Anh Tuan Tran

François Huet
email: francois.huet@upmc.fr

Kieu Ngo

Philippe Rousseau

A.-T Tran

Influence on the electrolyte resistance of the contact angle of a bubble attached to a disk electrode

Keywords: Two-phase systems, Electrolyte-resistance fluctuations, Contact angle, Collocation method, Gas evolution

In a previous work, the analysis of the electrolyte-resistance (ER) increment due to the presence of an insulating sphere above or in contact with a disk electrode, simulating a spherical particle, drop, or gas bubble close or attached to an electrode has been reported [Bouazaze et al., Electrochim. Acta 55 (2010) 1645]. In the present work, the influence on the ER of the contact angle with the electrode surface, which plays for example a major role in the size of bubbles on gasevolving electrodes, is quantitatively determined. The mathematical collocation method used in the previous work was improved to account for the change in geometry of the electrode-sphere system.

The theoretical results show that the ER increment due to the presence of the sphere depends on its size, position, and contact angle. For a given size and position of spheres of aspect ratio less than 0.4, the ER increment due to the contact angle varies roughly between -45% and +35% of the increment due to a perfect sphere, depending on the interplay of the surface and volume competing effects influencing the ER. Despite their low values, the ER increments could be experimentally measured for spheres of different contact angle placed at the electrode centre, owing to a highprecision motorized translation stage and a specific low-noise ER measurement device. An excellent agreement was obtained between the theoretical and experimental results.

Introduction

Formation of electrolytic bubbles is encountered in many industrial electrochemical applications because gas molecules are often generated from electrochemical reactions. This phenomenon has important implications because a part of the active electrode surface is screened by the attached bubbles, which affects charge, mass, and heat transfers at the electrode/electrolyte interface. The screening effect of electrolytic bubbles and the influence of the contact angle of attached bubbles, defined as the angle between the liquid-gas interface and the electrode surface, have been studied in several papers. For example, the modification of the primary distribution of potential and current lines (ohmic effects) due to the presence of a single spherical bubble attached to an infinite plane electrode has been analytically derived by Sides and Tobias and the incremental electrical resistance was calculated for a sparse array of spherical bubbles [1]. The electrode current density, which is quite negligible on a small area around the contact point, was found to approximately apply for nearly spherical bubbles having a contact angle lower than 17.5°. This analysis was later extended to bubbles making arbitrary contact angle with the electrode by Wilson and Hulme [START_REF] Wilson | Proc. R. Soc. Lond. A[END_REF]. Dukovic and Tobias studied the effects of attached bubbles on the local distribution of current and on the potential drop at the electrode [START_REF] Dukovic | [END_REF]. In addition to the increase in electrical resistance (ohmic effects), their model shows an increase in the surface overpotential due to the masked electrode area that increases the local current density, and a decrease in the concentration overpotential due to decreased local supersaturation near the bubbles. All these parameters have been shown to depend on the contact angle of the bubbles with the plane electrode.

The screening effect of attached electrolytic bubbles was also studied by Vogt et al. who introduced the bubble fractional coverage factor, defined as the area screened by the normal projection of the bubbles on the electrode surface. They showed this factor strongly depends on the electrolysis current density for both stagnant [4] and flowing [5][6] electrolytes. However, these authors neglected the influence of the contact angle when its value is lower than 90° (wetting electrolyte), considering that the actual current density on the shaded area below the attached bubbles is small.

Several authors have tried to take into account the influence of the contact angle on bubble growth rate, detachment diameter, and population density on the electrode, and to predict its dynamic variation at different stages of bubble evolution (nucleation, growth, and detachment).

Trieu et al. studied hydrogen evolution formed by formaldehyde oxidation during electroless copper deposition on a vertical wall [7]. They theoretically showed the dependence of the side contact angle and bubble detachment radius and observed experimentally that the smaller the contact angle, the larger the evolving bubbles, which strongly affects the quality of the product plate.

Buehl and Westwater studied the effect of contact angle on the growth rate of bubbles in water supersaturated with carbon dioxide [8]. Their theoretical work and photographic observations of bubbles coming out from an artificial site drilled on a horizontal wall concluded that the effect of contact angle on bubble growth rates was small for contact angles between 0 and 90 degrees, even if the contact angle changed during bubble growth. Baum et al. studied the influence of the attachment of hydrogen bubbles produced during the etching of Si (100) in aqueous KOH on the surface roughness of microstructures [9]. Indeed, these bubbles are one of the causes of the formation of pyramids on the Si surface. They showed that the decrease in contact angle of the attached bubbles due to alcohol or oxidizing agent addition improves the surface finish.

Gas evolution may also be studied using the electrochemical noise technique, which consists in measuring the potential or current or electrolyte resistance fluctuations generated by the growth and detachment of bubbles, in order to derive the size and departure rate of bubbles. Despite the ability of the technique to monitor gas evolution in real time, very few studies have been reported in the literature on this topic. Gabrielli et al. showed that the mean departure rate, the mean radius of detaching bubbles, and the gas evolution efficiency can be derived from the spectral analysis of the potential or current fluctuations [10]. Hodgson showed that the influence of various electrocatalysts on the departure rate of chlorine bubbles evolving on ruthenium-titanium oxide anodes could be monitored by current noise measurements [11]. Compared to the analysis of the potential or current fluctuations, which depend on several factors (ohmic, activation, concentration of dissolved gas) [START_REF] Dukovic | [END_REF]12], the analysis of the fluctuations of the electrolyte resistance (ER) measured between the reference electrode and the working electrode is easier since only ohmic effects are concerned.

Owing to the experimental set-up described in Ref. [13], Huet et al. simultaneously measured potential and electrolyte resistance (ER) fluctuations due to oxygen bubbles detaching from rough and porous horizontal Ni electrodes and showed that the size of detached bubbles depends on the electrode surface roughness [14]. Volanschi et al. studied the influence of various surfactants on the dynamic surface tension, which plays a significant role on the size and departure rate of evolving bubbles, from the simultaneous measurement of potential and ER on microcavity electrodes in aqueous solutions [15]. Benzaïd et al. also measured the ER fluctuations generated by hydrogen bubbles on cylindrical vertical carbon steel tensile specimens under cathodic polarisation [16].

However, their simplified model of the power spectral density of the ER fluctuations gave characteristic parameters of the gas evolution in only qualitative agreement with optical observations because of the complicated screening and dragging effects of rising bubbles for vertical electrodes.

In order to improve the theoretical models, it is necessary to quantify the effect of a bubble above or attached to a plane electrode of finite size on the ER. In a previous work, the ER increment due to the presence of an insulating sphere in contact with a disk electrode was calculated with the collocation mathematical method [17]. This configuration "single sphere -electrode" simulating a frozen bubble is the basic case in the study of gas evolution and can also find interest in other fields, such as when tracking the position of a moving spherical particle in a flow-channel [18]. However, only bubbles of contact angle equal to zero were concerned up to now. To extent the previous study, the influence of contact angle of an insulating sphere sitting at any position on a disk electrode is investigated in the present paper.

Theoretical treatment

The mathematical collocation method used to calculate the distribution of the potential  in the electrolyte when an insulating sphere simulating a bubble with a zero contact angle lies on a disk electrode has been detailed in Refs. [17,19] and is summarized in Appendix A. This method applies as well when the contact angle  of the bubble is different from 0. In that case, the bubble is simulated by a sphere cut off by a plane. Fig. 1 shows the notations used in this paper. The centre of the disk electrode of radius a e is the origin O of the Cartesian coordinate system (x, y, z) and the centre O' of the sphere of radius a p corresponds to the point (x 0 , 0, z 0 = a p cos ), where  is the contact angle of the truncated sphere, as defined in Fig. 1.

Once the coefficients A nm and C nm of the series expansion of the potential distribution in the electrolyte are determined (Appendix A), the ER can be calculated from the ratio of the potential  0 applied to the surface of the electrode and the current I flowing across the electrode, which is obtained by integrating the current density on the electrode

0 ) / (      z z
, where  is the electrolyte conductivity. The following expression of the ER is obtained for a sphere ( = 0) sitting on the electrode; it only depends on one coefficient (A 00 ) of the series expansion of the potential, which is a purely imaginary complex number (see Appendix D in Ref. [17]):

00 e 0 0 e 2 A j a I R       (1)
For a truncated sphere (  0), the derivation of the ER is more involved. Indeed, there is no analytical expression of the current I flowing across the electrode, in contrast with a perfect sphere, so that the current density must be numerically integrated on the electrode area not blocked by the sphere. When the truncated sphere is centred on the electrode axis, the expression of the ER depends on all coefficients A n0 of the potential series expansion but the numerical calculations are relatively simple. When the sphere is not centred, these calculations are much more complex and some convergence problems arise, especially when the sphere approaches the electrode edge. The convergence of the calculations was ensured for x 0 < a ea p sin , that is, when the disk below the truncated sphere lies entirely on the electrode surface, at least for the largest spheres considered in this work (a p /a e = 0.4 or 0.5).

