Role of Mixing Dynamics on Mass Convection-Diffusion in Sparkling Wines: A Laboratory Study

Abstract

This study is based on the hypothesis that the bubbles-induced vortex flows could enhance the release of carbon dioxide (CO₂) from a glass of effervescent wine. To provide tangible evidence, we conducted a series of experiments, the first of which aimed to correlate the filling height and the bubble-induced flow dynamics with the CO₂ volume flux released from the vessel during a tasting. The results obtained through micro-weighing and PIV experiments showed a correlation between the filling height, the mixing flow dynamics, and the amount of CO₂ released at the air/wine interface by several mechanisms (bubble burst, diffusion). In order to hide the role of bubbles, we proposed a simple experimental device that consisted in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding the phenomenon of nucleation. This mechanical stirring system allowed for controlling the intensity of convective movements of the liquid phase by varying the rotation frequency of a glass rod. The results of this experiment have provided irrefutable evidence of a close link between the stirring dynamics of a wine supersaturated in dissolved gases and the release of CO₂ by a mass convection-diffusion phenomenon.

1. Introduction

Sparkling wines are becoming increasingly popular internationally, thanks in part to the elegance of their foaming and effervescent properties, often synonymous with celebration and luxury. The oenophile appreciates a regular and long-lasting effervescence, ensuring a persistent cord of white foam at the edge of the glass. The fineness of the bubbles of champagne is also a suggestive criterion of the quality of the wine, which contributes to its appreciation by the consumer. Champagne and sparkling wines differ from flat, non-sparkling wines in that they are supersaturated with dissolved carbon dioxide (CO₂), formed with ethanol during a second fermentation process in sealed bottles [1]. A standard 75-centiliter bottle of champagne typically contains about 9 g of dissolved CO₂, which corresponds to a volume close to 5 L of gaseous CO₂ under standard temperature and pressure conditions [2]. Under normal tasting conditions, champagne and sparkling wines are, therefore, characterized by the much sought-after process of bubbling (called effervescence), which betrays the progressive desorption of dissolved CO₂ from the liquid phase [3,4,5]. Strictly speaking, there are two mechanisms involved in the release of gaseous CO₂ and volatile organic compounds (VOCs) under standard tasting conditions: (i) losses due to heterogeneously nucleated bubbling in the glass, and (ii) losses due to diffusion through the free surface of the glass (invisible to the naked eye), [2,6]. Moreover, in a liquid phase supersaturated with dissolved gaseous species, degassing can be achieved through the free surface by pure molecular diffusion, or by diffusion-convection, depending on whether the liquid phase is stagnant or moving [7,8]. The role of bubbles does not stop at the strictly aesthetic and ultimately subjective aspect during a tasting (cf. Figure 1). Indeed, when they migrate into the wine, the hundreds of bubbles nucleated in the glass drive the surrounding liquid by viscous effects in a very structured movement [9,10] which allows a very efficient stirring (as long as the champagne contains enough dissolved CO₂ to favor the nucleation of bubbles). Under standard tasting conditions, champagne agitation under the action of rising bubbles has, therefore, been strongly suspected to accelerate the release of CO₂ and gaseous VOCs across the air/champagne interface [11].

Recently, we performed measurements to determine the time evolution of dissolved CO₂ concentration in four differently shaped glasses filled with 100 mL of sparkling wine [12]. These novel results revealed that during a tasting, for the same quantity of wine and under identical tasting conditions, the dissolved CO₂ concentration evolves differently from one glass shape to another. PIV techniques have also been applied to investigate the contribution of glass shape to bubble-induced flow patterns [13,14]. The swirling intensity of the wine, called vorticity, has been shown to increase the release of gaseous CO₂ throughout the tasting experience [13]. Therefore, we assumed a link between the dynamic evolution of the liquid phase and the release of CO₂ by convection-diffusion, which is the superposition of two transfer mechanisms, molecular diffusion (Fick’s law), and mass transport (convective transport) induced by effervescence [15,16,17]. In this study, we attempt to provide concrete scientific evidence for a link between wine stirring dynamics and CO₂ release by convective-mass diffusion.

