letters to nature encesÐZn atoms locally destroy superconductivity9 while Ni atoms 25. Tokunaga, Y., Ishida, K., Kitaoka, Y. & Asayama, K. Novel relation between spin-¯uctuation and do not. superconductivity in Ni substituted high-TC cuprate YBa2Cu3O7: Cu NQR study. Solid State Comm. Finally, magnetic probes sensitive to spin ¯uctuations reveal 103, 43±47 (1997). 26. Mahajan, A. V., Alloul, H., Collin, G. & Marucco, J. F. 89Y NMR probe of Zn induced local moments in marked changes with Zn-doping24,26±31 but only weak perturbations YBa2(Cu1-yZny)3O6+x. Phys. Rev. Lett. 72, 3100±3103 (1994). with Ni-doping24,25,29,31. Explanations for these phenomena have 27. Bobroff, J. et al. Spinless impurities in high-TC cuprates: Kondo-like behavior. Phys. Rev. Lett. 83, been proposed5,6,27,28,30 whereby Zn behaves like a `magnetic hole' (a 4381±4384 (1999). 28. Bobroff, J. et al. Persistence of Li induced Kondo moments in the superconducting state of cuprates. spinless site in an environment of strongly exchange-coupled spins) Phys. Rev. Lett. 86, 4116±4119 (2001). that strongly alters NN exchange correlations and disrupts super- 29. Williams,G.V.M.,Tallon,J.L.&Dupree,R.NMRstudyofmagneticandnon-magneticimpuritiesin conductivity, whereas Ni retains a magnetic moment that barely YBa2Cu4O8. Phys. Rev. B 61, 4319±4325 (2000). perturbs the antiferromagnetic exchange correlations that facilitate 30. Julien, M.-H. et al. 63Cu NMR evidence for enhanced antiferromagnetic correlations around Zn impurities in YBa superconductivity. Although the NMR and INS data24±31 are quite 2Cu3O6.7. Phys. Rev. Lett. 84, 3422±3425 (2000). 31. Sidis, Y. et al. Quantum impurities and the neutron resonance peak in YBa2Cu3O7: Ni versus Zn. Phys. consistent with the magnetic component of such models, their Rev. Lett. 84, 5900±5903 (2000). predictions for local electronic phenomena at Ni and Zn can only 32. Bernhard, C. et al. Suppression of the superconducting condensate in the high-TC cuprates by Zn now be tested for the ®rst time. The STM data show that, despite substitution and overdoping: Evidence for an unconventional pairing state. Phys. Rev. Lett. 77, 2304± 2307 (1996). their magnetic moments, scattering at Ni atoms is dominated by potential interactions. Furthermore, whereas Zn atoms locally Acknowledgements destroy superconductivity within a 15 AÊ radius9, the magnetic We acknowledge H. Alloul, P. W. Anderson, A. V. Balatsky, D. Bonn, M. FlatteÂ, M. Franz, Ni atoms coexist with unweakened superconductivity. All these D.-H. Lee, K. Maki, I. Martin, P. Monthoux, A. Mourachkine, D. Pines, D. Rokhsar, phenomena are consistent with the above proposals. S. Sachdev, D. J. Scalapino and A. Yazdani for conversations and communications, and The resilience of cuprate-oxide high-T J. E. Hoffman for help with data analysis. Support was from the Of®ce of Naval Research, c superconductivity against what should be the destructive effects of a magnetic impurity atom, the Department of Energy through an LDRD from LBNL, the UCDRD Program, Grant- in-Aid for Scienti®c Research on Priority Area (Japan), a COE Grant from the Ministry of and its concomitant vulnerability to destruction by a `magnetic Education, Japan, the Miller Inst. for Basic Research (J.C.D.), and by the IBM Graduate hole', are remarkable. These atomic-scale phenomena are now Fellowship Program (K.M.L.). (through a combination of NMR, mSR and STM) coming into Correspondence and requests for materials should be addressed to J.C.D. much clearer focus. They point towards a new approach to studying (e-mail: jcdavis@physics.berkeley.edu). HTSC in which microscopic theories can be tested against an atomically resolved knowledge of impurity-state phenomena. M Received 8 January; accepted 3 April 2001. 1. Abrikosov, A. A. & Gorkov, L. P. Contribution to the theory of superconducting alloys with ................................................................. paramagnetic impurities. Sov. Phys. JETP 12, 1243±1253 (1961). 2. Monthoux, P., Balatsky, A. V. & Pines, D. Weak-coupling theory of high-temperature superconduc- Liquid marbles tivity in the antiferromagnetically correlated copper oxides. Phys. Rev. B 46, 14803±14817 (1992). 