Bubble cascade in guinness beer is caused by gravity current instability

ABSTRACT The downward movement of the bubble-texture in a glass of Guinness beer is a fascinating fluid flow driven by the buoyant force of a large number of small-diameter bubbles. This

texture motion is a frequently observed phenomenon on pub tables. The physical mechanism of the texture-formation has been discussed previously, but inconsistencies exist between these

studies. We performed experiments on the bubble distribution in Guinness poured in an inclined container, and observed how the texture forms. We also report the texture-formation in

controllable experiments using particle suspensions with precisely specified diameters and volume-concentrations. Our specific measurement methods based on laser-induced-fluorescence provide

details of the spatio-temporal profile of the liquid phase velocity. The hydrodynamic condition for the texture-formation is analogous to the critical point of the roll-wave instability in

a fluid film, which can be commonly observed in water films sliding downhill on a rainy day. Here, we identify the critical condition for the texture-formation and conclude that the

roll-wave instability of the gravity current is responsible for the texture-formation in a glass of Guinness beer. SIMILAR CONTENT BEING VIEWED BY OTHERS BUBBLES DETERMINE THE AMOUNT OF

ALCOHOL IN MEZCAL Article Open access 03 July 2020 SELF-REPLICATING SEGREGATION PATTERNS IN HORIZONTALLY VIBRATED BINARY MIXTURE OF GRANULES Article Open access 04 March 2024 ANOMALOUS

FLOCKING IN NONPOLAR GRANULAR BROWNIAN VIBRATORS Article Open access 17 July 2024 INTRODUCTION Following Archimedes’ principle, bubbles in liquid generally rise because of the gas-liquid

density difference. Despite the natural rising behaviour of bubbles, after pouring Guinness beer in a pint glass, the bubbles can be observed to descend. At the same moment, a vast number of

small bubbles with a mean diameter of 50 μm (only 1/10 the size of those in Budweiser or champagne1,2,3) disperse throughout the entire glass. We can also observe the fascinating texture

motion as a number-density distribution of bubbles travelling downwards. Curiously, although creamy bubbles have been served in Guinness beer for more than half a century, the mystery of

such a cascading motion of bubbles has been debated in terms of fluid dynamics ever since4,5,6,7. Because the black colour of Guinness obstructs the physical observation in a glass,

computational simulations have been a valuable tool to understand the bubble distribution and motion. The computational investigation has concluded that when Guinness is poured into a

typical pint glass, which widens towards its top, the rising motion of bubbles creates a clear-fluid (bubble-free) film above the inclined wall. The dense clear-fluid film falls, whereas the

bubble-rich bulk rises7, which is known as the Boycott effect8. Accordingly, we can observe the descending bubbles entrained into the downward flow in Guinness, which is seemingly

paradoxical in light of Archimedes’ principle. Although this physical explanation leads to the understanding of the descending motion of bubbles, the mechanism underlying the

texture-formation still remains an open problem. The texture motion of bubble swarm moving downwards, so-called “_waves_” or “_cascades_”, is a unique and frequently-observed phenomenon in a

glass of stout beer with nitrogen. Analogies to the texture-formation in Guinness have been noted in several studies4,5. The reduction in the rise velocity of bubbles in large

bubble-volume-concentration fluids, known as the hindered velocity9,10, was suggested to be one of the mechanisms, i.e., the velocity difference in the bubble swarm is involved in the

downward movement of the bubble swarm as waves, even when the buoyant bubbles themselves rise4. On the other hand, a one-dimensional flow model, which assumes an eddy viscosity due to the

variation in bubble-volume-concentration, was developed to include a mathematical structure of the roll-wave instability, which can be commonly observed in water films sliding downhill on

rainy days5. However, in previous studies, there have been inconsistencies in the movement directions and in the longitudinal wavelengths4,5,7. Moreover, the presence of a clear-fluid film

was not considered in the model5, and the hydrodynamic condition for the texture-formation have not been discussed so far. In this study, we propose a falling liquid film model assuming

