Tears of Wine. Europhys. Lett., 20 (6), pp (1992)

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1 EUROPHYSICS LETTERS Europhys. Lett., 20 (6), pp (1992) 15 November 1992 Tears of Wine. J. B. FOURNIER(*) and A. M. CAZABAT Physique de la MatiBre Condensbe, Collkge de France 11, place Marcelin Berthelot, Paris Cedex 05, France (received 30 April 1992; accepted in final form 11 September 1992) PACS C - Surface energy (surface tension, interface tension, angle of contact, etc.). PACS G - Interface activity, spreading. Abstract. - We present the first quantitative study of the &ears of wine,) phenomenon. The ethanol-water film presents a self-similar profile of parabolic shape and obeys a diffusivelike wetting law. Both the fluid velocity and the surface tension gradient along the film are deduced. In addition, we relate the existence of a star instability at the edge of the reservoir and a fingering instability at the front of the fdm. Water-alcohol mixtures spontaneously produce strange convecting effects, driving the liquid upwards in thin films and downwards in regular rows of drops known as <*tears of wine),. This can be easily observed in any glass of strong wine or spirits. The basic explanation was given in 1855 by Thomson [l]. As water has a much higher surface tension than alcohol, a nonhomogeneous evaporation of alcohol can create a concentration gradient inducing a gradient of surface tension [l-31. The latter produces a surface driving force which raises a thin film along the wine glass sides. The tears-of-wine phenomenon then follows. Surprisingly, no quantitative study has been performed yet, although tears-of-wine and similar phenomena have been qualitatively described long ago for various liquid mixtures [41. Since applications involve the wetting of substrates by volatile systems, gas-liquid absorption and various chemical engineering operations [5], it is of practical interest to understand more deeply this kind of dynamical wetting. In this letter, we first describe a typical tears-of-wine experiment under reproducible conditions. Then, we study the wetting law for different alcohol concentrations and different air moistures. We describe several instabilities of the microscopic film related to the formation of tears. Finally, we measure the film profile as a function of both space and time and we deduce the fluid velocity and the surface tension gradient. Our results lead to a quantitative formulation of the wetting law, although the exact relation with the evaporation process is still unknown. Our experimental set-up and procedure are the following. We use low curved borosilicated clock glasses of cm, cleaned with hot sulfochromic acid then heated at 500 "C, both for (*) Permanent address: Laboratoire de Physique des Solides, Universitk Paris-Sud, BBt. 510, Orsay Cedex, France.

2 518 EUROPHYSICS LETTERS half an hour. After this treatment giving reproducible results, the glass is not wetted by water. We deposit in the centre, at t = 0, a lcm3 water-ethanol mixture of alcoholic fraction +. At once, a microscopic film of length L(t) climbs the glass walls above the bulk. After ( ) min depending on #, the liquid front stops at a level close to the glass borders. In the film, the liquid is still driven upwards and fills large tear-drops rolling downwards under gravity. When they touch the bulk, they bounce periodically as they become lighter, loosing each time a finite amount of liquid (fig. 1). The process stops only when all the alcohol is evaporated. To study the effect of air moisture, we can operate in a dry atmosphere inside a closed box. Visualization is realized without dyes by illuminating with an optical fiber, and observing the projection image on a white screen 5 cm under the glass or directly painted on its outer side. To get information on the film profile, we make equal-thickness fringes on the film profile by illuminating with a He-Ne laser connected to the optical fiber. Observation is made with a video camera either attached to a binocular, either used directly. Finally, all the experiment is surrounded by a closed box to avoid air currents which drastically influence the dynamics, especially at short scales. We have studied the wetting dynamics for various concentrations (fig. 2). The film length L(t) is closely fitted by a diffusivelike law: L - (Dt) 2. (1) We find that the coefficient D( 0) - (1 + 40) mm2 /s strongly depends on the alcoholic fraction (fig. 3). Below 20% no spontaneous motion is observed if the glass is not pre-wetted. Against common intuition, the highest values of D are obtained for low concentrations in alcohol although the evaporation is then slower. D is minimum at $o - 90% and surprisingly does not vanish at 100%. As qualitatively suggested in ref. [2], this effect is due to water absorption from the atmosphere which also contributes to create concentration gradients. This is clearly Fig Projected overview of the clock-glass at long time for a 30% ethanol-rich mixture. The -tears of wine. are filled from the fim flux rising radially along the glass walls. Then they roll downwards under gravity and periodically spit out a cloud of water-rich liquid as they bounce on the bulk. Note the star instability, as forked dendrites, at the bulk edge. Fig The film length L measured from the bulk edge as a function of ~ (0 < t < 30 s) for A y - 40%. The bottom plot corresponds to the evaporation of both alcohol and water in a dry atmosphere. The top plot is faster, since it corresponds to the evaporation of almost only alcohol in a normal atmosphere.