The ER change due to the presence of the sphere was compared to the value of the theoretical ER of the disk electrode in the absence of the sphere, which is given by Newman's formula when the counter electrode is at infinity [20]:

e N e, 4 1 a R   (2)
To compare the contribution of spheres of different sizes and located at various positions on the electrode, the ER variation was normalized:

N e, N e, e norm e, R R R R    (3)
and the dimensionless radial position, X 0 , of the sphere centre was introduced: e 0 0 a x X  (4)

Case of a perfect sphere ( = 0)

As an example, Fig. 2 shows the normalized ER increment R e,norm due to the presence of an insulating perfect sphere in contact with a disk electrode at any radial position x 0 on the diameter y 0 = 0 of the electrode [17]. The two peaks, which are obtained for small spheres (a p /a e < 1), are due to the fact that the current lines are more importantly blocked at the electrode edge (X 0 = 1) where the local primary current density is higher. Despite the low values of R e,norm (maximum of 0.3% for a p /a e = 0.1 and 1.2% for a p /a e = 0.2), the experimental values of R e,norm measured in Ref. [17] were in excellent agreement with the calculated values in Fig. 2.

Case of a truncated sphere (  0)

In a first part, the truncated sphere is positioned at the centre of the disk electrode (x 0 = 0, y 0 = 0) where its influence on the ER is the lowest, according to Fig. 2. The ER increment, R e,norm , due to the truncated sphere is compared to that of a perfect sphere (= 0) by introducing the ER increment in percentage, R e,% , defined as follows :

100 ) 0 , 0 ( ) 0 , 0 ( ) , 0 ( ) , 0 ( 0 norm e, 0 norm e, 0 norm e, 0 e,%              X R X R X R X R
(5) Fig. 3 shows the values of R e,norm and R e,% for five aspect ratios a p /a e of the sphere and contact angles ranging between 0° (perfect sphere) and 90° (hemisphere). The R e,norm values at the electrode centre show a significant dependence on the sphere size (less than 0.1% for a p /a e = 0.1 and around 5.0% for a p /a e = 0.5) and weaker variations with the contact angle. For small spheres (a p /a e  0.2), R e,% is negative (for example, -5.9% for  = 40° and a p /a e = 0.1) regardless of the contact angle. For larger spheres, R e,% is positive for small contact angles (for example, +3.5% for  = 40° and a p /a e = 0.4) and negative when the contact angle increases ( > 62° for a p /a e = 0.4). For an hemisphere ( = 90°), R e,% is negative whatever its size, with a much larger variation for small hemispheres (-43.4% for a p /a e = 0.1 against -14.6% for a p /a e = 0.5). Two opposing effects have to be considered to explain the results: i) a surface effect: no current line can flow across the electrode surface under the truncated sphere, which increases the ER;

ii) a volume effect: the volume of a truncated sphere is smaller than that of a perfect sphere of same diameter, so that the current lines are modified on a smaller vertical distance; moreover, they rearrange more favourably around the foot of the sphere. Both effects decrease the ER.

For small truncated spheres, despite the fact that the surface area blocked under the sphere represents a large part of the projected surface of the sphere when it has a high contact angle (sin 2  = 41% for  = 40°), the R e,% value is less than that of a perfect sphere, indicating that the volume effect is dominant. This is because very few current lines reach the electrode below a perfect sphere when it is positioned at the centre of the electrode. The R e,% decrease with increasing  observed for small spheres disappears for bigger spheres, indicating a more important surface effect, up to a limiting value of contact angle ( = 63° for a p /a e = 0.4), from which the volume effect becomes dominant again. For the hemisphere ( = 90°), the volume effect is clearly dominant for all spheres, the effect of the rearrangement of the current lines above the hemisphere being more important than that caused by the blocking of the electrode surface by the hemisphere. The R e,norm values in Fig. 4a are obviously more important for the large sphere and increase with the distance X 0 to the electrode centre because the primary current density increases as well.

For the hemisphere of aspect ratio 0.4, the R e,norm values are almost twice higher at the electrode edge than at the electrode centre. Fig. 4b shows the R e,% values and allows the volume and surface effects identified above for a sphere positioned at the electrode centre to be compared. For the small sphere with a contact angle of 60°, the volume effect (R e,% < 0) observed at the electrode centre is still predominant when the sphere is moved towards the electrode edge up to a position X 0 = 0.7 (X 0,lim = 0.83) where the influence of the blocking of the strong current lines by the truncated sphere becomes significant. For the bigger sphere (a p /a e = 0.4), the surface effect is preponderant at all positions X 0 of the sphere of contact angle 41.4°. In contrast, for the larger contact angles, the volume effect predominates when the sphere is located near the electrode centre while the surface effect dominates at a position X 0 > 0.32 (X 0,lim = 0.625) for the sphere of contact angle 69.5° and X 0 > 0.55 (X 0,lim = 0.6) for the hemisphere.

Experimental

A glass crystallizing dish of 21 cm in diameter and 10 cm in height was used as an electrochemical cell (Fig. 5). The working electrode was the cross-section of a 1 cm in diameter stainless steel rod embedded in an epoxy resin and mounted flush in a polymethylmethacrylate holder. The electrolyte was a 0.1 M Na 2 SO 4 solution prepared with deionised water. A large graphite foil flattened against the wall of the crystallizing dish was used as a counter electrode. A potential difference of -300 mV was applied between the working electrode and the counter electrode with a home-made potentiostat in a two-electrode cell configuration. The maximum DC current flowing through the cell was 2 A. A sinusoidal voltage signal, v hf , of 100 kHz and amplitude of 50 mV was superimposed on the DC voltage of the potentiostat to measure the ER variations, R e . The sine wave current response, v hf /R e , at frequency f hf was amplified, rectified with a diode, and low-pass filtered with a cut-off frequency of 10 Hz, by using a home-made electronic device [13,21]. The amplitude of the voltage output signal, v R e , obeyed the following relationship:

d R b v R   e 1 e (6)
The parameters b and d were determined through a calibration procedure in which the electrochemical cell was replaced by pure resistors. From Eq. 6, the mean value of the ER, R e , could then be calculated from the mean value of v R e during the electrochemical experiments. For example, the ER mean value in the absence of sphere was R e = 33.8 . In addition, the variations of the ER, R e , could be derived from the measured variations v R e , with the equation:

e 2 e e ) 1 ( e R R b R b v R       (7)
obtained by differentiating Eq. 6 for ER variations of small amplitude.

Alumina spheres of 2 and 4 mm in diameter and excellent sphericity (Ceratec, The Netherlands) were used. Some of them were polished by the manufacturer to remove 0.1 mm, 0.5 mm, and 1 mm for the 2-mm-diameter spheres, and 0.5 mm, 1.3 mm, and 2 mm for the 4-mmdiameter spheres, so as to obtain truncated spheres of different contact angles (25.8°, 60°, 90° for the 2-mm-diameter spheres of and 41.4°, 69.5°, 90° for the 4-mm-diameter spheres). Using a stereo microscope, the spheres were carefully glued to the tip of a glass rod of about 100 µm in diameter, as shown in the scanning electron microscope (SEM) images in Fig. 6 for a perfect sphere of 2 mm in diameter and a hemisphere of 4 mm in diameter. The experiments were performed at room temperature. The position of the sphere was controlled with a three-axis linear translation stage (Newport, VP-25XA) and driven by an ESP300 motion controller (Newport) allowing a 25 mm range motion of the glass rod holding the sphere with a 100 nm resolution in the three directions.

Complementary information on the experimental set-up, measurement conditions and procedures may be found in Ref. [17].

In this work, the influence of the contact angle of the sphere on the ER was investigated for spheres located at the centre of the electrode because it was difficult to position the spheres far from the electrode axis at a very precise radial distance X 0 , a parameter that has a strong influence on R e,norm , according to Fig. 2 Although the values of R e,norm are lower at the electrode centre, they present a minimum at X 0 = 0 and the influence of X 0 could be negligible there.

Results and discussion

Case of perfect spheres

Because of the elasticity of the glass rod, it was difficult to know exactly when the sphere was in contact with the disk electrode. The procedure described in Ref. [17] was used. Under visual control, the sphere was first positioned above the electrode centre and the parameters x and y giving the lateral position of the sphere were set to 0. Then, the sphere was scanned above the electrode in the x direction (y = 0) and the v R e variations were measured during forward and backward scans performed after progressively approaching the sphere to the disk electrode. As shown in Fig. 7a, the 2-mm-diameter sphere was in contact with the disk electrode since discrepancies can be observed in the v R e values of the first part of the backward scan and the second part of the forward scan. These discrepancies, due to the friction of the sphere with the electrode surface, disappeared when the sphere was raised at a height h = 3 µm above the electrode (Fig. 7b), so that the forward and backward v R e curves overlapped quite well.