For this purpose, we conducted a series of experiments. The first of these experiments aimed at correlating the filling height (which affects the dynamics of effervescence, the engine of the flow) and the bubble-induced flow dynamics with the volume fluxes of gaseous CO₂ released from the vessel during a tasting. To hide the role of bubbles (which also release CO₂), we have developed an experimental device that consists of stirring the wine (supersaturated in dissolved gas) mechanically while avoiding the phenomenon of nucleation.

2. Materials and Methods

2.1. Physical Evidence of Mass Transfer Processes in Sparkling Wines

From a chemical point of view, champagne can be considered as a complex hydroalcoholic solution [18]. In a glass of effervescent wine, the transfer between the liquid, gaseous, and atmospheric phases results in a mass loss measured by micro-weighing. The measured mass loss is the result of the desorption of carbon dioxide added to the cumulative evaporation of ethanol, water molecules, and some volatile compounds [17].

Thus, during a tasting, the mass transfer between the liquid phase, supersaturated with dissolved gases, and the atmosphere will mainly involve dissolved CO₂ molecules, ethanol, VOCs (Volatile Organic Compounds), and then water molecules (≈80% of the wine). Once the wine is poured into the glass, the mass transfer would take place through several distinct physical processes: evaporation, diffusion (molecular and/or mass convection-diffusion depending on the bubble nucleation process), and effervescence.

(a)

Evaporation: it is the passage from the liquid phase of a substance to its gaseous phase. In champagne wine (and other sparkling wines), evaporation will mainly involve ethanol, water, and to a lesser extent, some volatile compounds.

(b)

Diffusion: When the liquid releases 10 g of dissolved CO₂ molecules per liter of champagne, this is equivalent to a volume of carbon dioxide gas of 6 L at 20 °C. In an effervescent wine, the carbon dioxide, in a state of supersaturation in wine, is evacuated by:

–

Molecular diffusion: In the absence of effervescence in the glass, the mass transfer of CO₂ occurs solely by molecular diffusion. According to Fick’s law (Equation (1)), CO₂ molecules will progressively move from the liquid matrix, where they are contained in excess, to the air where CO₂ molecules are in the minority [19,20]. This process, which tends towards equilibrium between the two zones (wine and air), can last several days.

Fick’s law is given by the following relationship:

$$\overrightarrow{J_n}=-D.\overrightarrow{\nabla c}$$

(1)

where ∇c (mol/m³) is the CO₂ concentration gradient between the air/wine interface and the liquid matrix (mol/m³). D (m²/s) is the diffusion coefficient of CO₂ molecules (m²/s).

• –

  Mass convection-diffusion: With effervescence, the mass transfer of CO₂ occurs by mass convection-diffusion. This is the superposition of two transfer mechanisms, molecular diffusion (Fick’s law), and transport due to the mass transfer (convective transport) induced by effervescence (Figure 1) [15].

2.2. Experimental Process

We measured the progressive mass loss of wine by micro weighing [21]. The experimental tests consisted of recording the time evolution of the liquid mass contained in a vessel using an ultra-sensitive balance. In this study, we used sparkling wine with an initial CO₂ concentration measured by carbonic anhydrase at 7.45 g/L of wine [12]. A new bottle of the same batch was opened for each measurement performed with the sparkling wine. Thus, the initial CO₂ concentration was the same for each measurement performed in an air-conditioned room with an ambient temperature of 20 °C. Once the wine was served, the vessel was gently placed on the plate of a precision balance (Denver Instrument PI 314 balance with a capacity of 310 g and a precision of 0.1 mg). The timer was started, and the progressive loss of mass was measured during the first ten minutes after pouring. The precision balance was interfaced with a laptop computer that measured the mass of the liquid every five seconds. A mean and standard deviation were calculated from four sets of measurements.

