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Langmuir 2007, 23, 10976-10983
Flow Patterns of Bubble Nucleation Sites (Called Fliers) Freely Floating in Champagne Glasses Ge´rard Liger-Belair,*,† Fabien Beaumont,‡ Philippe Jeandet,† and Guillaume Polidori‡ Laboratoire d’Œnologie et Chimie Applique´ e, UPRES EA 2069, URVVC, and Laboratoire de Thermome´ canique, UTAP EA 3802, Faculte´ des Sciences de Reims, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 2, France ReceiVed June 14, 2007. In Final Form: August 14, 2007 Laser tomography techniques were used to capture the dynamics of bubbles released from particles (arbitrarily called fliers) freely floating in traditional flutes poured with champagne. By use of long exposure time photography, the trajectories of bubbles released by fliers were found to leave very elegant and characteristic “prints” as they crossed a section of champagne illuminated with a 1 mm thick laser sheet. This characteristic print was made with a succession of lighting filaments. Fine analysis of these prints left by fliers enabled us to deduce the bubbling frequency of each flier (which ranged from about 4 bubbles/s up to about 22 bubbles/s a few seconds after pouring), as well as its velocity through the liquid medium (which ranged from about 0.8 mm/s to about 7.6 mm/s). Finally, this flow visualization technique, very recently applied to the science of champagne and sparkling wines, also proved to be a useful technique to underscore fliers’ bubbling instabilities along their rather erratic way through the liquid medium.
1. Introduction Since the time of the benedictine monk Dom Pierre Perignon (1638-1715), champagne is the wine of celebration. This fame is undoubtedly largely linked to the elegance of its effervescence and foaming properties.1 This is the reason why considerable efforts have been conducted the past few years to better illustrate, detect, understand, and finally control each and every parameter involved in the bubbling process. For a review see for example ref 2 and references therein. Champagne and sparkling wines are multicomponent hydroalcoholic systems supersaturated with CO2-dissolved gas molecules (formed together with ethanol during the fermentation process). In weakly supersaturated liquids such as carbonated beverages in general and champagne in particular, bubble formation and growing require preexisting gas cavities with radii of curvature large enough to overcome the nucleation energy barrier and grow freely.3,4 Jones et al. made a classification of the broad range of nucleation likely to be encountered in liquids supersaturated with dissolved gas.3 Bubble formation from preexisting gas cavities larger than the critical size is referred to as nonclassical heterogeneous bubble nucleation (type IV bubble nucleation, following their nomenclature3). Generally speaking, effervescence in a glass of champagne or sparkling wine may have two distinct origins. It can be “natural” or “artificial”. On one hand, natural effervescence is related to the bubbling process from a glass which has not experienced any specific surface treatment. Closer inspection of such glasses poured with champagne and sparkling wines recently revealed that most of the bubble nucleation sites were found to be located on preexisting gas cavities trapped inside hollow and roughly cylindrical * Corresponding author. Telephone/fax: 00 (33)3 26 91 86 14. E-mail:
[email protected]. † Laboratoire d’Œnologie et Chimie Applique ´ e, UPRES EA 2069, URVVC. ‡ Laboratoire de Thermome ´ canique, UTAP EA 3802. (1) Liger-Belair, G. Uncorked: The Science of Champagne; Princeton University Press: Princeton, 2004. (2) Liger-Belair, G. J. Agric. Food Chem. 2005, 53, 2788-2802. (3) Jones, S. F.; Evans, G. M.; Galvin, K. P. AdV. Colloid Interface Sci. 1999, 80, 27-50. (4) Lubetkin, S. D. Langmuir 2003, 19, 2575-2587.