3. Moriya, T., Takehashi, Y. & Ueda, K. Antiferromagnetic spin ¯uctuations and superconductivity in two-dimensional metalsÐa possible model for high T Pascale Aussillous & David QueÂre C oxides. J. Phys. Soc. Jpn 59, 2905±2915 (1990). 4. Bickers, N. E., Scalapino, D. J. & White, S. R. Conserving approximations for strongly correlated electron systems: Bethe-Salpeter equation and dynamics for the two-dimensional Hubbard model. Laboratoire de Physique de la MatieÁre CondenseÂe, URA 792 du CNRS, Phys. Rev. Lett. 62, 961±964 (1989). ColleÁge de France, 75231 Paris Cedex 05, France 5. Monthoux, P. & Pines, D. Spin-¯uctuation-induced superconductivity and normal-state properties of YBa .............................................................................................................................................. 2Cu3O7. Phys. Rev. B 49, 4261±4278 (1994). 6. Pines, D. Understanding high temperature superconductors: progress and prospects. Physica C 282± The transport of a small amount of liquid on a solid is not a simple 287, 273±278 (1997). process, owing to the nature of the contact between the two 7. Balatsky, A. V., Salkola, M. I. & Rosengren, A. Impurity-induced virtual bound states in d-wave phases. Setting a liquid droplet in motion requires non-negligible superconductors. Phys. Rev. B 51, 15547±15551 (1995). 8. Salkola, M. I., Balatsky, A. V. & Schrieffer, J. R. Spectral properties of quasiparticle excitations induced forces (because the contact-angle hysteresis generates a force by magnetic moments in superconductors. Phys. Rev. B 55, 12648±12661 (1997). opposing the motion1), and often results in the deposition of 9. Pan, S. H. et al. Imaging the effects of individual zinc impurity atoms on superconductivity in liquid behind the drop. Different methods of levitationÐelectro- Bi2Sr2CaCu2O8+d. Nature 403, 746±750 (2000). 10. Mendels, P. et al. Macroscopic magnetic properties of Ni and Zn substituted YBa static, electromagnetic, acoustic2, or even simpler aerodynamic2,3 2Cu3Ox. Physica C 235/240, 1595±1596 (1994). techniquesÐhave been proposed to avoid this wetting problem, 11. Salkola, M. I., Balatsky, A. V. & Scalapino, D. J. Theory of scanning tunneling microscopy probe of but all have proved to be rather cumbersome. Here we propose a impurity states in a d-wave superconductor. Phys. Rev. Lett. 77, 1841±1844 (1996). simple alternative, which consists of encapsulating an aqueous 12. FlatteÂ, M. E. & Byers, J. M. Impurity effects on quasiparticle c-axis planar tunneling and STM spectra in high-Tc cuprates. Phys. Rev. Lett. 80, 4546±4549 (1998). liquid droplet with a hydrophobic powder. The resulting `liquid 13. Tsuchiura, H., Tanaka, Y., Ogata, M. & Kashiwaya, S. Local density of states around a magnetic marbles' are found to behave like a soft solid, and show dra- impurity in high-TC superconductors based on the t-J model. Phys. Rev. Lett. 84, 3165±3168 (2000). matically reduced adhesion to a solid surface. As a result, motion 14. FlatteÂ, M. E. Quasiparticle resonant states as a probe of short-range electronic structure and AndreeÂv can be generated using gravitational, electrical and magnetic coherence. Phys. Rev. B 61, R14920±14923 (2000). 15. Haas, S. & Maki, K. Quasiparticle bound states around impurities in d ®elds. Moreover, because the viscous friction associated with x2 2 y2 -wave superconductors. Phys. Rev. Lett. 85, 2172±2175 (2000). motion is very small4, we can achieve quick displacements of the 16. Martin, I., Balatsky, A. V. & Zaanen, J. Impurity states and interlayer tunneling in high temperature droplets without any leaks. All of these features are of potential superconductors. Preprint cond-mat/0012446 at (2000). 17. Zhang, G.-M., Hu, H. & Yu, L. Marginal Fermi liquid resonance induced by quantum magnetic bene®t in micro¯uidic applications, and also permit the study of a impurity in d-wave superconductors. Phys. Rev. Lett. 86, 704±707 (2001). drop in a non-wetting situationÐan issue of renewed interest 18. Yazdani, A., Howald, C. M., Lutz, C. P., Kapitulnik, A. & Eigler, D. M. Impurity-induced bound following the recent achievement of super-hydrophobic excitations on the surface of Bi2Sr2CaCu2O8. Phys. Rev. Lett. 83, 176±179 (1999). substrates5. 