2.3. Influence of the Filling Height

In order to establish a link between mass transfer, mixing dynamics, and filling height, we performed mass loss measurements followed by Particle Image Velocimetry (PIV) measurements. First, we performed micro weights in a cylindrical vessel for three filling heights. A beaker, whose characteristic dimensions are shown in

Table 1. Characteristic dimensions of the container according to the filling height.

Filling Height (mm)	Capacity (mL)	Interface Area (cm2)
28	40	16
42	60	16
56	80	16

, was mechanically etched to force the nucleation process. Thus, bubbles were nucleated from the bottom of the beaker and ensured continuous stirring of the wine. All weighings were performed several times to calculate a mean and standard deviation and to ensure the reproducibility of the experiment. A bottle of sparkling wine, whose initial CO₂ concentration was measured at 7.45 g/L, was opened for each measurement. The same wine of an identical batch was used throughout the study.

In complement, we performed PIV measurements to assess the link between mixing flow dynamics and CO₂ mass transfer. Previous studies using flow visualization methods have revealed the annular behavior of the induced vortex flow, as well as the axisymmetric character of the flow [9,10]. In this particular case, a 2D analysis performed in the plane of symmetry can be considered sufficient to study the 3D flow dynamics. To avoid optical distortions by the curved surface of the glasses, the container was partially immersed in a parallelepiped tank full of water.

The experimental setup included a 2D PIV measurement system equipped with a Litron^®® Nd: YAG laser emitting at 532 nm for a maximum power of 135 mJ, a laser sheet (created through a cylindrical lens), and a CCD camera (Flow sense model) recording 14-bit black and white images. Sequences of 20 images in double frame mode were recorded with a frequency of 4 Hz and a laser pulse duration of 250 ms. Sparkling wines were considered as a two-phase flow with two co-occurring phases (a gas phase and a liquid phase). Thus, to prevent bubbles from being identified as tracers by the PIV system, an interference filter centered on the fluorescence emission wavelength of Rhodamine B was used. Finally, an average correlation was chosen as the post-processing algorithm to produce a vector field providing quantitative data on the mixing dynamics. To ensure the convergence of the results, three successive measurements were necessary for each filling height.

2.4. Influence of Wine Brewing

To establish a correlation between the wine stirring dynamics and the amount of CO₂ released by mass convection-diffusion, we designed an experimental device that consisted in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding nucleation. The experimental system was composed of an electric motor connected to a 0–30 volts DC power supply, and a glass rod fixed on the motor axis. The 3 mm diameter rod was eccentric by 2 cm concerning the motor axis (Figure 2) and was immersed in about 3 cm of wine. The rod was made of glass, smooth, and non-porous, and did not trap air when pouring. Furthermore, the rod was scrupulously cleaned with alcohol between each measurement, which avoided any parasitic nucleation site.

The progressive mass loss of the wine was measured and recorded every 5 s. All experiments were performed in a beaker filled with 80 mL of sparkling wine (Table 1), one bottle was opened for each weighing. The purpose of this experiment was not to reproduce faithfully the stirring processes induced by effervescence, but rather to highlight the relationship between mass convection and mass transfer. Since effervescence was the process that sets the wine in motion, we carried out the first weighing without nucleation to have a perfectly still liquid. In this case, the degassing would occur only by molecular diffusion due to the difference in concentration gradient (in dissolved CO₂) between the atmosphere and the wine. A second weighing was carried out with nucleation, so it was the bubbles that would set the liquid in motion. Next, we carefully cleaned the beaker to remove any nucleation site that could generate a parasitic train of bubbles. We then performed two more weighings with the mechanical device by stirring the wine at two rotation frequencies (ω ≈ 55 et 100 tr/min). The four curves were then compared, allowing us to highlight the influence of stirring on mass transfer phenomena.

3. Results

The most relevant parameter for characterizing the gradual release of gaseous CO₂ from a glass of sparkling wine during a tasting is the total CO₂ volume flux [22]. The total CO₂ volume fluxes, denoted as F_T (cm³/s), which was the sum of two terms: the loss due to CO₂ volume flux liberated by the bubbles, denoted as F_B, and the CO₂ volume fluxes discharged by diffusion through the free surface area denoted F_S.