cellulose-fiber-made structures on the order of 100 µm long with a cavity mouth of several micrometers.5-8 The fine structure of immerged cellulose fibers acting as bubble nucleation sites has indeed been thoroughly examined and discussed in a previous work,8 as well as the conditions which favor the entrapment of an air pocket inside a cellulose fiber during the filling of a glass.9 On the other hand, artificial effervescence in a glass is related to bubbles arising from scratches intentionally done by the glass maker to eventually replace a deficit of natural effervescence.10 It is worth noting that, in glasses without such a specific surface treatment, irregularities of the glass itself are far too small and unable to entrap gas cavities of a critical size needed to produce bubble formation.11 The mechanism of bubble release from cellulose fibers or microscratches has already been described in previous papers.8,9,12,13 Very recently, mathematical models have been proposed to better understand the role played by a collection of parameters (such as viscosity, temperature, and dissolved-CO2 concentration) on the kinetics of bubbling from cellulose fibers stuck on the glass walls.14-17 Fibers responsible for natural effervescence are released from the surrounding air, or from the (5) Liger-Belair, G.; Vignes-Adler, M.; Voisin, C.; Robillard, B.; Jeandet, P. Langmuir 2002, 18, 1294-1301. (6) Voisin, C. Quelques aspects de la nucle´ation des bulles dans une fluˆte et de leur ascension a` petits nombres de Reynolds. Ph.D. Thesis, Universite´ de Reims Champagne-Ardenne, Reims, France, 2005. (7) Voisin, C.; Jeandet, P.; Liger-Belair, G. Colloids Surf. A 2005, 263, 303314. (8) Liger-Belair, G.; Topgaard, D.; Voisin, C.; Jeandet, P. Langmuir 2004, 20, 4132-4138. (9) Liger-Belair, G.; Voisin, C.; Jeandet, P. J. Phys. Chem. B 2005, 109, 1457314581. (10) Liger-Belair, G.; Religieux, J.-B.; Fohanno, S.; Vialatte, M.-A.; Jeandet, P.; Polidori, G. J. Agric. Food Chem. 2007, 55, 882-888. (11) Lehue´de´, P.; Robillard, B. Proceedings of the 1st In Vino Analytica Scientia Symposium; Bordeaux: France, 1997. (12) Ronteltap, A. D.; Hollemans, M.; Bisperink, C. G.; Prins, A. Master Brew. Ass. Am. Tech. Quart. 1991, 28, 25-32. (13) Lynch, D. M.; Bamforth, C. W. J. Food Sci. 2002, 67, 2696-2701. (14) Liger-Belair, G.; Parmentier, M.; Jeandet, P. J. Phys. Chem. B 2006, 110, 21145-21151. (15) Uzel, S.; Chappell, M. A.; Payne, S. J. J. Phys. Chem. B 2006, 110, 7579-7586. (16) Chappell, M.; Payne, S. J. Acoust. Soc. Am. 2007, 121, 853-862. (17) Liger-Belair, G. Ann. Phys. Paris 2006, 31, 1-133.
10.1021/la7017693 CCC: $37.00 © 2007 American Chemical Society Published on Web 09/29/2007
Flow Patterns of Fliers in Champagne Glasses
Langmuir, Vol. 23, No. 22, 2007 10977
Figure 1. Photograph of a typical flute poured with champagne (a) and close-up on particles acting as bubble nucleation sites freely floating in the bulk of the flute (called fliers), thus creating charming bubble trains in motion in the champagne bulk (b). Photograph by Alain Cornu - Collection CIVC.
towel used during the wiping process. Fibers often adhere to the glass wall (due to electrostatic forces, especially if the glass or the flute is vigorously wiped by a towel). Flutes that have been cleaned with a towel before serving show an excess of bubble nucleation sites, and therefore an excess of effervescence.6 Therefore, there is a substantial variation concerning the “natural” effervescence between flutes depending on how the flute was cleaned, depending on the cleanliness of the room itself, and depending on how and where the flute was left before serving. When champagne is served, during the pouring process, a liquid edge advances over the glass wall at a velocity of several cm/s.9 Some of the particles adhering to the glass wall (most of them including cellulose fibers) may therefore detach from it to finally become completely immerged into the champagne bulk. Particles detached from the glass wall are nevertheless still active (in terms of bubbling capacity) provided that a gas pocket with a radius of curvature larger than a critical size has been trapped inside them.1 Those particles immerged in the champagne bulk produce easily recognizable bubble trains, which seem to dance erratically inside the glass during champagne tasting. In the following, those particles in suspension in