19. Yazdani, A., Jones, B. A., Lutz, C. P., Crommie, M. F. & Eigler, D. M. Probing the local effects of magnetic impurities on superconductivity. Science 275, 1767±1770 (1997). Liquid marbles are obtained by making a small amount of liquid 20. FlatteÂ, M. E. & Byers, J. M. Local electronic structure of a single magnetic impurity in a super- (typically between 1 and 10 mm3) roll in a very hydrophobic powder conductor. Phys. Rev. Lett. 78, 3761±3764 (1997). (we used lycopodium grains of typical size 20 mm covered with 21. Maeda, A., Yabe, T., Takebayashi, S., Hase, M. & Uchinokura, K. Substitution of 3d metals for Cu in ¯uorinated silanes). The grains spontaneously coat the drop, which Bi2 Sr0:6Ca0:4 3Cu2Oy. Phys. Rev. B 41, 4112±4117 (1990). 22. Kuo, Y. K. et al. Effect of magnetic and nonmagnetic impurities (Ni,Zn) substitution for Cu in can eventually be transferred onto other substrates. Figure 1 shows a Bi2 SrCa 2 n Cu12xMx 1 nOy whiskers. Phys. Rev. B 56, 6201±6206 (1997). marble of radius 1 mm, made of water and put on a glass plate 23. Bonn, D. A. et al. Comparison of the in¯uence of Ni and Zn impurities on the electromagnetic (which would be wetted by water), where it is observed to adopt a properties of YBa2Cu3O6.95. Phys. Rev. B 50, 4051±4063 (1994). 24. Ishida, K. et al. Cu NMR and NQR studies of impurities-doped YBa spherical shape. Thanks to the monolayer of grains at the liquid±air 2(Cu1-xMx)3O7 (M=Zn and Ni). J. Phys. Soc. Jpn 62, 2803±2818 (1993). interface, the wetting between the glass and the water is suppressed. 924 © 2001 Macmillan Magazines Ltd NATURE | VOL 411 | 21 JUNE 2001 | www.nature.com letters to nature The marble can even be transferred onto a water pool, on which it is after a short while (constant descent velocity, no liquid ®lm observed to ¯oat. Here we discuss the statics and dynamics of these remaining behind the drops). Thanks to the powder at the marbles. By using mixtures of water and glycerol, the liquid liquid±air interface, we can see that the marbles roll as they move. viscosity was varied over a large range (a factor of 103), which The ®rst series of experiments were performed with a small slope allows us to describe the viscous and inertial dynamical regimes. a (less than 108). Usually, droplets would remain stationary in such We ®rst consider the size l of the contact between the marble and a low ®eld (,0.1g), because of contact-angle hysteresis1. In contrast, the solid. If there were a contact angle v between the solid and the we found descent velocities that were rather large (of the order of liquid (as usually occurs), l would be given by a simple geometric 1 cm s-1), even for very viscous ¯uids (,1,000 mPa s). In Fig. 2b, relation: l = R sinv, where R is the radius of the droplet. Thus, l this velocity is plotted as a function of the droplet radius. The should tend to zero for non-wetting liquids (v = 1808). However, the velocity and drop size are respectively normalized by the puddle weight of the droplet needs to be considered4: the exact shape of the velocity Vo (which should be independent of the puddle size) and by drop results from a balance between gravity (which favours a the capillary length k-1. Because of the normalization, all the data lie contact) and capillarity (which opposes it, because of the deforma- on the same curve. (1) For large drops (puddles), the velocity is tion it induces)4. If the centre of mass is lowered by a quantity d, the indeed found to be independent of the drop size. It results from a difference in energy from a sphere tangent to the plane can be balance between viscous friction and gravity. Because the puddle written dimensionally as: DE < gd2 - rgR3d. Minimization of this thickness is also independent of the drop size and ®xed at a value of expression yields d, and thus, using the geometric relation l2 < dR: 2k-1 (the maximum gravity pancake thickness, reached for an angle l < R2k 1 v = 1808)6, the puddle velocity can be derived7: Vo < g/h sina, which p is drawn in Fig. 2b (the horizontal straight line), and found to ®t the where k-1 is the capillary length (k21 g=rg, where g and r are, data. (2) For small droplets, the velocity increases when the drop respectively, the liquid surface tension and the density). If the size is decreased, which implies a very unusual friction law. This Laplace equation is solved numerically, the contact size can be behaviour was recently predicted by Mahadevan and Pomeau4, and plotted as a function of the drop radius. It is indeed found to be observed to apply qualitatively to droplets running down a so-called quadratic in R, with a numerical coef®cient of the order of 0.8 super-hydrophobic plate7. In the limit of small Reynolds numbers, (M. Perez, personal communication). For drops of initial radius R Mahadevan and Pomeau4 propose that the droplet motion can be larger than the capillary length, gravity ¯attens the drop into a described as a superposition of a solid rotation (producing no puddle. As the thickness of the puddle is ®xed by gravity and surface dissipation) and a viscous friction localized in the contact zone. tension, it must scale with the capillary length6. By invoking conservation of liquid volume, we can obtain the scaling law for the contact size: l < R3/2k1/2. A liquid marble indeed develops a contact with its substrate a 10 (Fig. 1). We measured the contact size l as a function of the drop radius, for two different powders (the lycopodium mentioned above, and a silanized silica powder of size ,100 nm) and two kinds of substrate (glass and Te¯on plates). The results are displayed 1 in Fig. 2a, where the data are found to collapse onto two curves. l (1) For small droplets (R , k-1), the contact size indeed scales as R2, as predicted by equation (1), which proves that the contact is not a 0.1 classical wetting one; the numerical coef®cient is found to be 0.9, in close agreement with the numerical simulations. (2) Larger drops (R . k-1) form puddles, which yields the scaling behaviour in 0.01 R3/2. 0.1 1 10 We now consider the movement of such marbles on an inclined b 7 plane. We restrict our studies to the case of marbles formed from 6 rather viscous liquids (viscosity h . 200 mPa s), in order to stress the small friction, related to the non-wetting, and the unusual laws 5 of dissipation it generates. The motions are found to be stationary 4 V/V 0 3 2 1 0 0 0.5 1 1.5 2 2.5 3 R Figure 2 Contact of static liquid marbles, and their velocity on slightly tilted plates. a, The radius (l ) of the contact between marble and substrate plotted against the radius (R) of the spherical drop. Both are normalized by the capillary length k-1 = (g/rg)1/2. Lycopodium grains or silica were used as coating powders (represented by ®lled and open symbols, respectively). The liquid can be either water (triangles) or glycerol (circles). The marbles are deposited on glass, except in one case where glycerol was deposited on Te¯on (stars). The straight lines represent slope 2 (equation (1)) and 1.5. b, Drop velocity (V ) normalized by the puddle velocity (Vo) plotted against the drop radius (R) normalized by the capillary Figure 1 A liquid marble. Water is mixed with a very hydrophobic powder (silane-treated length (k-1), for different liquid viscosities, h, and slopes, a: open circles, h = 270 mPa s, lycopodium grains of typical size 20 mm). The powder spontaneously migrates to the a = 58; grey squares, h = 450 mPa s, a = 58; ®lled triangles, h = 1,150 mPa s, a = 48; water±air interface, and thus protects the water, which then behaves as if it were open triangles, h = 1,150 mPa s, a = 88. The hyperbola is derived from equation (2), with perfectly non-wetting when transferred on a glass plate. (Drop radius, 1 mm.) 1 as a numerical constant. NATURE | VOL 411 | 21 JUNE 2001 | www.nature.com © 2001 Macmillan Magazines Ltd 925 letters to nature Droplet deformation is small at low velocity, so that the size of this A toroidal shape for a revolving drop has been proposed12 and zone remains given by the static law (equation (1)). Typical velocity discussed10; but to the best of our knowledge such a shape has not gradients in the drop are of the order of V/R, and the viscous force been previously observed. (The formation of a torus has been can be