stratified two-fluids, and we experimentally quantify the critical condition for the roll-wave formation involved with the hydrodynamic instability in the gravity current in the inclined

wall vicinity. EXPERIMENTS EXPERIMENTAL APPARATUS We studied the motion of bubbles in three different containers: a pint glass (Fig. 1a), an inclined rectangular container (Fig. 1b), and a

trapezium container (Fig. 1c). The inclination angle _β_ was adjusted from 0 degrees (vertical) to 70 degrees. To observe the motion of the bubble-texture, we poured Guinness beer in the

containers from a 330-ml can of Draught Guinness. Note that we measured the density and viscosity of liquid in Guinness beer ourselves and found that the liquid density was _ρ_0 = 1006 kg/m3

and viscosity was _μ_ = 2.1 × 10−3 Pa·s (see also Supplementary Fig. S1). The mean diameter of bubbles in Guinness was 61 μm, and the volume-concentration of the bubbles was _α_ = 8%. The

details of the fluid properties are also summarised in Supplementry Table 1. PSEUDO-GUINNESS FLUID To conduct well-controlled experiments, we also used a particle suspension comprising tap

water with a mean temperature of 25 °C (_μ_ = 0.9 × 10−3 Pa·s) and hollow spherical glass particles with a mean diameter of 47 μm and a density of _ρ_1 = 140 kg/m3. The volume-concentration

of glass particles _α_ was adjusted to 0.5–10%, making it comparable with the volume-concentration of bubbles in Guinness. By using undeformable glass particles, we could neglect the

expansion of the bubble diameter due to the diffusion of mixture gas, comprising CO2 and N2, from the supersaturated solution into the bubble interior4,6. We could also neglect the

modification of the rise motion due to a nonuniform contamination distribution of beer components along the bubble surface, known as the Marangoni effect11. The particle suspension offers

another striking advantage: it is suitable for measuring the liquid phase velocity in the transparent liquid phase of suspension rather than the opaque Guinness. Consequently, for measuring

the liquid phase velocity, we could employ optical measurement instruments applying laser-induced-fluorescence. FLOW VISUALISATION USING MOLECULAR TAGS The photo-bleaching molecular tagging

visualisation12,13, which is the elaborated non-contact and non-invasive measurement technique for the liquid-phase of bubbly flows, was applied for the quantitative visualisation of the

liquid phase velocity. Figure 2a shows a schematic of the visualisation setup. Fluorescein was dissolved in tap water with _O_(10−6) mol/m3. An intense laser beam at a wavelength of 447 nm

was focused with 250 μm beam waist diameter using a convex lens, and was irradiated on the measurement (_x_-_y_) plane of the trapezium container. A 1 mm thick laser sheet at wavelength of

447 nm which is installed 5 mm away from the vertical wall illuminated the measurement plane. The irradiation time and the time interval between two-consecutive irradiations of intense laser

beams were adjusted to 20 ms and 100 ms for _α_ = 0.5%, whereas 100 ms and 200 ms for _α_ = 5%, respectively, using a function generator. As illustrated in Fig. 2b, the molecular tag formed

by the intense laser beam appears as a dark region, i.e., non-fluorescent region, on the measurement plane. The displacement and distortion of the molecular tags inform us of the liquid

phase flow pattern as a timeline image. The reflected light at 447 nm from the particle interface was blocked by an optical long-pass filter with a wavelength range of 480 ± 5 nm, whereas

most of the fluorescent light passed the filter. Therefore, the tag lines being the non-fluorescent region were clearly visualised in fluorescent images. MEASUREMENT OF THE LIQUID PHASE