The coordinates of the sphere and the v R e variations must be converted to the dimensionless units presented in the theoretical section in order to compare the theoretical and experimental results. The parameters X 0 and H give the normalized lateral position and the distance of the sphere above the electrode, respectively:

where x and z are the lateral and vertical coordinates given by the translation stage while x c and z c are the coordinates of the electrode centre. On the other hand, the dimensionless increment of the ER due to the presence of the sphere, R e,norm , is derived from the v R e values and Eqs. 6 and 7:

B v d v G v R R R R R R e e e e e norm e,          with ) ( e d v G B R   ( 9
)
where the factor G is the gain of the amplifier used in some experiments to improve the measurement accuracy of v R e , after elimination of the v R e DC component. Finally, to eliminate the DC level of about 0.48 V in Fig. 7 and take into account a possible tilt of the baseline (not observed in Fig. 7) due to a slight default in the horizontality of the electrode or to a linear drift in temperature that sometimes occurred, two new parameters,  and , have been introduced in the following expression:

B x v R R ) ( e norm e,       (10)
In summary, for each scan of the sphere in contact with the electrode, the R e,norm values were calculated from the raw v R e values after determining the four parameters x c , B,, and  by fitting the v R e (x) experimental curve to the theoretical curve R e,norm (X 0 ,  = 0) with the simplex algorithm.

In Fig. 7, the following values were measured: v R e = 0.481 V, d = -33 mV, which gives a B value of 0.514 V with G = 1. Fig. 8 shows the fit obtained between the experimental curve of the forward scan presented in Fig. 7a and the theoretical curve R e,norm (X 0 ,  = 0) presented in Fig. 2 for the sphere size a p /a e = 0.2. The excellent agreement between the two curves, obtained with a fitted value B = 0.543 V close to the expected value (relative error of 5.6%), validates the methodology used for measuring small variations of R e,norm (less than 1.2%) during the scan of the sphere.

Case of truncated spheres

The above method to ensure the contact between the sphere and the electrode was not appropriate for truncated spheres. Indeed, the contact area on the electrode is much greater than for perfect spheres, so that the glass rod broke during the forward and backward scans of the truncated spheres because of the important friction and a possible inclination of the electrode surface. A new method had to be developed in this work. The truncated sphere was firstly positioned above the electrode centre by measuring the v R e signal during successive scans of the sphere in the Ox and Oy directions without touching the electrode. The minimum value of v R e corresponds to the electrode centre above which the truncated sphere was placed before being moved down toward the electrode. Fig. 9a presents the v R e variations as a function of the vertical position z during the descent and rise of a 2-mm-diameter sphere above the electrode centre (z decreased when the sphere went down). The two curves are almost identical, the slight differences coming probably from slight variations in the electrolyte temperature during the experiment. The ER increased when the sphere approached the electrode because the current lines were more strongly deviated under the sphere. When the sphere touched the electrode, the v R e signal became erratic while the glass rod was still going down (z decreased) without breaking because of its elasticity. This is not obvious in the enlarged view of the approach curve shown in the inset of Fig. 9a because of the fluctuations observed on this curve. However, it will be clearer on the approach curve of truncated spheres, as shown below, and this will allow the vertical position z c at which the sphere was in contact with the disk electrode to be determined. Since the disk electrode and the plane of the truncated sphere were polished and because the elasticity of the glass rod could force the whole plane surface of the truncated sphere to touch the disk electrode, the quality of the contact between the sphere and the electrode was considered to be good. It must be noticed that this method is the only one that can be used for truncated spheres that cannot be scanned in contact with the electrode without breaking the glass rod. Also, performing measurements at only one point of the electrode, here the electrode centre, gives the advantage of being less dependent of the horizontality of the electrode surface. At last, there is no need to position the sphere exactly above the electrode centre before measuring the approach curve since the v R e (x) curve passes through a minimum at the electrode centre. mV, and B = 22.82 V. This B value was close to the expected value (relative error of 0.8%). This, together with the excellent agreement between the experimental and theoretical curves, validates the measurement of the low values of R e,norm (less than 0.5%) when the sphere approaches the electrode.

The influence of the contact angle of the sphere on the ER is now analyzed. Fig. 10a presents the v R e variations induced by the vertical approach of a 2-mm-diameter sphere (a p /a e = 0.2) of contact angle 0° (sphere), 25.8°, 60°, and 90° (hemisphere) above the electrode centre. The z distance corresponds to an arbitrary origin of the positioning device so that the contact point on the electrode did not correspond to the same z value for each experiment. Fig. 10b shows the normalized ER increment R e,norm as a function of the dimensionless height H of the sphere. These curves were calculated from the raw data in Fig. 10a, using Eq. 9 with a B value of 22.82 V and Eq.

8 to derive H from the z and z c values. It should be noticed that the theoretical approach curve was not available for the truncated spheres to fit the experimental v R e (z) curve and determine the vertical position z c where the sphere touches the electrode. As explained above, z c can be taken as the position where the v R e signal became erratic at the time the sphere touched the electrode while the glass rod was still going down because its elasticity. This is clearly shown in the inset of Fig. 10a for the hemisphere. The distance between two successive z values in the approach curve was 25 m so that the error on z c could be estimated to be about 10 m.

Fig. 10b shows that when a sphere of any contact angle was far above the electrode centre (H > 2), R e,norm was close to 0. In other words, a sphere of 2 mm in diameter (a p /a e = 0.2) located at a height twice larger than the electrode radius (5 mm) has no influence on the ER. When the sphere is in contact with the electrode centre, the R e,norm value was low, ranging from 0.27% to 0.42% depending on the contact angle of the sphere. It must be noted that the maximum value of R e,norm did not correspond to the contact position at the electrode centre; it was obtained when the sphere was slightly above the electrode centre, for example at a distance H max  0.1 for the truncated sphere of contact angle 60° and H max  0.13 for the hemisphere. For perfect spheres, the effect is much less pronounced but it was already observed in Ref. [19] (the down-pointing arrow in Fig. 3 shows the maximum of resistance increment). This phenomenon can be explained by the rearrangement of the current lines according to the position of the sphere. When a truncated sphere of high contact angle is located slightly above the electrode, the electrode surface under the sphere is not very active because very few current lines can reach the electrode surface through the thin electrolyte layer below the sphere, so that the surface effect on the ER is almost the same as when the sphere touches the electrode. In contrast, the volume of conductive electrolyte above the sphere that has been replaced by the insulating sphere and the rearrangement of the current lines around it lead to an increase in the ER (volume effect). At a distance higher than H max , the electrode surface under the sphere becomes more active because the current lines can reach the electrode more easily.

The surface effect on the ER decreases while the volume effect is not changed, which explains the decrease in ER observed. The R e,norm maximum value was observed at lower values of H max for the truncated spheres of small contact angle (for example, H max  0.04 for  = 25.8°), and this maximum value was much closer to that at H = 0, because the electrode surface screened by the sphere was narrower, which limited the rearrangement of the current lines when the sphere was moved slightly above the electrode centre.

The results concerning the 4-mm-diameter (a p /a e = 0.4) truncated spheres of contact angle 41.4°, 69.5°, and 90° are presented in Fig. 11. The v R e variations induced by the vertical approach of the sphere above the electrode centre were measured with an amplifier of gain G = 10 and are given in Fig. 11a while Fig. 11b shows the normalized ER increment R e,norm as a function of the dimensionless height H. Obviously, the R e,norm values were higher (between 2% and 3%) than those of the 2-mm-diameter spheres because of a more important screening of the electrode surface.

As for the smaller spheres, the maximum values of R e,norm were obtained when the spheres were slightly above the electrode (H max  0.09 for  = 69.5° and H max  0.15 for the hemisphere).

To compare the theoretical and experimental results, the experimental values of R e,norm (X 0 = 0,) for each truncated sphere of contact angle  placed at the electrode centre were used to determine the ER increment in percentage, R e,% , of the R e,norm (X 0 = 0, 0°) value for a perfect sphere also placed at the electrode centre (Eq. 5). Table 1 summarizes the theoretical and experimental results for the spheres of 2 mm and 4 mm in diameter in contact with the electrode centre (H = 0) and Fig. 12 presents the theoretical variations of R e,% as a function of the contact angle (Fig. 3b) and the experimental R e,% values given in Table 1. The excellent agreement between the theoretical and experimental values allows validating the methodologies used in this work, both in the modelling part and in the experimental measurements.