3 J. 13. FOTTRNIER et al.: TEARS OF WINE 519 Fig The diffusionlike coefficient as a function of the alcoholic fraction $. 0 normal atmosphere, + dry atmosphere. The thin curve is given by eq. (6). Essentially, the process is faster at low + because the evaporation of alcohol creates a larger surface tension gradient as the corresponding ay/a+ is higher. Fig Equal-thickness fringes on the film profile under the binocular ($ = 70%). The fingering instability on the left is visible at the front of the parabolic microscopic film. The black region on the right is due to the change of the reflected beam direction according to the interface curvature. The fingers are fairly flat and bear large terminal drops (black spots). a) t - 3 s, the instability wavelength is pm. b) - 5 s later, the period is twice as much since the growing fingers have merged. confirmed by our measurements in dry atmosphere where D is lower, monotonous and vanishes at 100% (fig. 3). In this case, the gradient is lesser because not only ethanol but also water evaporates. For closer investigations we use the binocular. We observe that the front of the film shows a large bump which after a few seconds results in a fingering instability (fig. 4). This behaviour, common to a few related experiments, was also observed during the spreading of volatile liquids [SI or surfactant solutions [7], where the fingers undergo tip splitting, or in viscous currents down slopes [8] and thermal Marangoni [9], where the fingers behave independently. The fingering in our system is rather similar to the latter ones: at the threshold, the instability wavelength is typically four times the transverse size of the bump as is usually observed in Rayleigh-like instabilities [ The main difference with ref. [8] and [91 is that the fingers, bearing large terminal drops, are not independent and merge as they grow, giving rise to successive period doubling or mass collapsing. The terminal drops (also merging) finally build the <<tears of wine.. The exact behaviour depends on $ and will not be detailed here. In addition, we also observe a star instability (fig. 1) near the bulk edge. The interference fringes pattern shows that it corresponds to a orthoradial modulation of the film thickness localized at the meniscus between the bulk and the film. At the beginning, the corresponding wavelength is very short, d 0.5"; then the strips merge from the base and the structure evolves towards forked dendrites - (3 + 6) mm distant also depending on $ in a nontrivial way. As this star instability appears at the crossover between the bulk and the spreading

4 520 EUROPHYSICS LETTERS film and not at the contact line, it probably belongs to another class of instability as the previous ones [6-91. Using now laser illumination, we obtain equal-thickness fringes giving the film profile (fig. 4). The optical indices of water and ethanol being very close (h/e '), we can neglect the contribution due to the concentration profile. One fringe then corresponds to a height variation 6h - A/2E !Am with A !Am and E Let us call x, x the reference frame, x being the coordinate along the film measured from the bulk edge (0 < x < L), and h(x, t) the film thickness profile. h(x, t) is closely fitted by a parabola (fig. 5a)) whose curvature radius R(t) = l/c(t) - Ut increases as a linear function of time (fig. 5b)). Therefore, we have where ho is a constant small thickness at the front in the middle of the fingers and H a larger thickness at the bulk edge. It is remarkable that H = (1/2)C(t)L(t)' = D/2U is time independent: the parabola curvature C(t) a l/t is the one adapted to connect two fixed heights H and ho at a distance of L(t) cz ~. Therefore h(x, t) depending only on the reduced variable x/m is self-similar. Typical values are ho - 2 [Am, U cm/s, giving H - 95 pm (at $ = 50%), and U cm/s, giving H - 55!Am (at $ = 70%). As R - 1 m after a few seconds, the film is locally almost flat. Some relevant information can be derived from h(x, t). Calling V(x, t) the average velocity across the film, the rising flux Q = hv must satisfy the volume continuity equation, which, subject to the boundary conditions hv(x = L) = hovo, takes the integral form where V, - al/at = (1/2)(D/t)1/2 is the front velocity. In (3), we have neglected the evaporation flux Q, << hv and used a planar geometry instead of a cylindrical one, since L(t) is much less than the reservoir radius. From (2) and (3), V is found self-similar and almost linear (fig. 6). Far enough from the front and assuming ho<<h, V is approximately given by 1 qx, t) - -v, ( I&)* Thus the fluid velocity is three times higher at the front than at the bulk edge. Let us now derive the surface tension gradient producing the motion. In the lubrifkation approximation and neglecting pressure gradients (the curvature is fairly constant and gravity can be neglected for thin films and low slopes), the Navier-Stokes equation reduces to V2v = 0. The velocity profile across the film is then linear. With the solid boundary conditions U = 0 at x = 0 and the surface force balance c(av/ax) = ay/& at x = h, V is given by the familiar equation [2,9] (4) where 7 is the viscosity and y the surface tension. Note that the thermal effect of evaporation needs not to be considered: indeed it does not contribute, since pure ethanol remains still in dry atmosphere although alcohol does evaporate. By integrating (5), the surface tension variation from the bulk y(x, t) - yb is again self-similar (fig. 6). The surface tension drop

