing this very action of which he is also the participant. The "rich" "wave" (l. 1) as the opening and closing of the vagina (a wave both opens and engulfs), the poet-rower "facing thus the crimson" (l. 3), or the redness of the opened wake, while his "boat her silent path pursues," making the boat entering the crimson collapse the distinction of penetrator and penetrated. The visual fixation, "see how dark the backward stream!/ A little moment past, so smiling!" (ll. 5-6), is caught in the rhythmic back and forth movement, and the jouissance is marked by the repetition of the climactic exclamation mark ("!") the intensity of which is augmented by the synesthetic vision of what has just been felt while also redoubled by being seen, the present smile at the past motion: "A little moment past, so smiling!" This doubled vision --of participant, yet also of spectator --explains the witness, the third, "some other loiterer" (l. 8), as the person in the action is ghosted by his own perception of the action. The "youthful bard" is "allure[ed]" by "Such views"; he "nurses his fond deceit" that the "colours" of "Such views" never fade, "shall endure" (ll. 9-13). In the moment, one is seduced into thinking that it is so good that it should never stop. But the purpose of the blank space in this second stanza of eight lines, a white space that separates the final three lines from these first five, is to figure the fact that such a moment cannot exist indefinitely, as it is told by the last two lines, "Who would not cherish dreams so sweet,/ Though grief and pain may come to-morrow?" (ll. 15-16). The poem is a celebration of the seeming endlessness of the moment of this sexual pleasure of penetration/being penetrated. It imaginatively exhorts the canal or river to remain forever wet, to "Glide gently, thus for ever glide" (l. 17), so that this rower-poet's vision of its lovely sides, its labia, its wave-lapped banks will come to other poets in the same seemingly gorged satiated orgasmic presence that this poet urges the river on to: "Glide gently, thus for ever glide,/ O Thames! that other bards may see,/ As lovely visions by thy side,/ As now, fair river! come to me" (ll. 17-20). The poet's desire is that the everflowing overflowing profound coming of the river become that coming of all who are in the sensation of its stream, where it is difficult not to see the wish for shared orgasm, shared sheer difference: "Oh glide, fair stream! for ever so" "'Till all our mind for ever flow/ As they deep waters now are flowing" (l. 21, ll. 23-24). If the poet knows, as the entire fourth stanza explains, that such a shared sheer difference is but a "Vain thought!" (l. 25), and that his predecessor Collins became frozen (frigid and non-flowing) from his inability to overcome the grief occasioned by death, by the end of such "pouring" (l. 30), it ends in the poised image of suspended sexual experience, the dripping oar as penis whose ejaculation is initiated, but suspended in a moment of determination to continue, to re-enter the stream, where others have stopped: "as we glide along,/ For him [Collins] suspend the dashing oar" (ll. 33-34), "The dripping of the oar suspended!" (l. 38) --where the exclamation mark now signifies the realization of the scandal of this interruption --"And pray that never child of Song/ May know his freezing sorrows more" (ll. 35-36). In these ways, the poem's reflection upon a permanent presence is inflected by a thinking of sexual difference, the difference of female and male sexuality, figured by the "river" (whore?) and the "poet"('s-oar), by the coming (together) of a certain feminine writing/sexuality and that of a certain male writing/ sexuality. Such transformation is the sharing of sheer difference, wherein river/woman and boat/poet-man are shorn by their mingled touching that shore, a touching that separates them at the same time as it joins the different shores. This transformation, by which the river becomes (in all the weird literariness of this verb) the poet, has partly occurred by and with the last occurrence of "glide": "as we glide along" (l. 33). 10 The human action of rowing (implicit in the poem, for how else would a wake, a "backward stream" be created?) is however never explicitly named, though it is perhaps suggested that more to row -to make more effort ("to-mor[e] row", l. 16), that is, to make effort, to cause "grief and pain" (l. 16) -is even stopped, "For him suspend the dashing oar" (l. 34), reinforced by the metaleptic "dripping of the oar suspended!" (l. 38). Already, the "dashing oar" (l. 34) echoes the "dash of oars" in "Rime of the Ancyent Marinere" (l. 527), made by the band of seraphs. Note that "seraph" denotes a spirit, an angel, but "seraph" is also a gold coin.