champagne glasses will be called fliers (due to their often complex and circling trajectories in the champagne bulk). Fliers are indeed a significant source of bubbles in glasses poured with champagne. The photograph of a typical flute poured with champagne is displayed in Figure 1a. A detail has been enlarged in Figure 1b, where some fliers are recognizable. Fliers undoubtedly catch the eyes of champagne tasters, who also often are fine observers. In this work, and for the very first time, classical flow visualization techniques were applied to freeze the dynamics of fliers, which are a significant source of bubbling in champagne glasses. Long exposure time photography combined with laser tomography techniques were used to determine the frequency of bubble formation as well as the velocity of fliers along their way
through the very complex flow patterns found inside a traditional champagne flute. 2. Materials and Methods 2.1. Champagne and Flute. A classical champagne wine holding about 10 g/L of CO2-dissolved molecules was used for this set of experiments. Some physicochemical parameters of the champagne were already determined at 20 °C, with a sample of champagne first degassed.5 The static surface tension of champagne γ was found to be on the order of 47 mN/m, its density F was measured and found to be 998 kg/m3, and its dynamic viscosity η was found to be on the order of 1.5 × 10-3 kg/m/s. Experiments dealing with the dynamics of fliers were performed at room temperature (20 ( 2 °C), with a traditional champagne flute, i.e., a slender and elongated glass with a deep tapered bowl. 2.2. Laser Tomography Technique. Classical tracer techniques which use dye emission are not suitable for such experiments in close confined domains due to their poor stability behavior against mixing with the surrounding fluid.18 It is the reason why the particlestreak technique, involving the seed of solid Rilsan particles, has been chosen for this series of experiments. Before pouring champagne into the flute, champagne was previously added with Rilsan particles (with a volume fraction condition of about 1.3 × 10-4). Rilsan particles (75 µm < diameter < 150 µm; F ) 1.06 g/cm3) are neutrally buoyant tiny reflective beads which exhibit a high degree of reflectivity with regard to a laser sheet. The planar laser sheet is built from an argon-ion laser source (Coherent - Innova 70 - 3W) whose incident beam crosses spherical and cylindrical optical lenses. The 1 mm thick laser sheet crosses the champagne flute in its plane of symmetry. Classical long exposure time photography of the laser sheet, with a digital photo camera (Minolta), was used to follow the movements of the beads, thus freezing the flow patterns inside the fluid section crossed by the laser sheet. A photograph of the optical workbench used to capture the champagne flow patterns is displayed (18) Merzkirch, W. Flow Visualization; Academic Press Inc.: London, 1987.
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Figure 2. Photograph of the optical workbench used to capture the champagne flow patterns, as well as the dynamics of fliers releasing bubbles in the champagne bulk; The laser sheet boundaries are materialized by solid blue lines. in Figure 2. In Figure 2, the laser sheet boundaries are materialized by solid blue lines. The dynamics of fliers was investigated by use of the same technique. To increase the density of fliers in the champagne bulk (in comparison with the natural abundance of cellulose fibers, which obviously depends on the cleanliness of the room that may vary from one day to another), each flute has been previously vigorously wiped with a towel before pouring champagne. This simple procedure considerably enhances the density of fliers inside the champagne bulk after pouring. Fliers which act as bubble nucleation sites in the champagne bulk continuously release bubbles all along their trajectory in the flute. Bubbles exhibit indeed a high degree of reflectivity with regard to the laser wavelength. Therefore, each bubble which crosses the laser sheet is materialized by a lighting filament whose length depends on the digital camera’s exposure time. A 1 s exposure time was systematically used in this series of experiments. It is worth noting that experiments specifically dealing with the dynamics of fliers did not require further adding of Rilsan particles into champagne.