dimensionally written as: f < hV/Rl2. Balancing the torque ¯ reported when a very viscous liquid drop, held by a ®bre inside associated with this force by the gravity torque rgR4 yields the another liquid of the same density, was rotatedÐwhich seems to be marble velocity4: a different experiment13). The torus is claimed to be unstable k21 compared with the peanut shape10,14; its stability here seems to be V < V promoted by the presence of an inclined plane below the marble. If 0 2 R this plane is removed (which may done by putting an obstacle like a As shown in Fig. 2b, such a hyperbolic law is found to ®t the data needle in the path of the drop, or more simply by observing what fairly well, taking a numerical coef®cient of the order of 1. This happens beyond the extremity of the plane), the axisymmetric shape con®rms that the hydrodynamics associated with these liquid evolves towards the peanut shape. This is illustrated in Fig. 4d. More marbles is very unusual, mainly because of the absence of a contact generally, the torus seems to be metastable, and often evolves line. From a practical point of view, we stress that by dressing a drop towards a peanut shape during its descent, usually because a small with a hydrophobic powder, a weak ®eld can drive the drop to a eccentricity in its shape makes it take off. A quantitative description rather high speed (and higher if the drop is small). of these different shapes, together with a comprehensive analysis of The model of ref. 4 should be valid provided that the drop keeps a this low-friction regime, remains to be made. quasi-static shape, where inertial and viscous forces do not deform Liquid marbles thus seem to be an interesting solution to the the spherical shape. This requires that both the Weber (rV2R/g) and problem of driving small amounts of liquid on solid (or even liquid) the capillary (hV/g) numbers, which compare inertia and viscous substrates. In the present work we used gravity as a ®eld to move the force with surface tension, respectively, are less than unity. Together drop; but we have found that other weak ®elds (such as electric or with the condition of small Reynolds number, this implies that the magnetic ®elds) also drive liquid marbles (data not shown). Under- drop must be large enough (R . k-1 sina) and the liquid viscous standing the shape changes that we have observed will require the enough (h . (grk-1sina)1/2). These conditions are ful®lled in the derivation of a friction law that takes shape evolution into account. series of experiments displayed in Fig. 2b. We were interested in We are at present examining the notable robustness of these observing what happened when the in¯uence of inertia was marbles, which are able to resist a series of shocks (such as those increased: this was examined by tilting the plate more (which observed in Fig. 4a). M generates larger velocities). Figure 3 compares what happens when using a viscous marble on a small slope and on a greater slope (a = 48 and a = 248). Again, the velocity (scaled by the puddle velocity) is plotted versus the drop a b radius, and compared with the model of ref. 4 (equation (2)). Avery large deviation is observed when the plate slope is increased, which reveals a regime of much smaller friction. The high velocities that are obtained (of the order of 1 m s-1) induce strong deformations in the drop, as shown in Fig. 4, where successive snapshots of the drop (obtained with a high-speed camera) are displayed. Two kinds of shape are observed, which can be both related to the c 254.00 action of centrifugal force. (1) A peanut shape, which has also been observed for drops rotating in space8,9, and which has been dis- cussed theoretically10,11. (2) A more unusual deformation, which conserves the axial symmetry of the drop: as it accelerates, it gradually passes from a sphere to a disk, and eventually to a doughnut (toroidal) shape. The light intensity for a horizontal Light intensity section crossing all the `doughnut' centres is drawn in Fig. 4c. It may be seen that the `holes' in the `doughnuts' are not totally black. This 182.060 99.60 means that the `doughnut' is not fully openÐopening could be Millimetres delayed by the viscous drainage in the thin zone, around the centre d of the doughnut, and implies the nucleation of a hole). 