Conclusions

This paper is an extension of previous works aimed at improving the analysis of the electrolyte resistance (ER) fluctuations generated by spherical insulating entities (gas bubbles, droplets, solid particles, etc.) passing close or attached to a disk electrode. In the study of gasevolving electrodes, the contact angle of bubbles with the electrode surface plays an important role on the size of the evolving bubbles. In the present work, the influence of the contact angle of spheres on the ER is investigated.

The mathematical collocation method allowed determining the ER increment due to the presence of a single sphere of any contact angle located at any position on the surface of a disk electrode. Low values of the ER increment were found for a sphere located at the electrode centre, R e,norm varying from 5% for a large sphere (a p /a e = 0.5) to less than 0.06% for a small sphere (a p /a e = 0.1). These values increased by a factor less than 2 that depends on the contact angle when the sphere was moved towards the electrode edge. For the sphere sizes investigated, the ER increment of a truncated sphere, R e,% , varied between -45% and +35% of the ER increment due to a perfect sphere. These variations, which depend on the size of the sphere, its lateral position on the electrode, and its contact angle, could be explained by the interplay of two competing effects

                                     0 0 2 p 2 p m n 1 n 2 p 1 p 1 p m n 1 n 1 p nm 0 even 0 e e m n e m n nm p e ) cos( ) (cos ) cos( ) (cos ) cos( ) (cos ) sinh ( ) , , ( n n m n n m n m m P m P C m P j Q A z y x (A5)
where j is the square root of -1 and m n P and m n Q are the Legendre functions of degree n and order m (m  n) of the first and second kind, respectively. This solution satisfies the simplest boundary conditions at infinity, Eq. (A1), and on the insulating plane, Eq. (A3). The coefficients A nm and C nm of the series expansion must be determined so that the boundary conditions on the metallic electrode, Eq. (A2), and on the insulating sphere, Eq. (A3), are satisfied. The method consists in choosing a certain number of points on the sphere and on the electrode and enforcing the boundary conditions at these points on the electrode:

    0 0 0 2 p 2 p
                             n n m n n m n m m P m P C m P j Q A (A6)
and on the sphere:

    0 ) cos( ) (cos ) cos( ) (cos ) cos( ) (cos ) sinh ( 0 0 2 p 2 p m n 1 n 2 p 1 p 1 p m n 1 n 1 p nm 0 even 0 e e m n e m n nm                                 n n m n n m n m m P m P n C m P j Q n A (A7)
The calculation of the coefficients A nm and C nm was performed with maximum values of degree n and order m, n max and m max , typically around 50 and 35, respectively. In that case, the number of points on the electrode and on the sphere was about three times the number of values A nm and C nm to be determined. Obviously, only a finite number of coefficients A nm and C nm were determined (see Appendix C in Ref. [17]). The potential  could then be calculated at any point (x, y, z) in the solution.

For a truncated sphere (contact angle  different from 0), the expression of the potential distribution (Eq. A5) is still valid if the angles  p1 et  p2 are now ranging between 0 and - instead of 0 and . The coefficients A nm and C nm are still calculated with the boundary conditions on the electrode (Eq. A6) and on the sphere (Eq. A7), the points on the sphere and on the electrode being obviously limited to the zone in contact with the electrolyte (  -).

Figure and Table Captions

Table 1 Theoretical and experimental values of R e,norm and R e,% as a function of the contact angle of the spheres of 2 mm and 4 mm in diameter in contact with the electrode centre.

Fig. 4

 4 Fig.4shows the values of R e,norm and R e,% for truncated spheres of aspect ratio a p /a e = 0.2 and 0.4, which are now positioned at any radial position X 0 on the disk electrode. The different contact angles chosen correspond to those used in the experimental part presented below. As mentioned above, some convergence problems arose when the sphere approaches the electrode edge. The calculation of the potential distribution in the electrolyte was performed with two sets of degree n and order m and only results with very close values of R e,norm were retained. No convergence problem could be observed for the largest sphere (a p /a e = 0.4 and  = 0°, 41.4°, 69.5°, and 90°) up to the limiting position X 0,lim = 1a p /a e sin . For the smallest sphere (a p /a e = 0.2), for which the values of R e,norm are very low, the convergence of the calculation was more difficult and only the results corresponding to the contact angles 0° and 60° are presented.

Fig. 9b shows

  Fig. 9b shows the fitting of the average of the approach and backward curves of Fig.9a with the theoretical normalized ER increment R e,norm as a function of the normalized height H above the electrode disk. In this example, the measured values, v R e = 0.195 V and d = -27 mV, give a B value of 22.64 V with G = 102, while the fitted values were z c = -10.362 mm,  = 6.3 V/mm,  = 25.8

Fig. 1 .

 1 Fig. 1. Schematic drawing of the truncated sphere in contact with the electrode.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Normalized ER increment R e,norm due to the presence of an insulating sphere in contact with the electrode as a function of the radial position X 0 for 2 sphere sizes (a p /a e = 0.1 and 0.2). [17] Fig. 3. Normalized ER increment R e,norm (a) and R e,% (b) as a function of the contact angle of the insulating sphere of various size positioned at the electrode centre.

Fig. 4 .

 4 Fig. 4. Normalized ER increment R e,norm (a) and R e,% (b) due to the presence of an insulating sphere of various contact angle and size (a p /a e = 0.2 and 0.4) as a function of its radial position X 0 .

Fig. 5 .

 5 Fig. 5. Experimental set-up used for measuring the ER variations due to the presence of a sphere shifted above or in contact with the electrode.

Fig. 6 .

 6 Fig. 6. SEM images of the sphere of diameter 2 mm (a) and hemisphere (θ = 90°) of diameter 4 mm (b).

Fig. 7 .

 7 Fig. 7. Variation of v R e as a function of the radial position x of an insulating 2-mm-diameter sphere plane (a) in contact with (h = 0) and (b) above (h = 3 µm) a 10-mm-diameter stainless steel electrode during a forward and backward scan at a 0.4 mm/s rate.

Fig. 8 .

 8 Fig. 8. Theoretical and experimental normalized R e,norm variations as a function of the normalized radial position X 0 of an insulating 2-mm-diameter sphere in contact with the electrode. The experimental data correspond to the forward scan in Fig. 7a.

Fig. 9 .

 9 Fig. 9. (a) Variation of v R e as a function of the vertical position z of an insulating 2-mm-diametersphere above the electrode centre for an approach and backward scan at a 0.2 mm/s rate;

Fig. 10 .

 10 Fig. 10. (a) Variation of v R e as a function of the vertical position z and (b) normalized ER increment R e,norm as a function of the normalized height H of insulating 2-mm-diameter spheres with different contact angles above the electrode centre (0.2 mm/s scan rate).

Fig. 11 .

 11 Fig. 11. (a) Variation of v R e as a function of the vertical position z and (b) normalized ER increment R e,norm as a function of the normalized height H of insulating 4-mm-diameter spheres with different contact angles above the electrode centre (0.2 mm/s scan rate).

Fig. 12 .

 12 Fig. 12. Theoretical and experimental normalized ER increment R e,% as a function of the contact angle of the spheres of 2 mm and 4 mm in diameter in contact with the electrode centre.

Fig. 1 .

 1 Fig. 1. Schematic drawing of the truncated sphere in contact with the electrode.

- 2 . 2 Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .

 222345 Fig. 2.Normalized ER increment R e,norm due to the presence of an insulating sphere in contact with the electrode as a function of the radial position X 0 for 2 sphere sizes (a p /a e = 0.1 and 0.2).[17]

Fig. 6 .

 6 Fig. 6. SEM images of the sphere of diameter 2 mm (a) and hemisphere (θ = 90°) of diameter 4 mm (b).

Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .

 78910 Fig. 7. Variation of v R e as a function of the radial position x of an insulating 2-mm-diameter sphere plane (a) in contact with (h = 0) and (b) above (h = 3 µm) a 10-mm-diameter stainless steel electrode during a forward and backward scan at a 0.4 mm/s rate.

Fig. 11 .Fig. 12 .

 1112 Fig. 11. (a) Variation of v R e as a function of the vertical position z and (b) normalized ER increment R e,norm as a function of the normalized height H of insulating 4-mm-diameter spheres with different contact angles above the electrode centre (0.2 mm/s scan rate).

Table 1

 1 Theoretical and experimental values of R e,norm and R e,% as a function of the contact angle of the spheres of 2 mm and 4 mm in diameter in contact with the electrode centre.

		Spheres of 2 mm in diameter	Spheres of 4 mm in diameter
			(a p /a e = 0.2)			(a p /a e = 0.4)
	Contact angle / degree	0	25.8	60	90	0	41.4 69.5	90
	TheoreticalR e,norm , % 	0.425 0.420 0.372 0.256 2.84 2.94 2.71 2.10
	ExperimentalR e,norm , %	0.424 0.414 0.369 0.267 2.85 2.94 2.73 2.17
	TheoreticalR e,% , %	0	-1.1 -12.5 -39.8	0	+3.5 -4.6	-26
	ExperimentalR e,% , %	+0.2 -2.6 -13.2 -37.2 +0.4 +3.5 -3.9	-24

in memoriam.

influencing the ER: a surface effect related to the accessibility of the electrode surface below the sphere to the current lines, and a volume effect related to the smaller volume of the insulating truncated sphere.