3. Results and Discussion 3.1. Flow Patterns in the Traditional Champagne Flute. It was already shown in a previous article that bubbles rising from the various nucleation sites found in a glass poured with champagne act as so many swirling-motion generators within the glass.10 Bubbles rising in the champagne bulk indeed induce a driving process of the surrounding fluid. Consequently, as long as effervescence lasts in a flute poured with champagne, the liquid is far from staying at rest, contrary to a still wine. A very typical 1 s exposure time photograph of the champagne flow patterns in the cross section of the flute used in this series of experiments is displayed in Figure 3a, together with the corresponding streamlines in Figure 3b. The velocity field in the champagne bulk showed velocities typically ranging from about 1 mm/s to about 1 cm/s. How do cellulose fibers, detached from the glass wall, behave in the bulk of a fluid showing a velocity field comparable with that displayed in Figure 3? The aim of the following paragraphs is to discuss the behavior of fliers freely floating in the champagne bulk, as determined by a combination of long exposure time photography and laser tomography techniques. 3.2. What Does a Typical Lapse-Time Photograph of the Laser Sheet Teach Us? A very typical 1 s exposure time photograph of the laser sheet which crosses the plane of symmetry of a flute poured with champagne (not previously added with Rilsan particles) is displayed in Figure 4. Any floating object which crosses the laser sheet is made visible depending on its
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Figure 3. Visualization of the mixing flow patterns in the cross section of the traditional flute showing natural effervescence, by use of the champagne previously added with tiny Rilsan particles with a volume fraction condition of about 1.3 × 10-4 (a). Scheme of the corresponding streamlines patterns (b). Streamlines are reconstructed from the lighting filaments left by Rilsan particles during the 1 s exposure time of the digital photo camera.
degree of reflectivity with regard to the laser wavelength. Rising bubbles indeed exhibit a high degree of reflectivity and appear as light streaks as they cross the laser sheet along their way toward the liquid surface. Two situations are therefore made possible. Bubbles may nucleate from nucleation sites that are (i) fixed (adhering to the glass wall) or (ii) in motion (i.e., from fliers). It happens that the 1 s exposure time photograph displayed in Figure 4a illustrates the “prints” left by rising bubbles in the two well-distinct and previously defined situations, i.e., (i) rising bubbles nucleated from a nucleation site adhering to the glass wall and (ii) rising bubbles nucleated from a flier in motion. A synopsis of the bubbles’ path lines in both situations is illustrated in Figure 5. As schematized in Figure 5a, during the 1 s exposure time of the digital camera, the trajectories of ascending bubbles rising from a nucleation site adhering to the glass wall superimpose on each other to finally produce a single light streak (see the enlarged photographic detail displayed in Figure 4b). As schematized in Figure 5b, in the case of the freely floating flier, because the nucleation site is constantly moving, trajectories of bubbles released during the 1 s exposure time photograph do not superimpose on each other. Therefore, the print left by a flier which crosses the laser sheet during the exposure time of the digital camera is a typical multiple filaments structure (a very elegant and characteristic scratch, as displayed in Figure 4c), each filament materializing the trajectory of a single rising bubble. In the case of a flier moving at a velocity V and releasing bubbles with clockwork regularity (with a period T), the spacing e between two filaments of the flier’s print is equal to e ) TV. In Figure 6, a collection of various prints left by various fliers is displayed. All those prints were captured with a 1 s exposure time of the digital photo camera. The aspect of each print gives us some precious information about the direction of movement of a given flier (i), its frequency of bubble nucleation (i.e., the number of bubbles produced per second by the flier) (ii), and some accurate information concerning its velocity of displacement through the liquid medium (iii). (i) A small bubble rising through a quiescent fluid exhibits a straight-line trajectory. However, a small bubble rising through a fluid in motion will be deviated in the direction of the fluid
Flow Patterns of Fliers in Champagne Glasses
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Figure 4. Typical 1 s exposure time photograph of the traditional champagne flute crossed in its plane of symmetry by the 1 mm thick laser sheet (a). Detail showing the lighting filament left by a bubble nucleation site adhering to the glass wall (b). Detail showing the characteristic print (made by a succession of lighting filaments) left by bubbles released from a flier (c).
Figure 5. Synopsis of the bubbles’ path lines in both situations, i.e., for a fixed bubble nucleation site (a) and for a bubble nucleation site in motion (a flier) with a velocity V in the liquid bulk (b), respectively; The cylinders materialize the path taken by the bubbles along their rise toward the liquid surface; U(t) is the velocity of a rising bubble; U(t) continuously increases with time because bubbles continuously grow in size on their way up (due to dissolved-CO2 diffusion1,2,5).