35 30 25 20 V/V 0 15 10 5 Figure 4 Different shapes taken by a liquid marble in the inertial regime. In pictures a and 0 b, both the camera and the plane are tilted. Arrow, direction of the motion; scale bar, 0 0.5 1 1.5 2 1 cm. a, a = 348, R = 1.3 mm, interval between two pictures, 9 ms; b, a = 368, R R = 2.5 mm, interval between two pictures, 23 ms. c, Light intensity for a horizontal Figure 3 Comparison of the mobility of a liquid marble on two different slopes. The section crossing all the `doughnut' centres of b; 255 means black, and 0 white. velocity V of viscous (h = 1,150 mPa s) marbles (scaled by the puddle velocity Vo) is plotted d, Successive snapshots (interval between each, 6.7 ms) showing the evolution of an against their radius R (scaled by the capillary length k-1), for a = 48 (triangles) and axisymmetric liquid marble as it leaves an inclined plane. The marble spontaneously a = 248 (circles). The full line corresponds to equation (2). transforms into a peanut shape. 926 © 2001 Macmillan Magazines Ltd NATURE | VOL 411 | 21 JUNE 2001 | www.nature.com letters to nature Received 19 February; accepted 5 April 2000. (NADW), and any assessment of past or future variation in the 1. Dussan, V. E. B. & Chow, R. T. P. On the ability of drops or bubbles to stick to non-horizontal surfaces global thermohaline circulation will depend critically on assessing of solids. J. Fluid Mech. 137, 1±29 (1983). the variation of this over¯ow. About half of the over¯ow passes 2. Frohn, A. & Roth, R. Dynamics of Droplets (Springer, Berlin, 2000). through the Denmark Strait, while the rest crosses the ridge in the 3. Perez, M. et al. Oscillation of liquid drops under gravity: in¯uence of shape on the resonance frequency. Europhys. Lett. 47, 189±195 (1999). Iceland±Scotland region2, mainly through the Faroese channelsÐ 4. Mahadevan, L. & Pomeau, Y. Rolling droplets. Phys. Fluids 11, 2449±2453 (1999). consisting of the Faroe±Shetland channel leading to the Faroe Bank 5. Onda, T., Shibuichi, S., Satoh, N. & Tsujii, K. Super water-repellent fractal surfaces. Langmuir 12, channel (Fig. 1b). 2125±2127 (1996). 6. Taylor, G. I. & Michael, D. H. On making holes in a sheet of ¯uid. J. Fluid Mech. 58, 625±639 (1973). The Faroe Bank channel has a sill depth of around 840 m, and the 7. Richard, D. & QueÂreÂ, D. Drops rolling on a tilted non-wettable solid. Europhys. Lett. 48, 286± deepest parts of the channel are constantly ®lled with cold over¯ow 291(1999). water ¯owing into the Atlantic with average velocities exceeding 8. Wang, T. G. et al. Bifurcation of rotating liquid drops: results from USML-1 experiments in space. 1 m s-1 in the core (Fig. 2). Since November 1995, an upward- J. Fluid Mech. 276, 389±403 (1994). 9. Lee, C. P. et al. Equilibrium of liquid drops under the effects of rotation and acoustic ¯attening: results looking acoustic Doppler current pro®ler (ADCP) has been moored from USML-2 experiments in space. J. Fluid Mech. 354, 43±67 (1998). at the sill of the channel and has measured the velocity pro®le 10. Brown, R. A. & Scriven, L. E. The shape and stability of rotating liquid drops. Proc. R. Soc. Lond. A 371, almost continuously. From these measurements, initiated in the 351±367 (1980). `Nordic WOCE' project, the ¯ux of water colder than 3 8C was 11. Brown, R. A. & Scriven, L. E. New class of asymmetric shapes of rotating liquid drops. Phys. Rev. Lett. 45, 180±183 (1980). estimated5 to be 1.9 Sv (1 Sv 106 m3 s21), which is fairly consis- 12. Rayleigh, Lord The equilibrium of revolving liquid under capillary force. Phil. Mag. 28, 161±170 tent with previous estimates6,7. This ¯ux includes the over¯ow (1914). waters, but also some entrained Atlantic water. To avoid in¯uence 13. Plateau, J. A. F. Experimental and theoretical researches on the ®gures of equilibrium of a liquid mass withdrawn from the action of gravity. Annu. Rep. Board Regents Smithson. Inst. 207±285 from the entrained water, we focus on the well de®ned over¯ow, (1863). colder than +0.3 8C and with densities (jt) in excess of 28.0. From 14. Chandrasekhar, S. The stability of a rotating liquid drop. Proc. R. Soc. Lond A 286, 1±26 (1965). November 1995 to June 2000, the ADCP measurements indicate a weakening of this over¯ow ¯ux of 2±4% per year (Fig. 3), which is Acknowledgements signi®cantly different from zero (P , 0.001). We thank J. Bico and D. Richard for silanization of lycopodium grains and the Direct current measurements give the most reliable estimate of the achievement of a ®rst series of liquid marbles, C. Clanet for help with high-speed pictures over¯ow ¯ux through the Faroe Bank channel, but for information and for discussions, and P.