The words "as we glide along" suggest an entire conflation of the poet in his boat and the river, but also of the river with former poets. What this transformation entails is that pure presence is thought --conceived, grasped, understood --as thoroughly worked over by ghostliness, by a form of absence in presence or disembodied representation, by a notion of trace. [START_REF]Marc Porée calls this Wordsworth's "préférence pour un lyrisme de la hantise[END_REF] This doubleness, wherein pure presence is apprehended in the wake of spectrality, is manifested by the "for ever" "glide" of the river that is, all the while a seeming eternal present, strongly connoted as ghostly movement (from the associations of "glide," "gleam," "gloom," "beguile").

The fourth stanza acknowledges that the subjunctive wish ("Glide […] that […] may see" ll. 17-18) for continual presence of river and mind in the third stanza is, if fully poetic, rationally empty: "Vain thought!" Yet be that as it may, the subjunctive is repeated: "yet be as now thou art,/ That in thy waters may be seen" (ll. 25-26). If this poem, late in the Lyrical Ballads structured as they are as a movement toward thoughtfulness, calls "thought" "vain," this negative characterization of "thought" attenuates the positive connotation that "thought" progressively gains through the Lyrical Ballads, moving as they are, flowing, towards the thoughtful poem, "Tintern Abbey." However, though the wish for a fusion of river and mind is called empty thought, the subjunctive that follows it contains an important double image of the relation of nature and art, chiasmatically inverting itself, and thus imaging a gliding back and forth of two different things that cease, by the oscillation, to be distinguishable. The lines,

[…] yet be as now thou art, That in thy waters may be seen

The image of a poet's heart (ll. 25-27) confound the distinction between "art" and "heart," between nature and culture. "Art" is a verb used for the river, and "heart" is the capacity to feel of the poet, but the first line could be read as an apostrophe, an address: "be as thou, art." "Now," the river has been fully converted into art, having been the subject of this poem "Lines, written near Richmond, upon the Thames, at Evening" ever since that very title: such lines flow in verse between its blanks like the river water flows between its banks; the line of verse is held in place by the blanks of the Wordsworth poem just as the river is contained by the "banks of the Wye" river in the thoughtful poem, "Lines Written a Few Miles Above Tintern Abbey, on revisiting the banks of the Wye during a tour." Indeed, "thy waters" then means the waters of art, artistic representation of water. In the artistic representation of water, seen is not water but the writer's heart, or, more accurately, the writer's art of water. "Art" glides from denoting the river to naming artistry, and "heart" glides from the poet's talent to a muscle. Both become images of the other. The poet requests that art be as "now," that art be as the "now," as that which is present, alive, yet art cannot be that. Art is really inhabited by ghosts, by the trace, by an avenir itself inhabited by its own being-historical. Not only is art spectral, but any now (present, presence [START_REF]A way to put this would be that the present is the past of the future. We refer to the zigzagging movement and moment that, for Husserl, is the present conceived as both retention (past) and protention (future). Wordsworth's poetry, the flow of its syntax, we submit, narrates this experience. For a reading of protention and retention as zigzag, see Thomas Dutoit, "Upearthing the Field of English Studies: Jacques Derrida's Discourse of Pensées[END_REF] ) is also thusly inhabited.

Repeating like the word "glide," the word "now" is used three times (l. 20, l. 24, l. 25), but, owing to the high number of words with the letters "ow," its echo or ghostly shadow is elsewhere in the poem ("row" l. 16; "bestowing" l. 22; "flow" l. 23; "flowing" l. 24; "how" five times, ll. 28, 37; "know" l. 36). The poem ends on a suspended now: the moment when the oar is suspended, and the prayer is made ("pray that […] may know" ll. 35-36). The suspension of the "oar" is tantamount to how the "or" suspends the poem itself. Ending with the image of "evening darkness gathers round" that is itself waited upon by "virtue's holiest powers," the poem ends with two abstract forces, the former connoted to the devil, to the "other loiterer beguiling," the latter to that power to whom the prayer is, presumably, addressed. Holy and unholy wait, while the "oar" is suspended. By representing the alternative between pursuing a path forward and nostalgically gazing backwards, the poem leaves its reader with what appears as an either-or: darkness or virtue (unholy devil or holy god, art or heart)?