velocity field. Consequently, in the latter situation, the trajectory of the rising bubble deviates from vertical in the direction of the global fluid motion. Because fliers freely floating in the
champagne bulk naturally follow the streamlines of eddies induced by effervescence, the direction of the rising bubbles freshly released from the flier teaches us about the direction followed by the flier itself. The curvature of the lighting filaments which materialize bubble trajectories (just below the print’s base) indicates the direction of the flier’s displacement through the liquid medium (see for example the white arrow in Figure 6a which points in the direction of the flier’s displacement). It is also worth noting that the curvature of the various lighting filaments left by bubbles released from a given flier betrays the continuous acceleration of bubbles along their way up. Actually, the curvature of a light streak left by a rising bubble is the result of a combination of both the vertical component of the bubble’s ascending velocity U(t) and the champagne flow velocity components in the plane materialized by the laser sheet V(r,t) (as schematized in Figure 7). Because the curvature of a lighting filament left by a rising bubble continuously decreases as the distance from the flier increases (i.e., the tangent to the light streak tends toward vertical), it can be concluded that the vertical component U(t) of the bubble’s velocity continuously increases with time (in other words, the rising velocity of ascending bubbles continuously increases with time). This continuous acceleration of bubbles along their way up has already been observed and modeled in previous works.1,2,5 It is the result of the continuous bubbles’ growth, due to the continuous diffusion of CO2-dissolved molecules. (ii) During the exposure time t of the digital photo camera, the number of bubbles emitted from a given flier is accessible
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Figure 6. Collection of various prints left by the bubbles released from various fliers along their 1 s path through the laser sheet which crosses the flute in its plane of symmetry. The white arrow in frame (a) points in the direction of movement of the flier. Bar ) 5 mm.
by counting the number N of filaments arising from the bottom of the print. Generally speaking, the bubbling frequency f of a given flier (expressed in bubbles/s) is therefore simply accessible by the ratio of the number of filaments arising from the bottom of the print to the exposure time of the camera (f ) N/t). Concerning the collection of the various fliers prints presented in Figure 6, the bubbling frequencies were found to range from about 4 bubbles/s (frame 6c) up to about 22 bubbles/s (frame 6b). It is worth noting that the bubbling frequencies of fliers, as measured in the present work, are of the same order of magnitude as those of bubble nucleation sites adhering to the flute’s wall, as measured by use of a stroboscope in a previous work.1,2 This correspondence between the bubbling frequencies of fliers and those of a fixed nucleation site is rather satisfying.
(iii) The average velocity of motion V of a given flier freely floating through the liquid medium is also simply accessible by the ratio of the print’s length L to the exposure time t of the digital photo camera (V ) L/t). Concerning the collection of various prints presented in Figure 6, the corresponding velocities of motion of fliers were found to range from about 2.8 mm/s (flier on the left side in frame 6c) to about 7.6 mm/s (flier in frame 6f). However, it should be noted that, due to our experimental setup, only the velocity components in the plane materialized by the laser sheet can be quoted here. Actually, the fliers’ velocities may also have a component perpendicular to the laser sheet (unfortunately not accessible with our experimental setup). 3.3. May Fliers Be Used as Flow Tracers? The preceding question leads us to wonder about the buoyancy of immerged
Flow Patterns of Fliers in Champagne Glasses
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space between the microfibrils being filled by liquid or/and air, depending on the moisture content.20 The volume fraction of cellulose is therefore defined as
ΦC )
VC VFW
(1)
where VC is the volume of the cellulose microfibrils and VFW the total volume of the fiber wall (cellulose microfibrils + pore space). In such hydrophilic materials, it is also common to specify the cellulose fiber wall porosity in terms of the moisture content MC defined as follows,
MC )
Figure 7. Scheme of the various light streaks left by the bubbles released from a flier. U(t) is the vertical component velocity of a rising bubble, whereas V(r,t) is the champagne flow velocity component in the plane materialized by the laser sheet. Tangents to the various light streaks tend toward vertical as the distance from the flier increases. This observation betrays the continuous acceleration of ascending bubbles.
