Colloidal electroconvection in a thin horizontal cell: II. Bulk electroconvection ofwater during parallel-plate electrolysis

Yilong HanDepartment of Physics and Astronomy,

University of Pennsylvania209 South 33rd St., Philadelphia, PA 19104

David G. GrierDepartment of Physics and Center for Soft Matter Research

New York University, 4 Washington Place, New York, NY 10003(Dated: December 25, 2011)

We recently have reported (J. Chem. Phys. 122, 164701 (2005)) a family of electroconvectivepatterns that arise when charge-stabilized colloidal dispersions are driven by constant (DC) verti-cal electric fields. Competition between gravity and electrokinetic forces acting on the individualspheres in this system leads to the formation of highly organized convective instabilities involvinghundreds of spheres. Here, we report a distinct class of electroconvective patterns that emerge inconfined aqueous dispersions at higher biases. These qualitatively resemble the honeycomb andlabyrinthine patterns formed during thermally driven Rayleigh-Benard convection, but arise froma distinct mechanism. Unlike the localized colloidal electroconvective patterns observed at lowerbiases, moreover, these system-spanning patterns form even without dispersed colloidal particles.Rather, they appear to result from an underlying electroconvective instability during electrolysis inthe parallel plate geometry. This contrasts with recent theoretical results suggesting that simpleelectrolytes are linearly stable against electroconvection.

I. INTRODUCTION

Several processes occur when parallel plate electrodesare used to apply uniform electric fields to aqueous elec-trolytes. Below the threshold for electrochemical reac-tions, dissolved ions redistribute around the electrodesand screen the field in the bulk. At higher biases, waterdissociates into hydroxyl and hydronium ions that flow tothe oppositely charged electrodes, where they recombineinto molecular gases that dissolve into the electrolyte.The anionic and cationic fluxes ordinarily intermingle tomaintain local electroneutrality. This not only minimizesthe system’s electrostatic energy, but also helps to main-tain mechanical stability because the counterpropagatingfluxes exert no net force on the water.

The mechanical stability of steady hydrolysis can bedisrupted by adding macroscopic charged objects such asdispersed colloidal spheres. The spheres do not engagein electrochemical reactions, and their fixed charges favora departure from local electroneutrality in the surround-ing electrolyte1. Once the ionic fluxes are spatially sep-arated, they entrain counterpropagating flows of wateraround the spheres1–3. These flows exert hydrodynamicforces on the spheres, and their motions, in turn, redirectthe flows2–5. We previously reported6,7 that the interplayof microscopic electrohydrodynamic flows around indi-vidual spheres can give rise to large-scale convective in-stabilities characterized by highly organized flow patternsinvolving thousands of spheres. These colloidal electro-convective patterns form at biases just above the thresh-old for steady electrolysis, and their structure depends onthe properties and concentration of the colloidal spheres.Consequently, they appear not to reflect underlying elec-

troconvective instabilities in the electrolyte itself6,7.

The present article describes a distinct category of bulkelectroconvective patterns that form at higher biases evenwithout dispersed colloidal spheres. Their appearancedemonstrates that bulk electroconvective instabilities canoccur in simple electrolytes under steady driving by uni-form fields. These observations therefore provide an ex-perimental resolution to a long-standing debate regard-ing the mechanical stability of simple electrolytes in theparallel-plate geometry8–10.

Qualitatively similar instabilities have been observedduring the electrodeposition of copper from aqueous elec-trolytes in the parallel plate geometry11. In that case,convection was attributed to density gradients resultingfrom current-driven concentration gradients in the dis-solved copper ions. Electrohydrodynamically driven con-vection also has been reported during the electrolysis ofmodel non-aqueous electrolytes12,13 in vertical slit pores.In this case, fluid flow appears to be nucleated by a chargeinjection mechanism, and does not involve gravity.