Finally, total CO₂ volume fluxes released from a glass of sparkling wine during a tasting can be expressed as:

$$F_T\approx F_B+F_S$$

(2)

and

$$F_T=\left(\frac{RT}{MP}\right)\frac{{\Delta }_m}{{\Delta }_t}$$

(3)

where R is the ideal gas constant (equal to 8.31 J/K/mol), T is the wine temperature (K), M is the molar mass of CO₂ (44 g/mol), and P represents the ambient pressure (close to 10⁵ N/m²), the mass loss ${\Delta }_m$ between two consecutive data being expressed in g, and ${\Delta }_t$ being the period from one data record to the next (i.e., 5 s in our study).

Figure 3 represents the total CO₂ flux for three filling heights. The results reveal that the higher the liquid height, the higher the CO₂ flux.

With nucleation (as a consequence of the supersaturated state of the wine in CO₂), the mass transfer would not be done only through molecular diffusion but through a combination of molecular diffusion and mass convection-diffusion. The losses due to effervescence can be estimated via the volume flux of CO₂ released by the bubbles called F_B. The latter would depend on the number of nucleation sites, $N$, the bubbling frequency, $f$, and the volume of the bubble, $v$ (m³), when it reaches the surface [6].

$$F_B=Nfv\approx \frac{Nf{d}^3}{2}$$

(4)

In the present case and since we apply the same etched vessel for each measurement, we assumed that the number of nucleation sites was identical for the three filling heights. However, the size of the bubbles depended on the distance to the surface. Thus, the higher the filling height, the higher the amount of CO₂ released by the bubbles. The last element to consider was inherent to the mass losses through diffusion at the air/wine interface. Again, since the same vessel was being used, the interface area (Table 1) did not change regardless of the fill height.

Figure 4 represented the vector fields obtained through PIV measurements for the three filling heights (28, 42, and 56 mm). The quantitative data deduced from the PIV measurements were of great interest in understanding the liquid mixing mechanisms. These vector fields clearly demonstrated a relationship between the filling height and the velocity of the bubble-induced flows. If we focused on the order of magnitude of the velocities recorded for each filling height, we could see that the peak velocities were almost three times higher for a filling height of 56 mm, compared to a filling height of 28 mm.

In fact, the higher the filling height, the greater the distance covered by the bubbles. In a beaker filled to the top, the bubbles reached higher rising speeds, which generated higher shear stresses on the surrounding fluid. What can also be inferred from the vector fields was the topology of the flow, which depended on the space left for vortex ring formation. For a low filling height (e.g., 28 mm), the vortex ring occupied all available space and the whole fluid was stirred homogeneously but with little intensity. On the contrary, for a higher filling height, the vortex flow occurred in the upper third of the beaker. As the bubbles’ ascension velocity was higher, the velocity within the vortex ring was logically higher than for lower filling heights.

Role of Mixing Dynamics on Mass Convection-Diffusion

To highlight the contribution of convective stirring processes to the intensity of mass transfer, we mechanically recreated convective movements normally induced by bubbles. For this purpose, we have designed a mechanical stirring system that allows controlling the intensity of the convective movements of the liquid phase. Thus, it is possible by varying the rotation frequency of a glass rod, to study the influence of the stirring speed on the evolution of the amount of CO₂ released over time. The cleaning of the beaker allows for avoiding any parasitic nucleation site, which would be detrimental to the control of the stirring process. Figure 4 represents the CO₂ volume fluxes measured without effervescence compared with the fluxes obtained with mechanical stirring (also without nucleation). We can see a close link between the dynamics (and intensity) of stirring and mass transfer. When we accelerated the stirring (from 55 to 100 rpm), the CO₂ fluxes increased (Figure 5).