Owing to a high-precision motorized translation stage and a specific low-noise ER measurement device, the small ER increments due to the presence of single spheres of different contact angle located at the electrode centre could be experimentally determined. An excellent agreement was found between the experimental and theoretical results.

Appendix A. Calculation of the potential distribution

The calculation of the potential primary distribution in the electrolyte, when an insulating sphere is sitting on a disk electrode, is based on the integration of Laplace's equation (   = 0), where  is the electrical potential in the solution, when the concentration and temperature of the electrolyte, and therefore its conductivity, are uniform. The boundary conditions are: This problem can be solved using the mathematical collocation method. In this approach, the general solution of Laplace's equation is written as:

where  e represents the potential in the coordinate system related to the electrode (oblate spheroidal coordinates  e ,  e ,  e , with the origin at the centre of the electrode) and  p represents the potential in the coordinate system related to the sphere (spherical coordinates  p ,  p ,  p with the origin at the centre of the sphere). It can be shown [17], after introducing the concept of "double-sphere" (a second sphere of radius a p and centre O'' (x 0 , 0, -z 0 ) is added), that  can be written as the sum of base functions:


Jean-Louis Limam

D Yengue

Morabito

Mg2al Mg2cr

S Bourgerie

M Motelica-Heino

I Limam

E Yengué

D Morabito

Soil microbial diversity and related soil functioning in urban parks

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction Results

The main thrust of this work was to improve the knowledge concerning soil biodiversity and related ecosystem services in soils from urban parks in several cities of the Région Centre, France. In this work, the pedological, geochemical and microbiological characteristics of surface soils were investigated in order to make an inventory of soil fertility in several urban parks of the major cities of the Région Centre, France. The effects of agricultural practices on biomass, community structure and activity of micro-organisms were investigated in these soils in parallel with the determination of various pedo-physical and chemical parameters.

Results from this study showed that except for one site the microbial biomass for all samples was high. Metabolic quotients (qCO2) were in contrast variable for the different parks whether Shannon diversity indexes were quite similar for all the samples. The soil ecosystem has significantly influenced the functions of soil microbial community and hence probably its composition. More generally, catabolic diversity of soil microbial community is variable under the influence of various gardening practices and geological contexts. .

Région Centre (France)

The microbial biomass and community level physiological profiles were determined by using the MicroRespTM system in topsoils. Surface soil samples (0-20 cm) were also evaluated for physico-chemical characteristics such as the organic carbon and nitrogen concentrations, conductivity and pH together with their structure and texture and other soil physical parameters.

Physico-chemical characteristics of the surface soils

Microbial study Physico-chemical study

  sieving LaMotte textural soil kit (code 1067) Large green area (type 1): Lacustrian Limestone (Oligocene) Parc de l'Arrou, Blois Neighborhood green area (type 2): Flint clay Parc Central, Chartres Historical park (type 3): Sand and lacustrian limestone (Eocene) Parc Pasteur, Orléans Semi-natural area and woodland (type 4): Jurassic Limestone and marls Prairie St-Gildas, Châteauroux Jardin Lazenay, Bourges Family gardens (type 5): Cretaceous sup. chalk and sands Jardins familiaux de la Bergeonnerie, Tours


Clément Pillias
email: clement.pillias@cnam.fr

Raphaël Robert-Bouchard
email: raphaelrb@hotmail.fr

Guillaume Levieux
email: guillaume.levieux@cnam.fr

Designing Tangible Video Games: Lessons Learned from the Sifteo Cubes

Keywords: Sifteo Cubes, tangible user interface, tangible video game, video game design, mixed-reality games, player strategies, ACM Classification H.5.2. Information Interfaces and Presentation (e.g., HCI): User Interfaces-Input devices and strategies, K.8.0. Personal Computing: General-Games

Figure 1. Fat and Furious is a collaborative tangible video game running on Sifteo Cubes.

INTRODUCTION

Reality-Based Interaction is a concept that describes a current trend in HCI research and commercial product design, where user interfaces "attempt to make computer interactions more like interacting with the real, non-digital world" [START_REF] Jacob | Reality-based interaction: a framework for post-wimp interfaces[END_REF]. In the domain of video games, this trend is epitomized by the emergence of products such as the Wii remote or Kinect. These interfaces invite the player to interact with the gaming system by using her whole body in a way that usually requires her to reproduce real-world movements. They also allow for an increased expressiveness of the players' gestures, letting other players and spectators observe how they act, and build a rich social experience from the game. This trend continues with new products such as Sifteo Cubes [START_REF] Merrill | Sifteo cubes[END_REF], where the trend applies not only to the controllers but to the whole game system, by implementing a Tangible User Interface (see fig. 1). With these cubes, players can actually manipulate physical objects instead of relying on manipulation metaphors.

Video games have different goals than traditional user interfaces and have thus been described using different concepts: they take place in a specific negotiated state of mind known as the magic circle, and provide players with, among other things, a sense of competency, autonomy and relatedness [START_REF] Juul | The magic circle and the puzzle piece[END_REF][START_REF] Ryan | The motivational pull of video games: A self-determination theory approach[END_REF]. We show, from the analysis of players behaviors, how Sifteo Cubes modify the game design process as well as the plasticity of the magic circle and the motivational aspect of games.

We first present Fat and Furious, a game designed for this platform by students as part of a three month post-graduate coursework project. We then present an analysis of players' behavior observed during recorded play sessions. Finally, we discuss how the Sifteo Cubes are different from other gaming interfaces, and how it impacts both the game design process and the player experience.

Fat and Furious (FnF) is a runner-type collaborative multiplayer game. Each cube features crossroads, sometimes with an element in the middle (see fig. 1). The main character is a fat (and furious) hamster, who runs along the road at an ever-increasing speed, randomly choosing its direction at each crossroads, never turning back. Two of the elements are bonuses that increase the score and momentarily stop the hamster when it reaches them, while twelve elements are obstacles that must be avoided. The game ends when the hamster attempts to leave the cube with no connected path or when the hamster runs into an obstacle. The main goal is to beat the highest score by making the hamster run as long as possible. Each cube traversed gives two points and players can make the hamster go faster for a short time by touching it, also increasing the score.

Every time the hamster leaves a cube, an element may or may not appear on that cube. Players can use alchemy to get rid of obstacles: connecting two cubes that contain elements can destroy or transform them according to one of 28 possible combinations. For instance, combining water and fire destroys both obstacles, but combining tree and fire only transforms the tree into fire. In addition, water, fire and ice obstacles can be cleared by respectively tilting, shaking and repeatedly touching them (fig. 2). Each of these operations gives a number of points that increases according to the rarity of the elements involved.

Design intentions

The game was designed to put the players in a feverish state of excitement -almost frenetic at times. In order to provoke this excitement, the game was intended to be played in short sessions with easily understandable interactions and a strong time pressure. Also, a game with n players should be played with 2n + 1 cubes. In this way, players cannot hold all the cubes in their hands and need to pay attention both to the cubes they manipulate and the cubes left on the table .   The designers also wanted to promote collaboration. They designed two parallel and complementary tasks (keeping the hamster running and alchemy) so that each player can concentrate on a specific task, but still needs to collaborate with other players to reach the common goal. The scoring system and difficulty were also tuned so that experienced solo players could not easily perform better than a team of average players.

Technical issues

During game development and play-testing, developers faced some unexpected technical issues:

Hardware: Collisions between cubes can momentarily disconnect a cube's battery. The cube will then reboot and remain offline until the end of the current game, destroying the game experience. The screen's backlight is mono-directional. If not viewed from the correct angle, a cube's screen may appear to be off. In an attempt to resolve this issue, developers chose to create graphical assets that appear upside down when the cube is misoriented, but this did not prove to be effective. Software: Lag and graphical glitches were observed.

Glitches became more frequent as the number of cubes increased, preventing the game from being played with seven or more cubes. In addition, this kind of problem never appeared in the emulator, making them very hard to debug. The platform's graphical capabilities are surprisingly low: there is no alpha blending, very few sprites can be displayed simultaneously on a cube, and the foreground layer can only cover half of the screen. Developers maintained the game speed at the cost of a lower animation rate.

How the game uses the interface

Playing FnF requires good reflexes, as keeping the hamster running requires quickly placing a free cube in the short time between the moment the hamster reaches a crossroad and the moment it leaves the cube. FnF is, however, a game where the discovery of new strategies is an important aspect of the gameplay. Indeed, as the speed increases, the player must think about the best way to arrange cubes on the table, about which cube she should give to another player, which hand she should use, and so forth. This search for strategies is where the real game is, and every player finds herself starting to think about it, even during the first play session.

