Pit Initiation on Aluminum as a Queueing Process

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 ( λ ) of chloride ions is determined from quantitative XPS intensity data. The servicing rate ( μ ) 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 ( L q ) in the queue, the number of units ( L ) in the system (queue plus server), the average time ( W q ) a unit spends in the queue, and the average time ( W ) 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 ( W ) in the system corresponds to a low rate for the ongoing corrosion reaction. The time ( W ) 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 λ = μ ).