4. Discussion

The dynamics of bubble-induced flows is one of the only parameters actively affecting the amount of CO₂ released from a glass of sparkling wine. Indeed, there is a direct correlation between the fluctuation of the velocity inside a fluid supersaturated with gaseous species and the velocity of gas molecules released from the liquid medium [23,24]. In a glass of champagne, the hundreds of bubbles nucleated each second carry the surrounding liquid in a more or less structured motion [9,10,13,14]. By viscous effects, the bubbles allow a continuous mixing of the wine (Figure 1). The laws of diffusion suggest that the convection movements generated by effervescence accelerate the mass transfer between the liquid and gaseous phases [15,16]. To further investigate this point, we have performed dynamic measurements by PIV method for three different filling heights. PIV measurements have shown a relationship between the filling height and the velocity of effervescence-induced convection movements. Quantitative data deduced from PIV measurements have shown that the filling height strongly influences the overall mixing conditions of the liquid phase, leading to a potential increase in the release of gaseous CO₂ through the convection-diffusion process. More interestingly, the higher the flow velocities of the liquid phase, the higher the CO₂ volume fluxes, which was confirmed by comparing Figure 3 and Figure 4. These unprecedented results thus confirmed a strong coupling between the flow velocity of the liquid phase and the amount of gas molecules released by the convection-diffusion process across the air/wine interface of the beaker. Ultimately, the results showed that the filling height was an essential parameter for the release of dissolved CO₂ by bubble nucleation and mass convection-diffusion. However, an accurate estimation of the amount of CO₂ released by the bubbles during a tasting remains difficult because it is based on a semi-empirical relationship (Equation (4)). To be more accurate, it would be necessary to know precisely and in real-time, the number of bubbles nucleated at the bottom of the glass, which was very difficult to achieve. By analogy, it is therefore difficult to estimate precisely the amount of CO₂ released by diffusion at the air/wine interface. For this reason, we undertook an experiment that provided irrefutable evidence of a direct link between the stirring dynamics of a wine supersaturated with dissolved gas and the release of CO₂ through a mass convection-diffusion phenomenon. Figure 5 shows us that the slope of the curves with mechanical stirring presents an almost linear aspect in comparison with the molecular diffusion curve (0 rpm), the stirring speed remaining constant throughout the twenty minutes of the experiment. In contrast, with natural effervescence, the flow engine naturally depletes as the dissolved carbon dioxide level in the wine decreases. Thus, the CO₂ flux with nucleation is more important, since the losses due to effervescence must be added to the losses by diffusion at the air/wine interface. In the context of a tasting, it is undeniable that a glass in which the wine is actively swirled will rapidly lose its dissolved gas, which will result in a depletion of the surface aromatic components that are carried by the bubbles.

5. Conclusions

This study was based on the hypothesis of a relationship between the dynamics of wine stirring (induced by bubbles) and the release of CO₂ by mass-convection diffusion. To provide concrete scientific evidence, we conducted a series of experiments, the first of which aimed to correlate the filling height (which acts on the dynamics of effervescence, the driving force of the flow) with the CO₂ volume fluxes released from the vessel during a tasting. The results showed a correlation between the filling height and the amount of CO₂ released through the air/wine interface. The measurements obtained by micro weighing allowed us to quantify the total mass loss related to the release of CO₂ contained in the bubbles added to the CO₂ released by diffusion at the air/wine interface. In complement, we performed PIV experiments to demonstrate a link between the filling height and the bubble-induced flow dynamics. By comparing the amount of CO₂ released for each filling height with the dynamics of wine mixing, it was evidenced that the higher the liquid velocities, the higher the CO₂ fluxes outgassing from the liquid medium. The relative part of the quantity of gaseous CO₂ released by the bubbles can be estimated by a semi-empirical relation, which leads to an imprecise deduction of the amount of CO₂ released by diffusion. In order to hide the role of the bubbles, we proposed a simple experimental device that consists in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding the phenomenon of nucleation. This mechanical stirring system allows controlling the intensity of the convective movements of the liquid phase by varying the rotation frequency of a glass rod. The results of this experiment have provided irrefutable evidence of a direct link between the stirring dynamics of a wine supersaturated in dissolved gases and the release of CO₂ by a mass convection-diffusion phenomenon.