VELOCITY The velocity of the liquid phase was obtained via direct cross-correlation particle image velocimetry (PIV)14. To distinguish tracer particles in particles suspension, we applied

the laser-induced-fluorescence (LIF) technique to PIV15. Fluorescent tracer particles with 15 μm in diameter (specific gravity: 1.1, absorption wavelength: 550 nm, emission wavelength: 580 

nm) were seeded at 0.03 vol. % in the particle suspension. A diode-pumped-solid-state laser at wavelength of 532 nm illuminated a light sheer at _x_ ≈ 100 mm with 1 mm thickness in the

rectangular container. The reflected light at 532 nm from the particle interface was blocked by an optical long-pass filter with a wavelength range of 580 ± 5 nm, whereas most of the

fluorescent light passed the filter (Fig. 2c). We treated bubbles in Guinness as behaving like tracer particles. The outlier velocity vectors were eliminated by comparing with the

surrounding vectors16, and any missing vectors were interpolated. RESULTS INCLINED ANGLE DEPENDENCY ON TEXTURE FORMATION We start by showing qualitative features of the texture-formation in

a pint glass. Figure 3a shows a snapshot of the texture as the number-density distribution of bubbles in a pint glass 10 seconds after pouring Guinness. Visually, the texture can be easily

observed at 30 mm < _x_ < 70 mm, where the wall is inclined due to the tapered shape of the glass with inclined angle of ≈ 15 degrees. Figure 3b shows the temporal change in the phase

separation: the black region (liquid of beer), the grey region (bubbly flow), and the white region (head of foam). The bubbly flow region gradually decreases with increasing time and the

amount of foam head increases. Finally, the glass of Guinness is completely separated into two contrasting phases (namely, the liquid and the head of foam), corresponding to the phase

separation owing to the buoyant rise of each bubble. The texture appearing in a glass propagates downwards with a travelling velocity of ~−35 mm/s (Fig. 3c, Supplementary Movie S1), which is

consistent with previous experimental observation5. Because of the differences in the travelling velocity of each wave and the three dimensionality of the flow, the neighbouring waves

collide and coalesce, and thus the diagonal stripes in the travelling-wave exhibit the bifurcations and crossovers in the texture. To test the effect of inclination angle on the

texture-formation, we repeated the observation of the texture-formation but after adjusting the inclination angle _β_ of the rectangular container. The texture-formation result is shown in

Fig. 4a. We found that the bubbles were uniformly distributed at _β_ = 0, 45 and 65 degrees. For 5 degrees < _β_ < 20 degrees, however, the texture appeared and exhibited spatial

development: from organised waves to unstructured motions, similar to that of the Tollmien-Schlichting wave or the roll-wave17,18. This finding suggests that the appearance of the texture is

triggered by the inclination of the wall and depends on the length of the system. In spatially developing flows, disturbances grow with distance from a flow entrance and can be clearly

observed as wave at a sufficient distance to downstream. Although the texture was not clearly found at _β_ > 45 degrees in Fig. 4a, it might possibly appear if the container were taller.

We restrict ourselves to the study of the texture-formation in a glass with a height of ~150 mm (the typical size of pint glasses) and focus on the effect of inclination angle. To address

the moving direction of bubbles yielding inconsistent results between previous investigations, i.e., whether bubbles move upwards4 or downwards7, we examined the velocity of bubbles near the

inclined wall at _y_ ≈ 0.5 mm and _x_ ≈ 80 mm. The corresponding video can be viewed in Supplementary Movie S2. From the superimposed movie of bubble-diameter/velocity, we conclude that

this approach provides an excellent measure for both the diameter and the velocity of bubbles. The instantaneous velocities are shown in Fig. 4b, and the time series of the brightness in

image _B_ involved with the local-volume-concentration of bubbles and the time series of bubble velocities are shown in Fig. 4c, respectively. The bubbles move downwards with both the

vertical and horizontal fluctuations. The cross-correlation between the brightness _B_ and the vertical component of the bubble velocity _v__x_ is ≈0.8, exhibiting sufficiently high value.

Such a high correlation indicates that bubbles are likely to move downwards more quickly in lower local bubble-volume-concentration regions, and vice versa. These findings suggest that the

fluid blobs containing few bubbles descend in the bubble-rich bulk; it is likely that a water film (heavy fluid) falls in air circumstances (light fluid). Here, we consider a particle

suspension comprising tap water and hollow glass spherical particles, rather than Guinness containing bubbles, to determine the effect of the volume-concentration of dispersed bodies _α_.