Figure 8. Cellulose fiber acting as a bubble nucleation site on the wall of a glass poured with champagne (a), modeled as an ideal cylindrical microchannel where a tiny gas pocket has been trapped (b).
cellulose fibers. Are immerged cellulose fibers neutrally buoyant or not? The aim of the present section is to approach the own buoyancy of a cellulose fiber acting as a flier. Cellulose fibers, also commonly referred to as wood fibers, are the primary components of plant cell walls. Cellulose fibers acting as bubble nucleation sites in champagne and sparkling wines were recently identified as being tiny cylindrical microchannels structures whose walls consist of closely packed cellulose microfibrils oriented mainly in the direction of the fiber.8 A photographic detail of a typical hollow and roughly cylindrical fiber releasing bubbles is displayed in Figure 8a, together with a scheme detailing the geometrical parameters of the tiny fiber in Figure 8b. The central cavity within the fiber (where an air pocket has been trapped during the pouring process) is denoted the lumen. The fiber wall section consists of densely packed cellulose microfibrils, with a preferential orientation along the fiber axis. For a current review on the molecular and supramolecular structure of cellulose, see the article by O’Sullivan19 and references therein. The cellulose fiber wall is a highly hydrophilic and porous material with the microfibrils as the solid porous matrix, the pore (19) O’ Sullivan, A. Cellulose 1997, 4, 173-207.
mL mC
(2)
where mL and mC are the masses of liquid and cellulose microfibrils, respectively. With the assumption of densities of both the liquid and the cellulose phase, eq 1 transforms, and a relationship between ΦC and MC can be obtained,
(
ΦC ) 1 +
FC MC FL
)
-1
(3)
where FC and FL are the densities of cellulose and liquid, respectively. Though the kinetics of moisture taken up by the fibers are not so well-documented, cellulose fibers adsorbed on the inner wall of a glass poured with champagne are supposed to experience 100% relative humidity (RH). Consequently, the fiber wall pore space is considered as being completely saturated with liquid. The fiber wall has reached what we call the fiber saturation point20 (FSP). Experiments on the changes of the cellulose fiber wall structure during drying have already been conducted by using NMR self-diffusion of water sorbed in cellulose fibers.21,22 The FSP of a cellulose fiber wall was shown to occur at MC ≈ 0.8 g/g. The authors of the two above-mentioned works used beaten and unbeaten bleached kraft pulps fibers and viscose fibers. With use, in eq 3, of the latter value for the moisture content at the FSP, FC ) 1.55 g cm-3,23 and with the assumption FL ≈ 1 g cm-3, the volume fraction of cellulose in the fiber wall can be deduced at the FSP. A value of ΦFSP ≈ 0.45 is found. Consequently, with knowledge of the volume fraction of cellulose in the fiber wall, the apparent density FjFW of the fiber wall may be deduced through the following relationship:
FjFW ) ΦFSPFC + (1 - ΦFSP)FL
(4)
With replacement, in the latter equation, of each parameter by its numerical value, a value of FjFW ≈ 1.25 was found. However, this apparent density, larger than that of the liquid medium, is not that of a real flier. Actually, the flier releasing bubbles along its trajectory in the champagne bulk possesses a gas pocket trapped in its lumen (as clearly seen in Figure 8a). Therefore, the apparent density Fjflier of a flier is obtained by use of the following equation,
Fjflier )
FjFWVFW + FGVGP VFW + VGP
(5)
(20) Stone, J. E.; Scallan, A. M. Tappi 1967, 50, 496-501. (21) Topgaard, D.; So¨derman, O. Cellulose 2002, 9, 139-147. (22) Topgaard, D. Nuclear magnetic resonance studies of water self-diffusion in porous system. Ph.D. Thesis, Lund University, Sweden, 2003. (23) Fengel, D.; Wegener, G. Wood: Chemistry, Ultrastructure and Reactions; W. de Gruyter: New York, 1984.
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Figure 9. Successive 1 s exposure time photographs of a given flier followed with time as it crossed the laser sheet. The time interval between the successive frames is about 2 s. In frames (b), (c), and (d), we have reported little white velocity vectors whose lengths are proportional to the flier’s velocity and whose locations and directions of movement correspond to those of the given flier in the preceding frames. Bar ) 5 mm.