Until recently, the onset of electroconvection with-out gravity in simple electrolytes was believed to re-semble the intrinsic convective instability in plasmas8.Unlike plasma convection, however, the electrohydrody-namic instability in electrolytes is entirely suppressed byhomogeneous boundary conditions9. Bulk gravity-freeelectroconvection in simple electrolytes therefore shouldoccur only in the presence of inhomogeneous bound-ary conditions10, and the resulting patterns should bepinned to the underlying inhomogeneities. This is con-sistent with observation of bulk electroconvection dur-ing the electrodeposition of branched metallic structuresfrom aqueous electrolytes14,15. We find, by contrast,

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that electrolysis of pure water in a horizontal planar slitpore yields drifting cellular electroconvection patternsnot obviously associated with electrode structures un-der conditions not conducive to plasma-like convectiveinstabilities8,9.

Because the high-bias electrohydrodynamic patternsdescribed below emerge from and supplant the low-biascolloidal electroconvective instabilities we have previ-ously described6,7, we organize our present observationsas extensions of that work. The patterns’ phenomenologythen allows us to distinguish the pattern forming mech-anism. Section II describes the experimental apparatus,whose ability to create large-scale electroconvective pat-terns is discussed in Sec. III. Observations described inthis section also demonstrate that the electroconvectivepatterns are largely insensitive to the dispersed colloids’properties or concentration. Section IV discusses the pat-terns’ dependence on other experimental conditions suchas pH and electrode uniformity. The full set of observa-tions is summarized in Sec. V to provide an overview ofelectroconvective pattern formation in water.

II. EXPERIMENTAL SYSTEM

−OHH3O+ H3O

+

ℓ L

H

V

FIG. 1: Schematic cross-section of the system showingcounter-rotating convection rolls between parallel transpar-ent conducting surfaces, driven by counter-propagating ionicfluxes. Negatively charged spheres concentrate near the fluxof hydrolytically generated hydronium ions.

Our experimental system was described in Ref.7 andis shown schematically in Fig. 1. Each sample consistsof an aqueous dispersions of micrometer-sized colloidalspheres confined to a thin horizontal layer between aglass slide and a glass cover slip. Both inner surfacesare coated with 10-nanometer-thick gold electrodes on10-nanometer-thick titanium wetting layers. These elec-trodes are transparent enough that individual particlescan be imaged with a standard light microscope and theirmotions recorded for analysis. Their 50 Ω/ resistivityis small enough to yield an essentially uniform electricfield across the H = O(100) µm inter-electrode gap inthe roughly 4 cm2 accessible sample area.

Sealed electrochemical cells were mounted on the stageof a Zeiss S100TV Axiovert inverted optical microscope.We applied constant (DC) voltages across the electrodes,and recorded the resulting time evolution of the distribu-tion of spheres in the gap. The resulting electric field isvertical and oriented with gravity to within 0.1 degree.

Water dissociates in these sample cells at biases above2.5 ± 0.2 V, with bubbles forming at the electrodes af-ter a few minutes. Because bubbles disrupt the electro-hydrodynamically driven patterns, the results reportedbelow were obtained in the interval before macroscopicbubbles evolve. Adopting the conventions from Ref.7, wereport the number density φ of sedimented colloidal sil-ica spheres in units of the areal density of a close-packedlayer, with φ = 200% referring to two complete layers.We define the applied DC voltage to be positive if theupper electrode is positive.