Through the galleries and veins of what is called, in the poem "The Female Vagrant" from Lyrical Ballads, "the mine's dire earthquake" ("Female Vagrant," l. 150, p. 94), the "oar suspended" and the "dashing oar" channel or tunnel the shock waves of an earthquake throughout Lyrical Ballads, an earthquake of literature, an earthquake that is the literary and the poetic in so-called communicative language.

This "ore" of the "or" is capable of, as it is put in "The Female Vagrant," of "shearing time" (ll. 23, emphasis mine), ripping through, nay verily apart, any linear construction of Lyrical Ballads. It rips through the word, through words like "forlorn," "orphan," "roar," "store," "story," "glory," "shore," "lord," and so on, endlessly in abyssal verification and versification. 13 For, in "The Female Vagrant," a "twinkling oar" (l. 9, p. 88) is the "more than mines of gold" (l. 4), more than any "proffered gold" (l. 90). This "oar," associated with the "flood" (l. 3), is infinitely richer than the earth's finite ore. The ore of the gold comes from underground, has to be pulled out of the earth (presumably from a mine owned and operated by the wealthy master who turns up with his "proffered gold"): not the case for the wealth of the woman's father. The father's "boat and twinkling oar" is a different kind of "ore" than the gold (or or in French). This difference between the "oar" and the ore of the gold tells of an alternative in the poem (one kind of wealth against another) that we found in the alternative between "gathering darkness" and "virtue's holiest powers" (at the end of "Lines […] upon the Thames) and its suspended "oar."

This literary "ore" is perhaps, mine de rien, a mime de rien. Representing nothing but the scrambling, the dissemination, of representation, it is the mine of mimesis. We seem to have a "vain belief" in this vein that is so rich and extensive in Wordsworth. This "vain belief" --like the "vain belief" in "Tintern Abbey" (l. 51) that turns the "banks of the [river] Wye" into the seemingly infinite source of the richness of imagination, richer than any monetary Bank of England or World Bank -this "vain belief" gives us to think the "banks of the Wye" in a radically different way than the ontological motivation of asking "Why?", of seeking a traditionally classic notion of truth. Our "vain belief" in the "banks of the Wye" accredits truth in literature: truth-in/as-literature, in the bed under the river, beneath the verity, under the riverity of erasure. This "vain belief" in the literary banks of Why operates according to an other economy, an economy that makes the name of the house into an uncanny, an unheimlich place, to wit, the earth, "earth" sharing the same origin as "ore." 14 This uncanny earth or ore is how literature gives us to experience the world (Welt, monde) in its relation to the earth (Erde, terre). It follows other laws, such as that given in the poem "Anecdote for Fathers," when the boy makes truth by eyeing the "vane" on the top of the house. This "vain belief" is therefore a belief in the emptiness of belief, the vanity or veinity of thought, in other words, it is a belief in mimesis evacuated of any ontological pretensions.

In "Anecdote for Fathers," in response to his father's question of "Why? Why?" ("Why? Edward, tell me why?", l. 48), our five year old, non-adult, and thus non-normal consciousness, makes a "reply" that he snatches from the "house-top" (ll. 49-52, p. 110): "'Why, Edward, tell me why?'/ -there was in sight/ It caught his eye, he saw it plain -/ Upon the house-top, glittering bright,/ A broad and gilded vane" (l. 52). This "eye" is a passive "I," caught by a sight, a "vane" ("vein" and "vain thought"), its gilding gliding into his poetic vision. The question is at least, but the question divvies itself with infinite speed: how stop the post, how spot the stop, how post the tops: "house-stop"? How stop radical dissemination, scrambling, scattering? Try poetry. Try, poet, try.