-G. de Gennes for discussions and encouragement. on long-term variations we are restricted to more indirect methods. Correspondence and requests for materials should be addressed to D.Q. Historical hydrographic data may be used for this purpose if they (e-mail: quere@ext.jussieu.fr). can be related to the over¯ow on a theoretically sound basis. In the ................................................................. Arctic Ocean a 8°W 4°W 0° b Decreasing over¯ow from the Nordic Norwegian OWS-M Sea seas into the Atlantic Ocean through Nordic Nor- Seas 3,000 m Green way IFR 64° the Faroe Bank channel since 1950 land 2,000 m Faroes Ic 1,000 m Bogi Hansen*, William R. Turrell² & Svein ésterhus³ A IFR FBC SC DS FSC W E * Faroese Fisheries Laboratory, PO Box 3051, FO-110 ToÂrshavn, Faroe Islands Shet- ² FRS Marine Laboratory, PO Box 101, Aberdeen AB11 9DB, UK 60° Atlantic Ocean S land ³ Bjerknes Centre for Climate Research and Geophysical Institute, N-5024 Bergen, FBC Norway 0 A W S E M 27.5 .............................................................................................................................................. 200 The over¯ow of cold, dense water from the Nordic seas, across the D Greenland±Scotland ridge1 and into the Atlantic Ocean is the 400 28.0 main source for the deep water of the North Atlantic Ocean2. This 600 H ¯ow also helps drive the in¯ow of warm, saline surface water into the Nordic seas1. The Faroe Bank channel is the deepest path 800 across the ridge, and the deep ¯ow through this channel accounts 1,000 Sill for about one-third of the total over¯ow1,2. Previous work has 1,200 200 km c demonstrated that the over¯ow has become warmer and less < 0.5 °C 0.5 ­ 3 °C 3 ­ 7 °C > 7 °C saline3,4 over time. Here we show, using direct measurements and historical hydrographic data, that the volume ¯ux of the Faroe Figure 1 Topography and temperature change across the Greenland±Scotland ridge Bank channel over¯ow has also decreased. Estimating the volume (light-brown areas are shallower than 500 m). a, Map of the Greenland±Iceland (Ic)± ¯ux conservatively, we ®nd a decrease by at least 20 per cent Scotland (Sc) region. Black arrows show over¯ow paths through the Denmark Strait (DS), relative to 1950. If this reduction in deep ¯ow from the Nordic seas over the Iceland±Faroe ridge (IFR), and through the Faroe Bank channel (FBC). b, Bottom is not compensated by increased ¯ow from other sources, it topography of the study area (indicated by box in a) and location of a longitudinal (red line implies a weakened global thermohaline circulation and reduced from A to OWS-M) and three transverse (green lines labelled W, S and E) standard in¯ow of Atlantic water to the Nordic seas. hydrographic sections. Arrows indicate the Iceland±Faroe ridge (IFR), the Faroe± The Nordic seas and the Arctic Ocean are dominated by cold Shetland channel (FSC), and the Faroe Bank channel (FBC). c, Temperature (colour water below about 500 m depthÐthe typical sill depth of the shading) and jt isopycnals (contours) along the longitudinal section, based on CTD Greenland±Scotland ridge (Fig. 1). The over¯ow of this water (conductivity±temperature±depth) observations from RV Magnus Heinason in May± across the Greenland±Scotland ridge into the North Atlantic is August 1991 and observations at OWS-M in the same period. The de®nition of the the most important source for North Atlantic Deep Water2 interface depth D and height H is illustrated. NATURE | VOL 411 | 21 JUNE 2001 | www.nature.com © 2001 Macmillan Magazines Ltd 927