III. BULK CONVECTION: DOUBLE-ROLLLABYRINTHS, HONEYCOMBS AND MORE

System-spanning convection rolls appear at biasesabove roughly 4 V and disrupt any self-regulating mi-croscopic clusters formed at lower voltages6,7. The rollsorganize the particles into macroscopic patterns with fea-tures ranging in size from 0.2 mm to 2 mm. Positivebiases in the range 4 to 10 V produce bulk patternssuch as labyrinths and cellular honeycomb rolls. Un-like microscopic patterns, which form only for chargedspheres, and even then only for a limited range ofdiameters and densities and concentrations, the samelarge-scale convective patterns form for colloidal sphereswith various compositions and characteristics. Patternssimilar to those described below form in aqueous dis-persions of negatively charged silica spheres, sulfate-terminated PS (polystyrene sulfate) spheres, carboxy-lated PS spheres, weakly charged PMMA (poly-methylmethacrylate) spheres and neutral hydroxyl-terminatedPS spheres. Whereas microscopic patterns arise as co-operative many-sphere phenomena over a very limitedrange of concentrations, φ, macroscopic patterns can bediscerned in the motions of individual spheres at van-ishing low number density, as well as at number densi-ties exceeding φ = 300%. Consequently, dispersed col-loidal spheres appear to contribute little to the patternformation mechanism in the high-bias regime, and themacroscopic patterns we observe instead appear to re-sult from convective instabilities in the electrolyte itself.Surprisingly, these instabilities appear not to have beendescribed previously.

Figures 2(a) through 2(d) show the evolution of mi-croscopic colloidal vortices into macroscopic labyrinthineelectroconvection rolls with increasing voltage for a sam-ple of 3 µm diameter silica spheres at an initial num-ber density of φ = 120% in a parallel-electrode cell atH = 200 µm. The labyrinths’ spatial period increaseswith the bias, as can be seen in Figs. 2(b), 2(c), and2(d).

Although the labyrinth in Fig. 2(b) at 5 V qualitativelyresembles the lower-bias pattern at 3 V in Fig. 2(a), theirmicroscopic structure is quite different. The bright fea-tures in Fig. 2(a) consist of individual wormlike colloidalvortices, whose microstructure can be seen in Fig. 3(a).

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(a) (b)

(c) (d)

FIG. 2: Labyrinthine patterns of 3.0 µm diameter silicaspheres at φ ≈ 120% in a cell H = 200 µm thick. (a) 3.0 V: amicroscopic labyrinth consisting of microscopic clusters. (b)5.0 V: a macroscopic labyrinth composed of counter-rotatingdouble-rolls. (c) 7.0 V. (d) 9.0 V. Lighter regions contain ahigher concentration of spheres. Scale bar indicates 1 mm.

(a) (b)ℓ

FIG. 3: Microscopic views of labyrinthine colloidal convectionrolls formed by 3.0 µm diameter silica spheres at φ ≈ 120% ina layer of water H = 200 µm thick. (a) Uncorrelated colloidalvortices at V = 2.6 V. (b) A double-roll convection roll atV = 4.0 µm. The arrows indicate the inter-roll separation, asin Fig. 1. The scale bar indicates 50 µm.

These structures were described in Ref.7 and consist ofrolling clusters of spheres hovering near the middle ofthe sample volume. Individual spheres appear dark inthese images, so that the bright domains in Fig. 2 ap-pear dark here. Although the circulation direction is welldefined in individual wormlike colloidal vortices, neigh-boring vortices’ circulation direction is uncorrelated. Bycontrast, the bright domains in Fig. 2(b), (c) and (d)consist of paired counter-rotating convection rolls, an ex-ample of which appears in Fig. 3(b). Unlike wormlikecolloidal vortices, these rolls span the sample thickness,

H, and are correlated throughout the observable sam-ple area. Charged colloidal particles, such as the silicaspheres in Figs. 2 and 3, are concentrated at the interfacebetween the counter-rotating rolls and flow downwardalong the interface at positive bias, as shown schemati-cally in Fig. 1.

FIG. 4: Electroconvective tornado formed at 6 V in a cellwith H = 200 µm. Scale bar indicates 50 µm.

Double-roll labyrinths replace wormlike colloidal vor-tices at roughly 4 V. Convection becomes more vigorousas the bias increases, and rolls tend to evolve into itiner-ant tornado-like structures, such as the example in Fig. 4by roughly 6 V. These structures twirl rapidly, complet-ing more than one cycle per second. They also can travelthrough the sample at several micrometers per second asbubbles nucleate and expand at the electrodes.