where FG is the density of the gas pocket trapped inside the flier’s lumen and VGP is the volume of the gas pocket trapped inside the flier’s lumen. Therefore, the density of a given flier logically depends on the respective volumes of the fiber wall and trapped gas pocket. Each flier, characterized by its own fiber wall and gas pocket geometry, is therefore characterized by its own apparent density denoted Fjflier. When VGP is rewritten as a fraction R of the fiber wall volume, i.e., VGP ) RVFW, and given that FG , FjFW, the apparent density Fjflier of a flier may be approached as follows:
Fjflier )
FjFW FjFW + RFG 1.25 ≈ ≈ 1+R 1+R 1+R
(6)
Numerous observations of cellulose fibers acting as bubble nucleation sites on the walls of champagne glasses have already been conducted up to now.1 Actually, it happens that the volume of the gas pocket VGP rarely exceeds that of the fiber wall VFW, i.e., 0 < R < 1. Therefore, with retrieval of eq 6, the apparent density of a flier is found to range between 0.62 < Fjflier < 1.25, the exact value depending on the gas pocket volume fraction R. In the present case, the pertinent parameter is rather the difference of density between the flier and the champagne bulk, denoted ∆F ) Fjflier - FL. This difference of density is thus in the range -0.38 < ∆F < 0.25. Depending on the gas pocket volume fraction R, the buoyancy of a given flier may therefore be negative or positive. It means that each flier exhibit its own vertical velocity (of free-rise or free-fall) due to its own buoyancy. To get an idea of the order of magnitude of the velocity of cylindrical fliers (due to their own buoyancy), we retrieved analytical results concerning the settling of cylinders, at low Reynolds numbers, reported in the book by Clift et al.24 The authors reported their results by use of the so-called “settling factor” defined as follows,
S)
Ucylinder Uvolume-equivalent sphere
(7)
where Ucylinder is the settling velocity of the cylinder and Uvolume-equivalent sphere is the velocity of a volume-equivalent sphere (24) Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic Press: New York, 1978; Chapter 4.
of the same density. The velocity of a volume-equivalent sphere of the same density is given by the Stokes velocity (at low Reynolds numbers) which stipulates that
Uvolume-equivalent sphere )
2∆Fg 2 R 9η
(8)
where g is the acceleration due to gravity and R is the radius of a sphere with a volume equivalent to that of the flier. In the case of a typical cylindrical flier with a diameter of 20 µm and a length of 100 µm (as the one schematized in Figure 8b), R is on the order of 20 µm. With retrieval, in eq 8, of each parameter by its numerical value, and ∆F in the range -0.38 < ∆F < 0.25, Uvolume-equivalent sphere was therefore found to be bounded by
-0.22 mm/s < Uvolume-equivalent sphere < 0.15 mm/s (9) In the case of a cylinder falling or rising parallel to its axis of symmetry, Clift et al.24 reported the following settling factor,
S)
χxψ 0.622(χ - 1)
[
exp
xψχ0.345
]
(10)
where Ψ is the so-called “sphericity” factor defined as the ratio of the surface area of a volume-equivalent sphere to the surface area of the cylinder and χ is the so-called “shape” factor defined as the ratio of the diameter of a volume-equivalent sphere to the diameter of the projected-area-equivalent sphere. In the case of a typical cylindrical flier with a diameter of 20 µm and a length of 100 µm, the sphericity and shape factors are Ψ ≈ 0.7 and χ ≈ 2, respectively. By use of the numerical values Ψ ≈ 0.7 and χ ≈ 2 in eq 10, a settling factor of S ≈ 0.9 was found. Finally, by use of, in eq 7, the settling factor of 0.9, as well as the limiting values of Uvolume-equivalent sphere given by eq 9, the own velocity of free-rise or free-fall of a typical cylindrical flier, due to its own buoyancy, was found to be bounded by
-0.19 mm/s < Uflier < 0.13 mm/s
(11)
The own velocity of free-fall or free-rise of fliers is therefore about 1 or 2 orders of magnitude less than the characteristic velocities of the flow patterns found in the champagne flute. The
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bubble formation from those tiny cellulose fibers may suddenly be broken as time proceeds, during the gas discharging process.25 The various filaments left by bubbles released from the fliers’ paths in Figures 6 and 9 are clearly regularly spaced. This observation is formal evidence that all the fliers in question were releasing bubbles with clockwork regularity during the 1 s exposure time of the camera (i.e., the time interval between the release of two successive bubbles is constant). Nevertheless, the two frames displayed in Figures 10a and 10b clearly highlight a bubbling regime different from the clockwork period-1 bubbling regime where bubbles are released with a constant time interval T. Both prints displayed in Figures 10a and 10b exhibit a succession of filament pairs close to each other regularly spaced by a larger interval. The aspect of these two prints is formal evidence for the period-2 bubbling regimes, where the time interval between two successive bubbles alternates between two different and well-distinct values, T1 and T2. A typical cellulose fiber (adhering to the wall of a champagne flute) in its period-2 bubbling regimes is displayed in Figure 10c. This original observation seems to indicate that the fliers in motion in the liquid medium may also experience bubbling instabilities, as nucleation sites stuck on the glass wall do.25,26
4. Conclusions and Summary
Figure 10. Characteristic prints left by two fliers releasing bubbles by pairs along their 1 s path through the laser sheet (a and b). Bars ) 1 mm. Close-up of a tiny cellulose fiber releasing bubbles by pairs on the wall of a flute poured with champagne (c). Bar ) 50 µm. Reprinted with permission from ref 25 (Copyright 2005 American Physical Society). Synopsis of the successive bubbles’ path lines, for a bubble nucleation site blowing bubbles by pairs (d).
