Evolution of mud-crack patterns during repeated …

1 Evolution of mud-crack patterns during repeated drying cyclesLucas Goehring,1, 2, 3 Rebecca Conroy,1 Asad Akhter,1 William J. Clegg,2and Alexander F. Routh1, 3, 1 Department of Chemical Engineering and Biotechnology,University of Cambridge, Pembroke Street, Cambridge, UK, CB2 3RA2 Department of Materials Science and Metallurgy,University of Cambridge, Pembroke Street, Cambridge, UK, CB2 3QZ3BP Institute for Multiphase Flow, University of Cambridge,Madingley Rise, Madingley Road Cambridge, UK, CB3 0EZ(Dated: March 26, 2010)In mud, crack patterns are frequently seen with either an approximately rectilinear or hexagonaltiling. Here we show, experimentally, how a desiccation crack pattern changes from being dominatedby 90 joint angles, to 120 joint angles.

2 Layers of bentonite clay, a few mm thick, were repeatedlywetted and dried. When dried, the layers crack. These cracks visibly close when rewetted, but asimilar crack pattern forms when the layer is re-dried, with cracks forming along the lines of previ-ously open cracks. Time-lapse photography was used to show how the sequence in which individualcracks open is different in each generation of drying. The geometry of the crack pattern was ob-served after each of 25 generations of wetting and drying. The angles between cracks were found toapproach 120 , with a relaxation time of approximately 4 generations. This was accompanied by agradual change in the position of the crack vertices, as the crack pattern evolved. A simple modelof crack behavior in a layer where the positions of previously open cracks define lines of weakness isdeveloped to explain these INTRODUCTIONWhen slurries dry, they tend to crack.

3 These cracksform sequentially, and when a later, or secondary, crackapproaches an earlier, or primary, one it curves to in-tersect it at 90 , forming a T-junction . The resultingcrack pattern divides the dried layer into roughly recti-linear pieces, such as those shown in Fig. 1(a,b). Thisbehavior has been reported in many materials, includingclay [1, 2], colloidal alumina [3], corn-starch [4 6], andcoffee grounds [7]. The patterns found in dried mud are,however, not always as suggested by these can, as shown in Fig. 1 (c,d), contain crack net-works that outline roughly hexagonal cells, with cracksintersecting at 120 , forming Y-junctions . The origin ofthese differences in geometry is not this paper, we consider the cracks that form whenclay dries.

4 We describe how the junctions between crackscan evolve when the layer is repeatedly wetted and dried,and show how a rectilinear crack pattern changes intoa hexagonal crack pattern. These observations are ex-plained using a simple model of crack formation, wherethe positions of previously open cracks influence the de-velopment of the next generation of MATERIALS AND METHODSS lurries of bentonitite clay (Acros Organics, BentoniteK-10) and de-ionized water were prepared by addingwater to dry bentonite powder until it could be easily 1: There are a variety of fracture patterns commonlyfound in dried mud. (a,b) show rectilinear patterns , wherecracks typically meet at T-junctions of 90 and 180 . (c,d)show, in contrast, hexagonal patterns , where cracks meet at Y-junctions of 120.

5 [Panels (a,c) courtesy of B. Hallet.]stirred. Slightly less than two parts of water were addedfor every part bentonite, by mass. These slurries werepoured into flat-bottomed polystyrene petri-dishes (150mm diameter, 10 mm height). At the end of each ex-periment, the thickness of the clay layers was measuredby picking up several dried pieces, and measuring theirthickness with were placed approximately 50 cm below a pairof 150 W halogen heat lamps, and allowed to dry, andcrack, over a period of two to three days. The clay re-mained gently bound to the bases of the dishes, and couldbe rewetted by gently spraying the surface with a finemist of deionized water, using a spray bottle held ap-proximately 30 cm away from the clay surface.

6 Water2was added until the cracks in the center of the dish wereseen to visibly close; a mass of water between 1 and the dried slurry mass was images of the clay surface were taken after eachgeneration of drying. In some cases additional time-lapseimages were taken throughout the course of drying. Per-manent marks were made on the outside of each dish,which were used to align images in different these markers could be realigned to within oneor two pixels, or an error of mm. The geometriesof the resulting crack patterns were measured in theseimages. For most measurements the dominant error wasdue to sample size: there were large standard deviationsin the observables, and each data set had approximatelyone hundred measurements.

7 To avoid edge effects all cellseither adjacent to, or one cell removed from, the walls ofthe dish were ignored. For layers thicker than 7 mm thisdid not leave enough remaining cells to report significantdata. When studying the Evolution of patterns over mul-tiple generations, data were averaged over four separatedishes, in order to minimize statistical RESULTSA. Crack formationWhen a clay layer was dried, rewetted, and then stirredto homogenize the slurry, the crack pattern in the nextgeneration had no relation to the original pattern. Simi-larly, in layers that were rewetted until the clay was sub-merged, the subsequent crack pattern was largely unre-lated to the original. Some similarities could be seenbetween generations, particularly in thicker layers, butmost crack positions changed.

8 If the clay was rewettedto the point where the cracks visibly closed, but the sur-face was not submerged, the crack pattern in the redriedclay closely matched the pattern in the initially driedclay. However, this persistence was dependent on thelayer thickness. For the thinnest layers, approximately1 mm thick, rewetting the dried clay with a fine mistchanged the positions of most photos were taken every 5 minutes of mm thick drying clay layer, during the first3 generations. In the first generation most cracks ap-peared between images. When cracks met, they formedT-junctions, as a later crack will preferentially meet anearlier one in a normal direction [5]. The cracks showedclear, well-defined edges, and the surface of the claywas smooth.

9 After rewetting, cracks in later generationsopened more slowly, often through the coalescence of sev-eral smaller cracks opening along some previous crack,and their faces become more uneven and jagged. Open-ing could take several minutes to occur, as observed ina few sequential images. After the first generation, thecracks formed shallow depressions in their vicinity, whichremained visible in the rewetted layers. These depres-sions were less than a mm deep, but imply that the clay5 mm(a)(b)(c)(d)!x(e)(f)(g)(h)FIG. 2: Panels (a-d) show the Evolution of two vertices indried clay, after each of the first four generations of drying,respectively. There is a gradual change in fracture position,and an increase in the roughness of the crack with time.

10 Thevertices also move, such that all angles begin to approach120 . This is highlighted in panels (e-h), which sketch outthe positions of the same cracks, and demonstrate how thejoint angles and vertex positionsxare of order 10% thinner in the vicinity of a previously opencrack. The surface of the clay become rougher in latergenerations, but this was likely a result of the methodsof rewetting the clay, which involved misting the surfacewith droplets of water. The changes in surface and crackroughness can be seen in Fig. each generation the pattern of cracks and verticeswas similar, but the sequence in which cracks appearedwas different. At any vertex there are three directionsalong which there are cracks.