Whereas microscopic colloidal vortices only form un-der positive bias, macroscopic electroconvection can bedriven by biases of either sign. Suddenly inverting thebias on an already-formed electroconvection pattern re-verses the direction of circulation in about one secondwithout disrupting the large-scale pattern. Negative bi-ases also tend to push spheres onto the lower electrode,where they eventually deposit. This limits opportunitiesto study electroconvection at negative bias in our system.

Figure 5 shows how a microscopic colloidal vortex ringis transformed into a pair of convection rolls as the biasincreases. The colloidal vortex ring in Fig. 5(a) formedspontaneously from a dispersion of 2.9 µm diameter silicaspheres in a cell with H = 200 µm under 3.6 V bias. This80 µm diameter cluster consists of a circulating toroidalvortex of spheres. This vortex ring does not span thesample’s thickness, but rather is stably levitated to about40 µm above the lower electrode. Spheres rise near thecluster’s center and fall back along the outer edge, com-pleting one cycle in roughly 2 sec. Increasing the biascontinuously to 4.8 V over several seconds speeds the cir-culation until finally the toroid elongates and breaks intotwo counter-rotating rolls that span the H = 200 µmsample thickness, as shown in Fig. 5(b).

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FIG. 5: Transforming a colloidal vortex ring of 2.9 µm diam-eter silica spheres into paired convection rolls with increasingbias. (a) 3.6 V: colloidal vortex ring. (b) 4.8 V: the coronabreaks into rapidly circulating double-rolls.

FIG. 6: Labyrinthine patterns of 1.58 µm diameter silicaspheres. H = 200 µm. φ ≈ 50%. (a) 4.0 V: labyrinthineconvection rolls in the bulk. (b) 10 V: labyrinth of crystal-lites deposited on the upper electrode.

A. Dependence on sphere diameter

Under the same conditions that 3 µm diameter sil-ica spheres form well-organized microscopic colloidal vor-tices, 1.58 µm diameter silica spheres form only tum-bling clouds6,7. Although these clouds show none ofthe internal organization of colloidal vortices, they nev-ertheless tend to organize themselves into labyrinthinepatterns on substantially larger length scales, as can beseen in Fig. 6(a). Like the labyrinths formed by largerspheres, these patterns also coarsen with increasing bias.By about 10 V, however, the smaller lighter particlesare driven onto the upper electrode, where they stickirreversibly. These adsorbed spheres typically are ar-ranged into static labyrinthine domains with crystallinemicrostructure, an example of which appears in Fig. 6(b).

B. Dependence on sphere composition

To avoid particle deposition under negative bias con-ditions, we repeated these experiments with 0.5 µm di-ameter PS spheres, whose density of 1.05 g/cm3 is moreclosely matched to that of water. These particles formlabyrinthine patterns comparable to those in Fig. 2 un-der comparable positive biases. Figure 7(a) shows theseparticles also form steady-state labyrinths in the bulkat −6.0 V. A similar trend of domain coarsening with

(a) (b)

FIG. 7: Labyrinthine electrohydrodynamic convection of0.5 µm diameter PS spheres in a sample with H = 390 µm.(a) −6.0 V: labyrinth in the bulk. (b) Effect of reducing thebias to −4.0 V. Scale bar indicates 1 mm.

increasing driving also is observed with negative biases.These observations suggest that gravity plays no signif-icant role in establishing the observed electrohydrody-namic convection patterns. They also confirm that thepatterns are sensitive to neither the spheres’ density northeir diameter.

Labyrinth coarsening appears not to be reversible. Re-ducing the bias to −4.0 V might be expected to select afiner-grained pattern. With the coarser pattern alreadyestablished, however, the result is to coalesce the colloid-rich convection rolls into thinner domains, separated bywider margins, as shown in Fig. 7(b).

C. Concentration dependence: Honeycombpatterns

Although the nature of the electroconvective patternsformed at a given bias does not depend on the spheres’diameter, it does depend somewhat on their concentra-tion, as can be seen in Fig. 8. Honeycomb patterns, suchas the example in Fig. 8(a), appear more often at highersphere concentrations. These periodic cellular patternsare characterized by three-way junctions between dou-ble convection rolls. In other respects, they resemblethe labyrinthine patterns. In particular, the dispersedspheres continue to be concentrated near the region offastest circulation at the junction between adjoining rolls.