5 J. B. FOURNIER et al.: TEARS OF WINE 521 (L-x)~ (cm2) , I I gl h g 100 t -I 50 '- 0' 'a. Fig. 5. Fig XlL Fig Measurements on the microscopic film. a) Full-arrow axes: film thickness variation h - ho as a function of the squared distance to the centre of the fingers (L- x )~. Measurements can be performed within 0 < (L- x) < L/2; error bars are related to the orthoradial periodic perturbation due to the star instability. b) Hollow-arrow axes: film curvature radius R(t) as a function of time. Due to both linear behaviours, the profile h(x, t) is self-similar. Fig Reduced hydrodynamic variables, deduced from the self-similar film profile, as a function of the reduced variable x/m. In addition to the film profile h/h, both the mean velocity across the film and the surface-tension drop from the bulk are displayed. between the front and the bulk, b'y = yf - yb - (1 + 3) dyn/cm is much smaller than the difference between pure water and ethanol of respective values - 72 and - 23 dyn/cm. It corresponds to a relatively small 6+ which is constant due to self-similarity. Finally, we can give a scaling argument to justify both the.diffusive,> law (1) and the order of magnitude of 87. From the property of self-similarity we strictly have aylax = y' /L, where y'(x/l) is a function only of x/l. Then at the front, setting y' = ~(b'y), we can write aylax = a(6y)/l - (ay/a#)(a6+)/l, where a 8g - 1 (the gradient is larger at the front). Using (5) together with i/(x = L) = al/at, we obtain the diffusivelike law d(l2) = (Da6+) dt, with D given by With ho - 2 pm, ~($1 and ay/a+ taken from ref. [12], D(+) has a satisfactory shape and a fairly agreeing order of magnitude (see fig. 3). In conclusion, we have described quantitatively the early wetting dynamics of the tears-of-wine phenomenon. E thanol-water mixtures spontaneously wet their glass containers against gravity, following a diflusivelike law. Against intuition, the velocity of the process is higher at low ethanol concentrations. It also strongly depends on the air moisture. On a microscopic scale, the advancing film is parabolic and self-similar. It presents a fingering instability at the front and a star instability at the base. From the profile measurements we have deduced the surface tension gradients and found that the difference in concentration along the film is constant and relatively small during the film growth. This agrees with the diffusivelike law and shows that the velocity of the process is proportional to (6)

6 522 EUROPHYSICS LETTERS the derivative of the surface tension with respect to the concentration in alcohol, and not to the absolute concentration of the mixture as one might guess. Finally, many things still remain to be understood concerning the precise evaporation/absorption mechanism which maintains the film concentration gradient and the self-similar parabolic profde. *** We thank P. G. DE GENNES, J. P. HULIN and G. DURAND for stimulating discussions. This work has been partly supported by a D.R.E.T. grant. REFERENCES [ll THOMSON J., Philos. Mag., 10 (ser. 4) (1855) 330. [2] NEOGI P., J. Colloid Znteflace Sci., 105 (1985) 94. [3] BORCAS M. S. and GROTBERG J. B., J. Fluid Mech., 193 (1988) 151. [4] LOEWENTHAL M., Philos. Mag., 12 (ser. 7) (1931) 462. [5] LEVICH V. G., Physico-Chemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, N. J.) [6] WILLIAMS R., Nature, 266 (1977) 153. [7] TROIAN S. M., WU X. L. and SAFRAN S. A., Phys. Rev. Lett., 62 (1989) [81 HUPPERT H. E., Nature, 300 (1982) 427. [91 CAZABAT A. M., HESLOT F., TROIAN S. M. and CARLES P., Nature, 346 (1990) 824. [lo] TROIAN S. M., HERBOLTZHEIMER E., SAFRAN S. A. and JOANNY J. F., Europhys. Lett., 10 (1989) 25. [ll] TROIAN S. M. and HERBOLTZHEIMER E., to be published. [E] Handbook of Chemistry and Physics (Chemical Rubber Publishing Co., Cleveland, Ohio) 1957.