Electrochimica Acta 65 (2012) 266–274 Contents lists available at SciVerse ScienceDirect Electrochimica Acta j ourna l ho me pag e: www.elsevier.com/locate/electacta Possible distribution of potential and corrosion current density inside corroding crevices George R. Engelhardt a,∗ , Digby D. Macdonald b,c a OLI Systems, Inc., 108 American Road, Morris Plains, NJ 07950, United States b Center for Electrochemical Science and Technology, Department of Materials Science & Engineering, Pennsylvania State University, University Park, PA 16802, United States c Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia a r t i c l e i n f o Article history: Received 11 November 2011 Received in revised form 16 January 2012 Accepted 17 January 2012 Available online 24 January 2012 Keywords: Crevice corrosion IR potential drop Iron Sodium acetate a b s t r a c t The case when the potential distribution inside a corrosion cavity obeys Ohm’s law is considered. Math- ematically, the potential drop in the crevice is described by a Poisson-type equation with a non-linear source term. A simple method for finding all possible solutions in a one-dimensional approximation and for investigating their stability has been developed. We derive a simple relation for estimating the critical depth of the crevice, L c (which is defined as the depth at which the active–passive transition just occurs within the crevice) as a function of the width of the crevice, w, electrolyte conductivity, , metal poten- tial, E met , and a polarization curve. It is shown that L c is proportional to √ (w) and is a linear function of E met . Calculation of the corrosion damage (maximum depth of the penetration into the metal, w max ) as a function of time and position inside the crevice has been performed. It is shown that during the initial stages of crevice corrosion, when the one-dimensional approximation is valid, w max is determined mainly by the polarization curve for the anodic dissolution of the metal. It is shown that, in the general case, it is impossible to neglect the potential drop in the external environment when quantitatively describing crevice corrosion. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction One of the principal tasks in theoretically describing crevice cor- rosion is to develop the ability to predict which geometries will be susceptible to this form of attack and to determine the critical crevice geometry that separates the region where crevice corro- sion initiates from that where crevice corrosion does not occur [1]. In those cases, when the occurrence of crevice corrosion cannot be avoided, the prediction of the corresponding corrosion damage as a function of time is of great practical importance. In this paper, we estimate quantitatively the value of crevice corrosion damage, which is expressed as the maximum penetration into the crevice wall. It has been suggested that different mechanisms must be invoked to describe the initiation of crevice corrosion in differ- ent systems (geometries). In accordance with the classical point of view, the initiation of crevice corrosion is attributable to the development of a differential aeration cell with the subsequent acidification of the crevice solution and/or migration of aggres- sive anions (for example, Cl - ) into the cavity [1–7], as embodied in the differential aeration hypothesis (DAH). However, as claimed ∗ Corresponding author. Tel.: +1 973 539 4996; fax: +1 202 738 3717. E-mail address: gengelhardt@olisystems.com (G.R. Engelhardt). in Ref. [7] “this classical theory is not able to explain cases of immediate corrosion or cases of crevice corrosion in systems which show no significant acidification or aggressive ion buildup in the crevice solution”. In these cases, crevice corrosion can be caused by IR (ohmic) potential drop in the cavity, which places the local metal potential existing in the crevice wall in the active dissolution region of the polarization curve, as developed extensively by Pick- ering and co-workers [1,7–15]. Generally speaking, in the absence of significant concentration drops in the crevice, the IR drop can be calculated by solving a Poisson-type differential equation rela- tive to the potential in the solution by using a numerical method. In particular, such calculations lead to the definition of the loca- tion of the active–passive transition and to the definition of the so-called critical crevice depth. Here, the critical crevice depth, L c , is defined as the depth, as measured from the crevice mouth, at which the active–passive transition just occurs within the crevice [1,7]. It is assumed that for crevices that are deeper than L c , the active–passive transition will manifest itself and lead to crevice cor- rosion. For crevices that are shallower than L c , the active–passive transition and, accordingly, crevice corrosion will not occur [7]. It has also been stated that computation of the critical crevice depth could be made solely on the basis of the polarization curve and the conductivity of the solution [1]. However, in our opinion, the last conclusion is valid only if the nonlinear, Poisson-type equation has a unique solution for the 0013-4686/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2012.01.065