Lower concentrations favor discontinuous honeycombpatterns, which appear in Fig. 8(b), with spheres con-centrated at vertices joining three convection rolls ratherthan at interfaces between two. Similar polka dot pat-terns also are obtained with 0.29 µm or 7.0 µm diameterPS spheres in a 390 µm thick cell at comparable fillingfractions φ.

As for the labyrinthine patterns, bulk honeycomb pat-terns gradually deposit their spheres onto the electrodes.The image in Fig. 8(c) shows 1.8 µm PS spheres at the up-per electrode of a H = 390 µm thick sample during bulkhoneycomb convection at 3.0 V. Dark regions in this im-age consist of multilayer colloidal crystals. Removing the

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FIG. 8: Honeycomb and dots patterns. Dense regions ofspheres appear white in (a), (b) and (d), but dark in (c).(a) 1.8 µm PS sphere; H = 390 µm; 4.0 V. Typical honey-comb pattern formed at high number density. (b) 1.8 µm PSspheres; H = 90 µm; 8.0 V; φ ≈ 10%. Spots pattern. (c)1.8 µm PS spheres at the upper electrode for H = 390 µmand 3.0 V. Multilayer crystals are apparent in dark areas. (d)0.29 µm silica spheres; H = 390 µm; 10 V. Convective cloudyrings.

bias frees all but the uppermost layer to sediment backto the lower electrode. The remaining crystalline layer isirreversibly bound to the upper electrode and retains theconvection rolls’ honeycomb structure.

Honeycomb rolls form just as readily with sulfateterminated PS, carboxylated PS, neutral hydroxyl-terminated PS and PMMA particles. In all cases, apply-ing a positive bias causes particles to flow upward withineach cell’s core and to circulate back downward along theborders between neighboring cells.

D. Dependence on sample geometry

Figures 9 and 10 show that bulk labyrinthine patternsare not strongly affected by the boundaries of the obser-vation channel, but rather extend right up to the walls.Nor are labyrinths oriented in any obvious way by theboundaries. The images in Figs. 9 and 10 were obtainedin two cells 1 mm deep, the first with in-plane dimensions4 cm × 0.9 cm and the second 4 cm × 0.3 cm. Despitethis difference, both cells produced similar patterns, withany differences being ascribable to differences in parti-cles density. This further illustrates that the transverseboundary condition has little influence on bulk patternformation in the electroconvective regime. Figures 9 and10 also highlight the wide range of parameters underwhich labyrinths form, including cells at least as deep

FIG. 9: Labyrinth in theH = 1 mm cell (high particle density,wide cell). 1.5 µm diameter silica spheres. White areas havehigher particle density. (a) 4.0 V. (b) 8.0 V. (c) 12.0 V. (d)20.0 V.

as H = 1 mm and at biases as high as 20 V.

IV. THE ROLE OF CHARGE, IONICCONCENTRATION AND PH

Trends in electroconvective pattern formation suggestsome minor role for the dispersed colloidal particles ininitiating the instability. The particles’ charge, however,appears to be surprisingly unimportant. Bulk honey-comb patterns form just as easily with electrically neutralhydroxyl-terminated polystyrene particles as with highly

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FIG. 10: Labyrinth in theH = 1 mm cell (low particle density,narrow cell). 1.5 µm diameter silica spheres. Dark areas havehigher particle density. (a) 8.0 V. (b) 16.0 V.

charged sulfate-terminated particles. This contrasts withthe formation of microscopic levitated clusters in our pre-vious reports6,7, to which the particles’ charge proved in-tegral. It suggests that bulk honeycomb or labyrinthineconvection patterns are due to an instability in the elec-trolyte itself and that the particles serve only as visibletracers of these flows.