There is an emptiness here in the boy: it is the emptiness of truth, of truth understood classically as pre-existent, extra-textual, and stable. It is the truth of the "answer" as if the "answer" existed somewhere outside representation. This emptiness of the boy, his pure passivity, and thus receptivity to this sight of the "gilded vane," is what Wordsworth glimpses in the Preface, when defining his language:

The language too of these men is adopted […] because such men [and children] hourly communicate with the best objects from which the best part of language is originally derived; and because, from their rank in society and the sameness and narrow circle of their intercourse, being less under the action of social vanity [my emphasis] they convey their feelings and notions in simple and unelaborated expressions. Accordingly such a language arising out of repeated experience and regular feelings is a more permanent and a far more philosophical language than that which is frequently substituted for it by Poets. (p. 290)

The "vane" is the pure poetic passivity by which the socially "vain" is undone. The passivity of the boy is not the "action" of "social vanity"; the child's language is a "more permanent and far more philosophical language" precisely by being utterly aleatory: its permanence and its philosophy consist in its unpredictability, its lack of predication prior to its actual, passive, diction. This passive diction is what Wordsworth substitutes for the "poetic diction" (Preface) that he sees being used as false substitute by over-active Poets. It is the "wise passiveness" (l. 20) that the passive poet William in the poem "Expostulation and Reply" posits as that which makes it possible that "things for ever speak," as long as one de-activate thought which seeking ontological truth. This "wise passiveness" is Why's/ Wye's passiveness. [START_REF]Cette 'pathologie' a d'ailleurs le sens éthique profond d'une chute dans la 'passivité', d'une incapacité à se rendre 'responsable' du sens dans une activité ou une 'réactivation' authentiques. L'activité technique -celle de la science aussi -en tant que telle, est une passivité au regard du sens ; elle l'agitation du malade et , déjà, le tremblement d'un délire[END_REF] The "vane" defies, belies, the "vain thought" from "Lines written near Richmond…" (l. 25) that here applies to the father who thinks that the truth, the answer, and responsibility, are the possession of a conscious, normal, adult's activity. value to lying, that assigns lying neither to Christianity-as-truth (morality) or homoîosis-as-truth (ontology). 18 The art of lying may thus be taught. But it's time, l'heure, to stop this exploration of Wordsworth's /orz/. To conclude, we can say, of this operation of "or" in Wordsworth: but this is what Mallarmé did! 19 The statement needs to be turned around. What Mallarmé did, Wordsworth already had done. In this way, I submit that Wordsworth is the advent of a poetics that will flourish in Mallarmé, and that to read Wordsworth, one must be alert to this poetics. But I am poorly armed to make this argument, not having the competence in Mallarmé. One will say I am playing with words. Yet I would rather play with them than make war with them, or even use them. Marc Porée is alert to this play; in the deed of his writing he displays it. But he does much more than just this jeu, because he opens it to both its joy and its cunning, in their oscillating imbricating sheer differance. Such differantial reading, flush with a differantial writing, are literary. They attest a poetic thinking, a poetic memory, a memory of thought and thought of memory, to forget which denies literary history any chance of being historical.

