Wormholes, long roughly cylindrical tubes of fully-dissolved material, can develop spontaneously in fractured  and porous rocks . The shape of the wormhole varies significantly with flow and reaction rates. The Peclet number, Pe = Q/WD, characterizes the volumetric flow rate Q (in cubic meters / second), the width of the fracture (W), and the diffusion coefficient of the dissolved ions, D. The simulated fractures are of a similar size to laboratory cores (50 mm x 25 mm x 0.1mm). A perturbation in aperture, corresponding to a small holed drilled a short distance (0.5 mm) into the center of the fracture inlet, has the effect of initiating a single well-defined wormhole running along the centerline of the fracture.
Different shaped wormholes can be observed, depending on the flow rate (or Pe). At very low flow rates (top left panel), dissolution occurs almost entirely within the inlet region; the reactant cannot penetrate into the fracture. At higher Peclet numbers a compact wormhole develops, illustrated in the first movie (Pe = 20). Almost all the reactant is consumed within the central wormhole and the concentration field outside is small. Once the wormhole has reaches the outlet it forms an almost perfectly circular tube. Nearer the inlet, the wormhole is elliptically shaped, with an aspect ratio that depends on Peclet number. At lower flow rates (Pe ~ 20) the inlet region is nearly circular, but as the Peclet number increases it spreads into a more elliptical shape. Then, at Pe = 80, there is an abrupt transition to a necked shape (second movie), where a secondary front, spanning the whole width of the system, develops behind the wormhole.
Finally, for Peclet numbers in excess of 100 the fracture opens uniformly along its whole length (bottom right panel). A similar progression of shapes can be inferred from Fig. 6 of Ref. . Further details can be found in Ref. .