As we will see in the next session, players spontaneously develop strategies as answers to these questions. Most of these strategies concern entities that seem to have only a minor role in the game's rules: other players, positions of the cubes in space, and how the cubes are manipulated between basic interactions. A large part of the game -if not the largestlies therefore in manipulations that are not recognized by the cubes, and thus not recognized by the game's software. This suggests that in FnF, the cubes should not be considered simply as a gaming interface, but rather as a component of the game system.

PLAYERS' BEHAVIOR

We recorded video of 38 players discovering the game and the platform in realistic settings, in teams of two, for more than 5 hours of total play time. From this video, we extracted the players' strategies that we list below, grouped by generic concerns. These concerns apply to other games and platforms, so we first describe what strategies are supported by the Sifteo Cubes, then how they were used in FnF.

Organizing routine: When a player has to complete similar tasks on a regular basis, she can adapt the way she plays in order to complete these tasks more efficiently. For that purpose, the Sifteo Cubes offer two powerful mechanisms that can be used in combination: the spatial organization of cubes and the planning of cube manipulation sequences. The latter can take many forms, as cubes can be grabbed individually or collectively, pushed, slid on a table surface, passed in the air, thrown, rotated, stacked, etc. with one or two hands. In FnF, completing the hamster's path with a free cube was a recurrent task that players accomplished by spatially organizing the cubes in one of two ways, either managing a pool of free cubes in a specific area, or letting the cubes form a serpentlike pattern as the hamster goes through them and pick the one at the end. Alternatively, they systematically used the cube that the hamster just left (if it is free) or the free cube that was the closest to the one holding the hamster. The most efficient strategy we observed was to keep only two cubes in hand, including the cube the hamster was in, and rotate the latter so that the hamster faces the other cube.

Time pressure: Players can adopt various strategies to deal with time pressure, each involving different levels of readiness and risk-taking. With Sifteo Cubes, most basic interactions are recognized after they have been performed by a player, so readiness can manifest itself in various levels of preparation of the actions, such as grouping the cubes that will be used, getting the hand close to the one that will be moved, picking a cube that will be placed somewhere, etc. It is also possible to anticipate an event to come, and respond to it before it happens (e.g. by connecting cubes). When an event's many possible outcomes call for different actions, the latter strategy is a gamble, while the others allow to take more or less risk. It is sometimes possible, however, to deal with all the possible outcomes: in FnF, some players tried to secure the hamster path by connecting free cubes to all the sides where the hamster could leave the cube it was in. All other strategies were also observed.

Collaboration between players is a rich source of strategy building. Of course, they can play opportunistically, performing an action that seems appropriate when they see the opportunity to do it. But they can also take turns, divide the space into areas of control, assign distinct objectives or subtasks to players, etc. With Sifteo cubes, the basic interactions only involve one or two cubes and the system cannot detect who performed them, giving few constraints to the players in the choice of a collaboration strategy. All the strategies listed above have been observed in FnF test games, the most efficient one being to have one player in charge of keeping the hamster alive and others managing elemental alchemy, with an area dedicated to each of these two objectives (see fig. 3).

Unexpected behaviors: As we have shown above, our players developed numerous gameplay strategies, some of which were hard to predict when designing the game. First, some players did not keep the cube in hand while tilting it, but simply left it on the table, lying on its side. This behavior is very efficient, and only a few players discovered it. But as soon as one player did, every other player started using it too. Also, players tried to play with the cubes in the air, away from the surface of the table. Designers did not anticipate this way of playing either, but as this method of play is impractical, players did not keep using it. Players also tried to interact with cubes in ways that are natural but that the system was unable to recognize: they literally tried to blow out the flames with their breath, or they poured water on the fire by tilting a water cube above a fire cube. They also tried to influence the hamster's decision by tilting the cube, by touching a specific area of the screen, or by connecting a cube. Some players even kept doing this after having been told it was useless.

DISCUSSION

Video game systems relying on Reality-Based Interaction principles can be classified according to various criteria, but two of them are of special importance to this discussion:

Interaction style: Connecting and touching Sifteo cubes are two basic interactions that can only be recognized by the system after they have been performed, and independently of the way it was done. Other video game systems usually only provide these kind of interactions for buttons or touch events. We call this interaction style action validation. Shaking a cube is, however, an interaction that is recognized as a gesture, after it is done, but only allowing some variability in the way it is performed. Other video game systems often allow the player to perform many more gestures, with varying spatial amplitude and duration. Finally, tilting a cube is an operation that allows the continuous tracking of a cube's tilt angle, which can then be directly mapped to some game variable. These three interaction styles thus differ essentially in which part of the expected actions are actually sensed by the system [START_REF] Benford | Expected, sensed, and desired: A framework for designing sensing-based interaction[END_REF].

Interaction instrument: Tangible video game systems such as the Sifteo Cubes or tabletop tangible interfaces rely on the manipulation of several physical objects for their input, with the possibility to have one physical object associated to an object of the game. On the other hand, controllers such as a Wii remote (or a mouse) are supposed to stay in the player's hand(s) during the whole play session, but will use different mappings between physical actions and game actions at different times. Finally, some systems such as the Kinect rely on continuous body tracking.

Of course, the interaction styles and instruments used during a game depend not only on the system, but also on a specific game design. In the rest of this discussion, we will focus on a class of game designs that we call AV+PO as they rely mostly on action validation (AV) and physical objects (PO). This class contains FnF and other games for Sifteo Cubes as well as most tangible games on multi-touch tabletop systems and a few games such as B.U.T.T.O.N. [START_REF] Wilson | Brutally unfair tactics totally ok now: On self-effacing games and unachievements[END_REF] that use more conventional hardware. We will analyze how AV+PO games differ from other video-games in terms of players' perceived freedom of action and relatedness, and the game's learnability and customization opportunities.

Freedom: As we showed in a previous section, the manipulation of physical objects with action validation allowed FnF players to devise numerous strategies. Because the cubes are real objects, players do not rely on a set of pre-defined actions: they can use any action available in the real world.

Because actions are only validated after they have been performed, players have a total freedom in the way to perform them. With so many opportunities, players are provided with a lot of freedom in strategy planning and action selection, leading to a greater feeling of autonomy, and thus to a better gaming experience [START_REF] Ryan | The motivational pull of video games: A self-determination theory approach[END_REF]. The game designers can use this freedom to make an AV+PO game richer than it appears at first sight, as in FnF. But they can also find it harder to tune the game's difficulty when the players get more freedom [START_REF] Aponte | Measuring the level of difficulty in single player video games[END_REF]. First, the designer cannot make the system enforce rules on player's actions the system is not aware of. Second, the more freedom the player has, the higher the probability that this player may think about something the designer did not, potentially degrading the gaming experience.

Relatedness is one of the motivational pulls of video games [START_REF] Ryan | The motivational pull of video games: A self-determination theory approach[END_REF], and AV+PO games support a high level of social interaction. Indeed, players communicate and interact more easily when they are in the same place, manipulating a common set of physical objects. For instance, body language can enrich the communication between players, e.g. in FnF, holding my cube next to yours means "I'm waiting for you to finish". Of course, playing like this is easier when the game relies on action validation, as the gestures used to communicate with other players will not be misinterpreted by the gaming system as a game command. Moreover, a new player may show up and take an object from the table and use it to accomplish one of the game's goals. It is therefore easier to achieve multiplayer gameplay in AV+PO games, e.g. by providing many tasks to accomplish simultaneously using different objects.

Learnability: One of the assumed strengths of tangible user interfaces is that the manipulation of physical objects does not need to be explained. Indeed, FnF players understood immediately how to take a cube, and how to shake or tilt it. In addition, action validation sets fewer constraints on the movements to be performed than gestures or continuous tracking, and it should therefore be easier to learn how to do these actions. Thus, as soon as the player has understood the simple goals of the game, she is fully functional as a player and can begin playing strategically and cooperatively. On the down side, a player might have trouble discovering what action should be performed in a given context, whatever her ability to perform that action. For example, with Sifteo cubes, instructions can only be displayed on the cubes, and not around. It is therefore harder to display an in-game tutorial than with classical video games or tangible tabletop games [START_REF] Hunter | Make a riddle and telestory: designing children's applications for the siftables platform[END_REF].

Customization: AV+PO games allow players to easily customize the gameplay. Indeed, a game needs a certain form of agreement between players, and can always be modified as long as this modification is negotiated [START_REF] Juul | The magic circle and the puzzle piece[END_REF]. For instance, players may decide to set a specific meta-rule, like using only one hand or having a player responsible for making the game harder by shuffling the objects. Sifteo cubes and other tangible platforms allow such modification as it is very easy to modify the real world part of the game, while its digital component cannot be modified by players. In addition, it is easier to devise a meta-rule if the players' actions are only validated by the system, because the meta-rule will not ask for movements that conflict with gesture recognition or continuous tracking.