Dispersed particles also may serve as tracers for otherproperties as well. For instance, charged spheres are morelikely to congregate in regions of high counterion concen-tration. In the absence of added salt, H3O+ and OH−

are the predominant ionic species in our systems, so thatthe spheres thus may serve as pH tracers. To test thisidea, we performed experiments on dispersions of highlycharged polystyrene sulfate spheres with molecular pHindicators and in cells with ITO (indium tin oxide) elec-trodes.

Adding trace amount of the pH indicator methyl redinto the cell does not affect the sequence of macroscopicpatterns formed with increasing bias. However, the milkywhite bulk labyrinth that forms in an unlabeled suspen-sion appears bright red with added indicator. The re-gions of low sphere concentration, on the other hand,appear yellow. Methyl red turns yellow at pH > 6.0, redat pH < 4.4 and orange in between. Thus the pH in thesphere-rich areas is lower than 4.4, and that between thedense stripes exceeds 6.0.

The highly negatively charged spheres themselves actas strong acids. The color gradients therefore might re-flect the influence of the spheres on the pH, rather thanthe ionic concentrations’ influence on the spheres’ dis-tribution. Repeating the experiment with more weaklycharged silica spheres yields similar profiles in the distri-bution of spheres, but with much weaker color gradients.Repeating the experiment with no spheres at all yields novisible patterns in the indicator even though related ex-periments with very small numbers of dispersed spheresstill reveal patterns of convection rolls under comparableconditions. The absence of visible color gradients underthese conditions does not guarantee the absence of pH

FIG. 11: Oxidation patterns on the lower, negatively biasedITO electrode. Darker areas have been oxidized and lighter,transparent areas remain in the initial unoxidized state. (a)The pattern in the central region of the electrode. (b) Aregion near a corner of the sample cell. (c) Central region ofanother electrode after 30 sec at 8 V bias.

gradients. Rather, it may reflect the difficulty of detect-ing subtle color changes in thin electroconvection cellswithout the additional contrast provided by concentra-tions of spheres.

Consequently, we performed additional experimentsusing electrodes fabricated from thin films of indium tinoxide (ITO). ITO is a transparent conductor that devel-ops a tint under oxidizing conditions that ranges fromlight yellow to dark gray depending on the degree of oxi-dation. Colloidal dispersions form labyrinthine and hon-eycomb convection patterns just as readily with the ITOelectrodes as with the gold. In this case, however, theITO electrodes show clear signs of oxidation, with yellowbands replicating the millimeter-scale patterns displayedby the convecting spheres. Repeating the experiment indeionized water without dispersed spheres yields compa-rable results, with well defined yellow stripes appearingon the negatively biased lower electrode after just a fewseconds of hydrolysis. Typical results appear in Fig. 11.

These observations suggest that water itself undergoeslarge-scale electroconvective instabilities leading to theformation of labyrinthine and honeycomb patterns. Theyfurther suggest that these patterns result from a spatialseparation between the anionic and cationic fluxes gen-erated by hydrolysis of water, and thus a departure fromlocal electroneutrality.

This large-scale separation of ionic fluxes, depictedschematically in Fig. 1, is consistent with the theory forbulk gravity-free electroconvection of water9,10. The for-going observations therefore appear to be an experimen-tal realization of this phenomenon. Although dispersedspheres may influence details of the intrinsic electrocon-vective instability, their presence is not required. Thiscontrasts with the formation of electrohydrodynamicallydriven colloidal vortices described in Refs.6 and7.

If indeed pure water is linearly stable against the onsetof electroconvection in the parallel-plate geometry9, thenthe phenomena described above must be initiated by im-perfections in the sample10. Figure 12, however, showsthat convection rolls pass over and across scratches inthe thin-film electrodes without distortion. Electrocon-vection rolls drift as freely across such defects as theydo across undamaged regions of the electrode surfaces.

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Moreover, oxidation patterns in ITO electrodes suggestthat electroconvective patterns extend undisturbed allthe way to the irregular edges of the sample volume.Irregularities, therefore, may be necessary to bootstrapelectroconvection in pure water10, but they do not appearto play a major role in establishing or maintaining theoverall pattern once electroconvection is fully developed.

