Pit Initiation on Aluminum as a Queueing Process

Abstract

The pitting corrosion of aluminum is modeled as a queueing process in which chloride ions (customers or units) enter the passive film and are serviced (form an emerging pit) at certain sites (servers) at the oxide/metal interface. X-ray photoelectron spectroscopy (XPS) data show that chloride ions penetrate the passive film on aluminum and are considered to lie in a queue. The servicing (or processing) stage includes chloride-assisted localized dissolution of aluminum, development of local acidity within the emerging pit, and buildup of chloride ions within the developing pit. The arrival rate of chloride ions is determined from quantitative XPS intensity data. The servicing rate has been determined from anodic polarization curves and also from Scully's criterion for stable pit growth. The following queueing characteristic parameters have been calculated: the number of units in the queue, the number of units in the system (queue plus server), the average time a unit spends in the queue, and the average time a unit spends in the system (queue and server). This is done for the following queueing systems: single queue with a single server, single queue with multiple servers, and multiple queues with single or multiple servers. A long time in the system corresponds to a low rate for the ongoing corrosion reaction. The time that a unit spends in the system is maximized for (i) a decrease in the number of servers, (ii) a decrease in the servicing rate μ, (iii) a decrease in the number of queues, or (iv) an increase in the arrival rate (up to ).