FUTURE WORK

In a near future, we will be able to investigate players' behavior with other multiplayer gameplays, as more games will be available for the Sifteo Cubes and other tangible or mixedreality platforms. The analysis framework introduced in the discussion section will then be tested with other settings (including the extreme case envisioned by Merrill et al. where a high number of small objects can be manipulated like puzzle pieces [START_REF] Merrill | Siftables: towards sensor network user interfaces[END_REF]), and eventually completed with new dimensions.

Figure 2 .

 2 Figure 2. Basic interactions with the Sifteo Cubes.

Figure 3 .

 3 Figure 3. A complex situation for players using the best strategy: the player on the left simultaneously breaks an ice cube (with her right hand) and slides a free cube toward the second player (with her left hand). The player on the right of the picture keeps the hamster alive.

ACKNOWLEDGMENTS

We would like to thank P. Cubaud, K. Neil, J. Eagan, all the play testers, and the other FnF developers: M. Bonneau, E. Corno, M. Gilleron, P. Salib & L. Saugé. This work has been funded in part by the ANR CONTINT Transread project.


Clément Pillias
email: clement.pillias@cnam.fr

Pierre Cubaud
email: cubaud@cnam.fr

Shuo-Hsiu Hsu

Reading With a Digital Roll

Keywords: ACM Classification H, 5, 2 [User Interfaces]: Input devices and strategies; H, 5, 2 [User Interfaces]: Interaction styles

We introduce the Digital Roll, a cylindrical hand-held device wrapped with a curved display, that can be rotated by hand to provide a continuous scrolling of text. We present design considerations for such a device and report on a preliminary experiment designed to assess its acceptance for casual reading, using a simulator. Encouraging results and their implications on the design of the device are then discussed.

Introduction

The need for small, hand-held and compact reading devices is old and universal and has fueled many innovations in the history of reading [START_REF] Fischer | A history of reading[END_REF]: In late antiquity, the papyrus scroll was replaced by the codex, a manuscript version of the modern book. During the renaissance period, emergent needs for mobility led to the creation of the first "pocket books." Innovation with paper continues: In 2009, Dutch editor Jongbloed created the Dwarsligger, a book concept of reduced size that uses horizontal binding. But obviously, it is digital technology that gathers today's attention. E-readers are now considered by consumers to be superior to print for reading on the move [START_REF] Rainie | The rise of e-reading[END_REF]. However, interaction with such devices is still limited compared to their paper counterparts. Fortunately, thin and flexible display technologies such as E-Ink and OLED offer new opportunities to bridge this gap.

In this paper, we study the roll shape as a reading surface, proposing in a way to revamp the antique scroll. Fig. 1 shows a mock-up of a digital roll, a hand-held digital device with cylindrical screen shape that allows a continuous scrolling of text using motion capture. A digital roll has a smaller form factor than a flat e-reader with similar screen surface. This could make it useful for readers on the move, such as commuters.

As with many e-readers, applications of digital rolls are limited due to technical considerations, e.g., image and video visualization seem pointless on a cylindrical display because of the distortion. Navigation within structured multimedia documents, such as Web pages, is therefore improbable. In addition, one can fear that the digital roll would inherit the well known drawbacks of the paper scroll: small reading context, difficult navigation and text skimming. However, many reading activities such as reading novels for pleasure are mostly sequential processes. Navigation through this kind of document could thus benefit from the infinite, continuous display offered by the digital roll. As novels are the most popular e-books bought by readers,1 we believe the digital roll may fill some kind of niche in the ecosystem of mobile appliances.

Related work

Reading scrolls continue to be used in Chinese culture (fig. 2) but, in general, reading on cylindrical shapes is mostly limited to instructions printed on manufactured goods (fig. 3). Some designs of digital devices based on cylindrical displays have been patented [START_REF] Cho | Mobile terminal using flexible display and method of controlling the mobile terminal[END_REF]. As far as we know, however, their potential use for reading devices has never been evaluated. Reading on a curved screen has been studied on short texts that do not require rotation of the device [START_REF] Häkkinen | Reading experience with curved hand-held displays[END_REF]. Folding, bending and rolling devices are being systematically investigated as an alternative to flat displays for media appliances [START_REF] Khalilbeigi | Foldme: interacting with double-sided foldable displays[END_REF][START_REF] Lahey | Paperphone: understanding the use of bend gestures in mobile devices with flexible electronic paper displays[END_REF][START_REF] Khalilbeigi | Xpaaand: interaction techniques for rollable displays[END_REF].

Research questions and methods

Digital rolls have three obvious potential drawbacks: (1) reading text on a cylindrical screen causes a distortion of letters that could make the text harder to read, ( 2) turning the roll could cause fatigue during long reading sessions and (3) the small display area reduces the amount of context that one can have. We are interested in finding how these issues (and other less evident ones) affect the reading experience with digital rolls. In early discussions with potential users, most of them expressed concerns about these issues. However, one minute of interaction with the paper prototype shown in figure 1 alleviated most of these concerns. We thus hypothesize that their impact on the reading experience is low.

We present in this paper the results of a preliminary experiment designed to roughly evaluate the overall impact of these issues, discover other overlooked issues, validate our design considerations and get basic knowledge of how users would operate the device during longer reading sessions. To conduct this research, we built a digital roll simulator, which is easier to build than a prototype and can be easily distributed. 2 It also allowed us to separate the design of the display from the one of the input method. In the future, it will allow us to refine these designs in shorter cycles and to separately investigate the effects of the input method (turning the roll) and the distortion of letters.

Design Considerations

The dimensions of the digital roll cannot be arbitrary. Roll diameter must obviously allow easy grip for the widest population. Since we target mobile use, a small volume is necessary. However, the roll should offer a usable display surface. For screen width, one can reproduce the width of a pocket book text line, which is 8 to 9 cm. This value is common for commercial e-readers. The volume of a roll 9 cm wide and 3 cm in diameter is 64 cm 3 . It is about half the volume of the Txtr Beagle, currently advertised as the smallest e-reader [1], which is 100 cm 3 with a 5" screen.

Diameter impacts on the rotation speed one has to provide in order to have a text display rate consistent with reading speed. A reading speed of 500 words/min. is observed for good readers [START_REF] Dehaene | Reading in the Brain: The New Science of How We Read[END_REF]. This may be considered as an upper bound for casual reading. A 9×9 cm screen displays roughly 125 words (half of a pocket book page in 10 pt font). Rolls with such a screen must therefore be turned at 4 RPM in order to match a fast reading speed. We shall see in the next section that, in practice, the rotation speed is much lower.

Whether the roll rotation should be provided directly by the user's hands or indirectly using some automatic control is an important design issue. We believe that both modes could be offered to the user -if a properly tuned automated display can be found. Direct control clearly has the advantage of a lower degree of indirection and higher degree of compatibility [START_REF] Beaudouin-Lafon | Instrumental interaction: an interaction model for designing post-wimp user interfaces[END_REF] which should result in an easier use. So, in this preliminary work, we choose to study it first. User's actions on the roll can be performed one-handed, or bi-manually. Ideally, the user should be able to change the operation mode during the reading. It is clear that one-handed rotation has a limited angular scope if the roll is pinched. However, continuous one-handed rotation is possible if the roll stays in the palm of the hand (fig. 4 and5). This might be interesting in the case of vertically oriented text, such as Chinese. Accelerometer-based gesture recognition can be used to provide other required functions of an e-book reader, such as jumping between paragraphs or chapters, skimming or calling a menu to navigate in the library. The form factor of the device provides an interesting design space for creating such gestures, including bi-manual ones (see fig. 6 and7).

The display of text during roll rotation can be handled in various ways. The easiest solution is to refresh all of the screen when a specific roll angle is reached, which would correspond to the border of the screen. In this setting, the screen is refreshed once per roll turn, which would be suitable for a low-consumption E-ink display with slow refresh rate. OLED screens exhibit a higher refresh rate, so the text display can react in real time with the roll's motion. It is thus possible to display, at each angle change, a new "window" of the text. Fig. 8 shows the mapping rules of this window on the screen. This second operation mode provides a continuous move in the text. However, it requires a clever way to detect what part of the roll the user is looking at.

Simulating the digital roll

Input The sensor is based on an Intersense InertiaCube BT. This wireless inertial measurement unit offers a 0.5 • absolute angle precision at 180 Hz with low drift for a weight of 67 g. As shown in fig. 9, this unit was encased in a hollow PVC tube so that its center of mass lies on the tube axis. The length of the tube is 11 cm and its diameter is 3.2 cm (2.8 cm internal), providing enough space to insert the thumbs, as it has no cap.