FIG. 12: Magnified view of three dark electroconvectivedouble-rolls at the vertex of a honeycomb pattern passingover scratches in the lower electrode. The rolls appear darkin this image, while the scratches appear bright white. Scalebar indicates 50 µm.

The macroscopic electroconvection patterns discussedhere qualitatively resemble patterns generated by ther-mal gradients during Rayleigh-Benard convection16.From a mathematical perspective, the analogy is reason-ably close8,9. In both cases, diffusive transport estab-lishes a threshold for the convective instability. The prin-cipal difference is that heated fluid layers are linearly un-stable against Rayleigh-Benard convection whereas sim-ple electrolytes are believed to be linearly stable againstelectroconvection, the stabilization arising from the en-ergetic benefit of maintaining local electroneutrality9.

Much of the literature on electroconvection conse-quently addresses field-induced instabilities in systemswhere local electroneutrality naturally is violated. In liq-uid crystal films, for example, charge separation alongindividual molecules provides the basis for electroconvec-tive instabilities17. Transitions between labyrinthine andcellular patterns in this system are influenced in largepart by phase transitions in the liquid crystal itself17.They differ, therefore, from the transitions in electro-convective pattern formation described here, which arenot associated with phase transitions in the simple elec-trolyte.

Another type of electroconvection similar to ours is in-duced by injecting space charge into apolar liquids18,19.Increasing the bias on such a system yields a sequenceof patterns ranging from hexagonal cells to filaments toturbulence. The dielectric liquids used in these experi-ments have extremely high degree of ionic purity so thatspace charges will be established during electrical conduc-

tion. Both electroneutrality and Ohm’s law break downin such systems. By contrast, our aqueous electrolytesare electrically neutral, and their conductivity is highenough that Ohm’s law holds. Observing electroconvec-tion in simple electrolytes therefore greatly expands therange of isotropic systems fluids capable of supportingbulk field-driven instabilities.

V. SUMMARY

We have observed the emergence of labyrinthine andhoneycomb electroconvection patterns with length scalesbetween 0.5 mm and 2 mm during the steady-state hy-drolysis of water at biases above 4 V in a parallel plateelectrolysis cell. These macroscopic patterns share somefeatures with the microscopic clusters we described inRefs.6 and7. Among the similarities are the circulationdirection of the convection rolls, the coarsening of thepatterns features with increasing bias, and the increasein circulation rate with increasing voltage.

Unlike microscopic colloidal electroconvection, macro-scopic electroconvection patterns form under both nega-tive and positive bias. Flipping the sign of the bias on apreformed pattern merely changes the circulation direc-tion. Also unlike microscopic patterns, which form undera very limited range of conditions, electroconvection pat-terns arise for both charged and uncharged colloid, andfor both neutrally buoyant polystyrene spheres and densesilica spheres. On this basis, we conclude that particlesare little more than passive tracers for electroconvectiveflows in this high bias regime.

Experiments with pH indicator show that regions con-taining negatively charged colloidal spheres are moreacidic. Experiments with ITO electrodes demonstratethat the pH distribution near electrodes display the sameperiodic patterns even without colloid. Consequently, weconclude that these macroscopic patterns constitute aninstability of electrolyte itself. Despite the experiment’ssimplicity and the effect’s generality, this process appearsnot to have been reported previously.

In this paper and Ref.7, we have demonstrated thata very simple electrokinetic apparatus can form an ex-ceptionally wide range of highly organized dynamic pat-terns, even under constant uniform driving. The appar-ent simplicity of colloidal dispersions subjected to con-stant and uniform fields is deceptive, however, becausecolloidal electrodynamics during steady hydrolysis in-volves a great many processes spanning a huge range oflength scales. Consequently, our most surprising result isthat robust self-organization emerges from such compli-cated processes even when the system is driven very farfrom equilibrium.

This work was supported by the donors of thePetroleum Research Fund of the American Chemical So-ciety.

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