The results for the texture-formation in particle suspension with various values of _α_ are compared with those in Guinness in Fig. 5a. In the particle suspension, as for the novel findings,

we can observe the texture, which is comparable with that in Guinness, at all particle concentrations _α_. The side view of the trapezium container answers the crucial question of where the

texture appears in a container. Although bubbles rise in the bulk because of the density difference between the liquid and gas phases, bubbles move downwards in the inclined wall vicinity

due to the Boycott effect8 (see accompanying Supplementary Movie S3). As also shown in Fig. 5b, for almost the entire region of the trapezium container including the vertical wall vicinity,

the texture cannot be observed in the container, except for the downward flow confined to the inclined wall vicinity. We re-plot this finding in temporally expanded images in Fig. 5c for

various distances from the inclined wall: _y_ = 0.1 mm (top), _y_ = 0.5 mm (middle), and _y_ = 1.0 mm (bottom). For both _y_ = 0.5 mm and _y_ = 1.0 mm, we observe a diagonal pattern with a

fluctuation in brightness corresponding to the waves travelling downward. For _y_ = 0.1 mm, on the other hand, the image includes a darker region corresponding to the so-called clear-fluid

(bubble-free) region7. MOVEMENT OF LIQUID PHASE FLOW We attempted to determine the exact liquid-phase velocity profile in this thin clear-fluid film. Timeline-image visualisation applying

photo-bleaching molecular tagging method was implemented to characterise the liquid-phase velocity at the wall vicinity, as shown in Fig. 5d. The displacements of timelines, which appear as

darker regions (molecular tag), exhibit the following behaviours: unsteady descending flow, a maximum descending velocity at a certain location, zero velocity relative to the boundary, and

ascending flow in the interior of the container. Furthermore, the number-density of particles significantly decreases below the location at which the magnitude of the liquid velocity is

maximised. This formation of the stratified layer causes a gravity current accompanying the global convection (the Boycott effect), as mentioned above8. The details in the velocity profile

of the liquid phase are also obtained via PIV. We apply PIV for Guinness (top) and a particle suspension with _α_ ≈ 5% (bottom). From the instantaneous wall-normal variations of the velocity

component along the wall, as shown in Fig. 6b, the descending and ascending motion of the liquid phase exhibit identical feature with that obtained from the photo-bleaching visualisation.

To address the velocity fluctuations along the inclined wall, we plot a velocity profile at _x_ = 100 mm in space-time diagram (Fig. 6c). The magnitude of the descending velocity decreases

with increasing time because of the reduced amount of the buoyant bubbles, the velocity fluctuations continue to form. Although we found that there are differences in the magnitude and

period in the velocity fluctuations between the Guinness and the particle suspension, we judge that these parameters are consistent with the spatio-temporal characteristics of the waves.

CRITICAL CONDITION FOR TEXTURE FORMATION To obtain an understanding of the texture-formation in the gravity current, we modelled a stratified flow of two liquids: a clear (heavy) liquid film

and a bubble-rich bulk (light) liquid, as shown in Fig. 7a. We consider a thin clear-fluid film that flows down on an infinite flat plate of inclination angle _β_ with respect to the

gravity due to the density difference between the clear and bubble-rich fluid. In a stable flow, the gravity or viscous force tends to keep the interface flat (left panel of Fig. 7a). The

bubble-texture forms as an interfacial wave (right panel of Fig. 7a) between the two fluids when the fluid motion becomes unstable. The texture-formation is reflected in the velocity

fluctuation. We determined the maximum values of the time-averaged velocity along the wall \({|{\bar{u}}_{x}|}_{{\rm{\max }}}\), the maximum root-mean-square values of the

velocity-fluctuation component along the wall \({u}_{x,\,{\rm{\max }}}^{^{\prime} }\), and the loci _h_ relative to the wall at which \({|{\bar{u}}_{x}|}_{{\rm{\max }}}\) was achieved via

particle image velocimetry (Fig. 7b). Note that it is nontrivial to define the film thickness because of no _sharp_ interface between the clear and bubble-rich fluids due to the discrete