tiny fliers are therefore definitely not sufficiently buoyant to overcome the vigorous eddies induced by effervescence in the flute. Consequently, fliers may correctly be used as velocity tracers of the liquid medium. The four pictures displayed in Figure 9 are four successive 1 s exposure time photographs of the same flier in motion along its way through the laser sheet which crosses the flute in its plane of symmetry. The time interval between the successive frames is about 2 s (which is the average acquisition time of our digital photo camera). By counting the number of filaments arising from the base of the print, it is found that this flier blows bubbles with a frequency of about 8 bubbles/s along its way through the liquid medium. By measuring the length of the print’s base, it was also found that the flier’s velocity decreases with time. It was observed that the flier’s velocity decreases from 2.3 mm/s (frame 9a) to 0.8 mm/s (frame 9d) along its way through the laser sheet. We have reported on each frame little white velocity vectors whose length is proportional to the flier’s velocity, and whose locations and directions correspond to those of the given flier in the preceding frames, respectively. 3.4. Fliers as Bubbling Instabilities Sensors. The regular and clockwork release of bubbles from a cellulose fiber is indeed the most common and usual way of blowing bubbles, but cellulose fibers were recently found to experience other various and sometimes very complex rhythmical bubbling regimes.25,26 In a previous work, it was recently observed that the periodicity of
In conclusion, and to the best of our knowledge, this study is the first one dealing with the dynamics of particles (arbitrarily called fliers) acting as bubble nucleation sites while freely floating in a champagne glass. The combination of classical long exposure time photography and laser tomography techniques revealed visually appealing pictures and quite unexpected patterns in a simple flute poured with champagne. Fliers were found to leave very elegant and characteristic “prints” as they crossed a section of champagne illuminated with a 1 mm thick laser sheet. The characteristic prints left by fliers enabled us to deduce their bubbling frequency as well as their velocity of motion through the liquid medium. This flow visualization technique also proved to be a useful technique to underscore fliers’ bubbling instabilities along their rather erratic way through the liquid medium. Through the present paper, we would like to bring our contribution to a better understanding of some of the fascinating processes hidden behind everyday phenomena such as the tasting of champagne and sparkling wines. Acknowledgment. We pay homage to the recently deceased Professor Pierre-Gilles de Gennes, Nobel Prize in Physics in 1991. Professor de Gennes was a pioneering scientist who invented and developed a new area of science devoted to what we call today “soft matter”. He recently wrote, together with two renewed colleagues, a wonderful book that provides numerous answers to common questions about everyday phenomena.27 Thanks are due to the Association Recherche Oenologie Champagne et Universite´ for financial support, to ARC International for supplying us with glasses and for supporting our research, to Thierry Gasco, from Champagne Pommery, for supplying us with champagne and to the CIVC for providing us with the photograph displayed in Figure 1. LA7017693 (25) Liger-Belair, G.; Tufaile, A.; Robillard, B.; Jeandet, P.; Sartorelli, J.-C. Phys. ReV. E 2005, 72, 037204. (26) Liger-Belair, G.; Tufaile, A.; Jeandet, P.; Sartorelli, J.-C. J. Agric. Food Chem. 2006, 54, 6989-6994. (27) De Gennes, P.-G; Brochard-Wyart, F.; Que´re´, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, WaVes; Springer: New York, 2003.