aujourd'hui ont à donner une leçon politique à ceux qui en ont besoin sur la question de la langue et de la nation," p. 87. 18 Cf. J. Derrida, "Histoires du mensonge," Cahiers de l'Herne. Jacques Derrida,here p. 517. 19 "Autre veine --à suivre l'or colore l'heure de tous les couchers [...] de Mallarmé." J. Derrida, "La double séance," in La dissémination (Paris: Seuil, 1972 [1969-70, first publication]), p. 321. The "or" (say, between the diabolical and the good ghost) instances undecidability: given a system of axioms, undecidable is when a proposition is neither an analytical consequence from axioms, nor a contradiction with them, this undecidable is not because of some enigma, some mystery, some content. Rather, it is made by the formal and syntactical; syntax is the law of pivoting, of alternative, of undecidability, and Derrida isolates the unit "or" as a very rich "alliage," allied metal, of this. What is important is the syntactical positioning of a word, where placement in syntax is what determines the word, not its semantic content. The undecidability is not the hidden depth of some "content"; the undecidability is the result of location on a sort of horizontal plane (there's something Saussurean in this definition of undecidability, like his saying "meaning" of a word is not in the word but in its relations to other words that it is not). Intelligibility is not unique meaning; intelligibility is the syntactic relationality, textuality. Intelligibility of Wordsworth that does not take stock of veins such as "ruth/root" or "ore, or, oar" is not at all intelligible, is missing almost the entirety of its poetic dimension, that is, its textual, written and spoken, dimension. If this insistence upon syntax is claimed to be, or dismissed as being, ahistorical or formal, then it will be necessary to accept also the annihilation of the unconscious, and accept a notion of history that does without the unconscious, the so-called ahistoricism or non-temporality of the unconscious. A literary historicism that evacuates this complex unconscious history is itself ahistorical and unliterary. Cf. Mallarmé Les mots anglais (1052-53) on "or," as monosyllable (by itself), as agglutination (combined with other letters in a word, like "W-or-dsw-or-th") and as flexion (distributed in a word, like "o-a-r").

  The mental prospects given to readers in La différence en partage are innumerable; in this study, I shall explore only one, under the heading of what I call "flowereason," in the wake of what Bonnecase and Porée refer to as floraison (DP

That is to say, the "vane" short-circuits the "vain thought," that thought of normative adults that presupposes a pre-existent foundation, itself the basis of the classical philosophical (Cartesian, Kantian) subject. 16 This "vane" counters the bleeding caused by a society that requires ever more payment, ever more ownership, ever more control, despite and even because of the inability of some to maintain such an economy. In the poem "The Last Flock," "it was a vein that never stopp'd,/ Like blood-drops from my heart they dropp 'd" (ll. 63-64, p. 125). That "vein" is opened, bleeding to death the owner of the sheep, as each sheep is extracted from him, from his "heart." "The Last Flock" recounts how an ownership society makes the sheepherder "owe" so much that he can own nothing, not even his "own children" that he envisions slaughtering to sell as food (l. 82) in this now ("now," l. 39). This-now, his present that disappears as fast as melting "snow" (l. 59, l. 90), is reduced to a repeating "woeful day" (l. 70), as his flock, "they dwindled, dwindled, one by one" "they dwindled one by one" (l. 60, l. 66), so that the marketplace won as he loses and dwindles. The many suffering people in Lyrical Ballads cry out "O woe is me" ("The Thorn," "The Mad Mother," "The Female Vagrant," etc.); the poet tries to respond with song that approaches the "owlet" (in "The Idiot Boy," l. 3) whose "curr" (l. 114) is, through the effort of poetry, through a revolution or inversion making the "owlet" into the palindrome of a poetic "tel(l) wo(e)," the poetic "magic cure" (l. 436) that, for the Wordsworth of 1798-1802, might have the might to transform, in a deferred "now" (deferred, to come), society based on the idea that even language itself can be owned (controlled, managed, marketed), won and one. [START_REF]Ce sont eux qui ont à expliquer, à enseigner, qu'on peut cultiver et inventer l'idiome, parce qu'il ne s'agit pas de cultiver un idiome donné mais de produire l'idiome[END_REF] The "vane" of the five year old is therefore a different "lore," a different learning and a different reading. The father's trying to force the child risks teaching the child to lie. The subtitle of "Anecdote for Fathers" is "shewing how the art of lying may be taught." Yet, given the positive connotation of "art" throughout the Lyrical Ballads, is it not possible to take the "art of lying" as saying something about "art," and not thinking "lying" under the two conventional dogmas, namely "truth" as positive value and "honesty" as moral value? If it is possible that je me trompe, that I make mistakes but also that I lie to myself, irreducibly, ineluctably, that I make mistakes accidentally but lie to myself on purpose, yet, vice versa, that I make mistakes on purpose and lie to myself unconsciously, then a different thinking of lying would be necessary, one that does not presuppose a negative or unnecessary