bubble distribution. In the present study, the film thickness _h_ is evaluated from the velocity profile instead of the bubble distribution. Following ref.19, in which the particle

sedimentation was theoretically studied, the definition of _h_ is the distance from the wall, at which the falling liquid velocity takes the maximum and thus the free-slip condition is

likely to be satisfied similar to the conventional roll-wave model18 with a free-slip interface. It should be noticed that from preliminary measurements of time-averaged profiles of the

velocity and the particle concentration _α_, the velocity-based film thickness _h_ has been confirmed to be comparable to the distance from the wall, at which _α_ takes the half of the

particle concentration in the bubble-rich fluid, and thus regarded as a natural choice to characterise the flow. Consequently, from these characteristic quantities, we obtain the Reynolds

number and the Froude number expressed respectively as $$Re=\frac{(1-\alpha )\rho \,h\,{|{\bar{u}}_{x}|}_{max}}{(1+\frac{5}{2}\alpha )\mu },$$ (1) $$Fr=\frac{2{|{\bar{u}}_{x}|}_{{\rm{\max

}}}}{3\sqrt{\frac{{\rho }_{0}-{\rho }_{1}}{{\rho }_{0}}\alpha \,h\,g\,\sin \,\beta }},$$ (2) where _g_ is the gravity acceleration. _Re_ is the ratio of the inertia force to the viscous

force and is an essential indicator for the transition from laminar to turbulent motion of flows due to the shear instability20,21. The fluid motion is stable (laminar) at very low _Re_,

whereas it becomes turbulent beyond the critical value _Re_c, e.g., _Re_c ≈ 1200 for the boundary layer on a flat plate (Blasius profile)22. _Fr_ is the ratio of the inertia force to the

gravity force and is an indicator for the onset of the roll-wave in a liquid-film18. The fluid motion of a falling liquid-film in an inclined open channel is described by the magnitude of

_Fr_. At very low _Fr_, the fluid motion finds gravity-driven Poiseuille (laminar, non-wavy) flow. At _Fr_ ≥ _Fr_c, the flow becomes unstable, and thus waves appear at the free surface owing

to the instability of the gravity current. Figure 7c shows the scaled velocity fluctuation \({u^{\prime} }_{x,{\rm{\max }}}/{|{\bar{u}}_{x}|}_{{\rm{\max }}}\) as a function of _Re_ and

_Fr_. Note that we performed experiments systematically parametrizing _α_ and _β_ on the basis of _α_ = 5% and _β_ = 10 degrees, but a few semi-systematic parameters were chosen for an

extensive investigation. We resolved the velocity profile 10 seconds after pouring to eliminate the flow disturbance induced by pouring a test fluid. An inclined rectangular container was

used to minimise the effect of the container shape on the flow. We plot several instances of a value averaged over 10 seconds. Note that both _Re_ and _Fr_ decrease with increasing time in

all observations because of the decrease of the buoyant force (convection velocity) due to the accumulation of the dispersed bodies at the free surface (see Fig. 6c). Figure 7c shows that

\({u^{\prime} }_{x,{\rm{\max }}}/{|{\bar{u}}_{x}|}_{{\rm{\max }}}\) gradually decreases with increasing _Re_, and weakly depends on _Fr_ up to _Fr_ ≈ 1, but for _Fr_ > 1,

\({u}_{x,\,{\rm{\max }}}^{^{\prime} }/{|{\bar{u}}_{x}|}_{{\rm{\max }}}\) rapidly increases, i.e., the magnitude of the velocity fluctuation increases owing to the texture-formation, implying

that the texture-formation is caused by the roll-wave instability rather than the shear instability. DISCUSSION AND CONCLUSION We have found that the velocity fluctuation depends on _Fr_.