Output To accurately render the text distortion caused by the cumulated effects of perspective and cylindrical projection, we use a two-pass OpenGL renderer: the content of the virtual roll display is first rendered in an OpenGL texture, then this texture is mapped on a cylinder using 16:1 anisotropic filtering and lightning. The first pass uses the Berkelium library that provides an off-screen OpenGL rendering of Google's Chromium open-source web browser. This allows a high-quality rendering of text with a great flexibility, as CSS3 and javascript are very well supported. In addition, we reorder the virtual screen content as explained in fig. 8. We used a virtual display size of 1000×942 pixels, mapped on a 10 cm-long cylinder (without the handles) with a 3 cm diameter. This provides a virtual resolution of 254 dpinow common on high-end mobile phones, but not on computer displays that need to render the roll bigger than its real size. Task During the experiment, subjects had to read a short but complete novel: Le Passe-muraille (The Passer-through-Walls) by Marcel Aymé. Task completion time was expected to be around 15-20 minutes, since the novel is 3580 words long. The novel is at a middle school reading level and is renowned for its humor. We hoped these qualities would encourage subjects to readily talk about their feelings during reading, make comments, ask questions and suggest improvements.

Preliminary Experiment

Subjects A call for participation was sent to our institution's staff mailing list, asking for volunteers who read regularly on their free time and especially when commuting. Thirteen participants answered the call (7 women, 6 men), aged from 28 to 65 year old (mean: 43.4, σ: 11.4). All subjects but one were right-handed. Eleven read books on a daily basis and 6 were frequent users of digital devices for casual reading.

Apparatus We ran a modified version of the simulator in fullscreen on a 27" iMac placed on a stand so that the bottom of the screen was at approximatively the same height as the knees of the person sitting in front of it. The display occupied most of the visual field of the subjects who had to slightly bend the head in order to look at the simulated roll, but not as much as if they were holding the real object on their laps. A video camera positioned one meter above the display took HD recordings of the subjects' hands during interaction. The simulator logged the sensor state (position in space) and the display state (total amount of rotation of the roll, i.e., part of the text that was visible). The novel was typeset in the Cambria font so that its line spacing and number of words per line matched that of the paper edition.

Protocol Subjects were first asked to fill in a one-page form about their personal data and their paper and digital reading habits. They were then asked to sit in front of the (then blank) simulator display and were given the paper prototype shown in fig. 1 and very short oral explanations about the digital roll. The simulator then displayed a virtual roll holding more detailed information about the task and instructions such as "roll until next paragraph," to ensure the subjects got some basic practice manipulating the sensor before the actual trial. Subjects were instructed to find a comfortable posture, possibly changing the chair settings and apparent size of the virtual roll in order to compensate for any change of distance to the screen. The simulator then displayed a new roll with the novel. Subjects had to call the experimenter when they reached its end. Finally they had to fill out a one page survey about their experience with the simulator and possible usage of the digital roll. The session ended with open discussion.

Results

The total reading time for each participant was between 10.3 and 25.3 minutes (mean: 15.8, σ: 4.9, median: 14.2), fitting in the planned interval. This suggests that reading on the simulated digital roll can be as fast as reading on paper, although it needs to be confirmed by a controlled experiment comparing the two. From an analysis of the logs, we noticed that some subjects read at an almost constant speed while others read faster at the end. This suggests that if there was any fatigue effect it may have been canceled by a learning effect, or simply because of the story's suspense. Indeed, fig. 12 shows that some parts of the text clearly require more or less time to be read. We coded the recorded videos for significant events such as changes in overall posture of the subject or in finger position, signs of fatigue or distraction, and backward or unusually fast rotations. The coding scheme also tracked hands cooperation and scrolling synchronism: Hands cooperation may be symmetrical, when both hands do the same movement to turn the roll, then are repositioned in any order; alternating, when each hand turns the roll alternatively while the other one is repositioning; or asymmetrical, when one hand is used to turn the roll and the other one only provides guidance or support. Scrolling synchronism is a strategy that can also be defined for scrollable text in a more conventional setup: it may be parallel, when reading and scrolling are done at the same time, or alternating, when reading phases alternate with scrolling phases.

For hands cooperation, the symmetrical mode was barely used, and only when starting a move. The real surprise came from the very large dominance of the asymmetrical mode: all subjects used it most of the time, some only using this mode, while only three subjects used the alternating mode for more than 30 s. However, most subjects used it for fast rotations without reading. Interestingly, there was no clear effect of handedness on the choice of each hand's role and some subjects switched many times the roles of their hands. The scrolling synchronism strategy is harder to analyze and probably needs more data. However, we think it is an important factor to understand reading with the digital roll, as we have found that most changes in the reading speed were associated with changes in any strategy or in finger position.

There were a few variations on the finger positions, the most surprising being the insertion of some fingers inside the PVC tube. Four subjects tried such a position, using either the thumb, the index, or a combination of the index and major (most of the time with both hands, always with the same fingers for both hands). Two subjects made the whole trial using such a position, and one of them stated in the later discussion that the object would seem less usable without such holes in the handles.

Interview

The questionnaire that users had to fill after the reading session was made of 5-values rating scales, all balanced in positive and negative values (with the exception of Attention to hands that was asking for a frequency, from 'continually' to 'never', with intermediary steps 'often', 'sometimes' and 'once or twice'). Fig. 11 presents the results and clearly shows that the digital roll technique was easy to understand and to use, and caused no fatigue for reading sessions of this length. In the open discussion, four subjects expressed fears about using it during commuting because of the risk of theft, while two others stated that its shape would reduce that risk. Two also complained that with so little text displayed, the high level of distraction in such environments would rise the chance to loose the reading context. This issue was also raised by one subject as a justification for his frequent backward rotations during the experiment, since he usually reads in a rather non-linear way.

Implications for design Our findings about hands cooperation strategy have implications for the design of the roll, as it may be useful to have a fixed handle in one hand, the other handle turning with the screen (see fig. 5). Hollow handles might also be a requirement for some people and could help single-handed manipulation.

Future Works

Duration (s) 0 5 10 15 20 25 We believe that these initial results are encouraging and that this research should be carried out. A methodological issue is to determine which results may be obtained concerning the user reading experience without having to build a prototype.

Position in text

In the short run, we plan to continue the experiments using the simulator with other types of documents, such as Tweets and news. Subjects younger that our initial panel will also be studied. To this day, our simulator only allows sequential reading. No navigation action has yet been implemented and tested. Our next task will be to refine the interaction and gestures for intra-text navigation. We will then specify an HCI for the general management of the device. The 3D simulator and focus groups sessions should facilitate the choice between several design alternatives.

We also want to develop a more advanced capture device, with dimensions corresponding to the targeted digital roll. We shall add touch sensors to investigate further the fine movement of the user's fingers during the rotation of the roll and the potential of these manipulations for interaction.

In the longer run, a prototype carrying a cylindrical screen must be developed, following for instance [START_REF] Lahey | Paperphone: understanding the use of bend gestures in mobile devices with flexible electronic paper displays[END_REF] guidelines. It would enable the study of reading on the move with the digital roll and interesting comparisons with current flat page-based devices.

Figure 2 :

 2 Figure 2: Contemporary Chinese scroll.

Figure 3 :

 3 Figure 3: Prints on cylindrical manufactured objects.

Figure 4 :

 4 Figure 4: Use of the digital roll for Chinese or other vertically organized writing system.

Figure 5 :

 5 Figure 5: One-handed use of the digital roll for horizontal text.

Figure 6 :

 6 Figure 6: Example of a navigation gesture: shaking the roll to access menu.

Figure 7 :

 7 Figure 7: Another example of a navigation gesture: tapping the end of the roll to validate the choice of a menu item.

Figure 8 :

 8 Figure 8: The top row shows, from left to right, some (unrolled) text while it is read. The red rectangle indicates the visible part of the roll. The bottom row shows the content of the roll display and how it is updated. The blue line separates what will be read next (above it) from what has already been read (bellow it).

Figure 9 :

 9 Figure 9: Input device for motion capture.

Figure 10 :

 10 Figure 10: Simulating the roll. Screenshot of the 3D application.

Figure 11 :

 11 Figure 11: Subjective evaluation results (5 values). Blue horizontal line represents 3 answers for the given value.

Figure 12 :

 12 Figure 12: Reading durations: the novel has been truncated into segments such that 4 segments can fit on the roll. For each segment we computed the total time it was in front of the subject. The graphics displays for each segment the median time among subjects (black line) and the interquartile range (cyan polygon).

In Jan.

2013, the top-30 bestsellers on the Amazon portal were all novels.

We provide a downloadable version that can be operated with a WiiMote at the URL: http://cedric.cnam.fr/ilj/d-roll/

Acknowledgements

This work has been partly funded by the ANR CONTINT Transread project.