The velocity fluctuation should be zero for the laminar regime of a falling liquid film comprising two immiscible fluids (e.g., air and water). However, our result reveals non-zero velocity

fluctuations at _Fr_ < 1 due to the disturbance induced by the rising bubbles or particles with a terminal velocity of _v__St_ ≈ 1.2 mm/s. A striking feature is that the rapid increase in

\({u}_{x,\,{\rm{\max }}}^{^{\prime} }/{|{\bar{u}}_{x}|}_{{\rm{\max }}}\) at _Fr_ > 1 is in excellent accord with the onset of the primary instability in the roll-wave, namely, _Fr_c = 

218, as theoretically estimated. Bubbles or particles rise by their buoyant force, and thus a clear-fluid film is created. The distribution of the dispersed bodies has a concentration

gradient (i.e., indistinct concentration interface) owing to the hydrodynamic diffusivity23 or the particle-size distribution24 in suspensions. Since the presence of bubbles within the

clear-fluid film reduces the density difference between the clear-fluid film and bubble-rich bulk, our oversimplified interpretation of the fluid separation may result in underestimation of

_Fr_. The effect of fluctuation in the motion of bubble-rich bulk, hysteresis effect25 with decreasing _Fr_, or the finite-size effect26,27 of the system on a decaying disturbance convected

by the large-scale circulating flow should also be reflected in the texture-formation in the subcritical-state regime (_Fr_ < _Fr_c). The criterion for the texture-formation is

successfully determined by our interpretation of flow, despite the imperfections in the experiment. Finally, we also performed experiments on light particles with a different mean diameter

of 34 μm or 75 μm. Even for the variation in the Stokes rise velocity of the dispersed bodies, the texture-formation and descending motion of bubbles were visually observed well. However, in

a glass of Budweiser beer, carbonated water, or champagne, which contains sub-millimetre-sized bubbles (300−500 μm)1,2,3, we cannot observe the texture-formation and the descending motion

of bubbles, i.e., characteristic flows in Guinness. Large bubbles rise rapidly, and thus they cannot be trapped into a downward flow by the liquid-phase convection, suggesting that the

criterion for the texture-formation also depends on the bubble diameter. To comprehend the generation of liquid phase convection depending on the bubble size is a challenge for future

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T. Nosoko, Ryukyus University, for giving us essential information and for fruitful discussion. Part of this study was funded by JSPS KAKENHI JP16H06936  and JP18K13686. AUTHOR INFORMATION

AUTHORS AND AFFILIATIONS * Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka, 560-8531, Japan Tomoaki Watamura, Fumiya Iwatsubo & Kazuyasu

Sugiyama * Research Laboratory for Beverage Technologies, Research & Development Division, Kirin Co. Ltd., 1-17-1, Namamugi, Tsurumi-ku, Yokohama, Kanagawa, 230-6826, Japan Kenichiro

Yamamoto, Yuko Yotsumoto & Takashi Shiono Authors * Tomoaki Watamura View author publications You can also search for this author inPubMed Google Scholar * Fumiya Iwatsubo View author

publications You can also search for this author inPubMed Google Scholar * Kazuyasu Sugiyama View author publications You can also search for this author inPubMed Google Scholar * Kenichiro

Yamamoto View author publications You can also search for this author inPubMed Google Scholar * Yuko Yotsumoto View author publications You can also search for this author inPubMed Google

Scholar * Takashi Shiono View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS T.W., K.Y., Y.Y., and T.S. conceived the project. T.W., F.I.,

K.Y., and Y.Y. performed the experiments. T.W., K.Y., Y.Y., and T.S. developed the experimental setup for visualisation of bubbles. T.W. and F.I. developed the experimental setup for

photo-bleaching molecular tagging visualisation and laser-induced-fluorescence applying particle image velocimetry in particle experiments. T.W. and K.S. wrote the paper, and all authors

contributed to analysing the data, discussing the results, and providing feedbacks. CORRESPONDING AUTHOR Correspondence to Tomoaki Watamura. ETHICS DECLARATIONS COMPETING INTERESTS The

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Bubble cascade in Guinness beer is caused by gravity current instability. _Sci Rep_ 9, 5718 (2019). https://doi.org/10.1038/s41598-019-42094-0 Download citation * Received: 20 September 2018

* Accepted: 19 March 2019 * Published: 05 April 2019 * DOI: https://doi.org/10.1038/s41598-019-42094-0 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

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