Velocity Sensitive Corrosion

One sometimes overlooked influence on corrosion is fluid motion past a surface. The influence can be somewhat complex. The degree of effect depends on both the alloy and the environment to which it is exposed. Fluid velocity can accelerate corrosion without solid particulate matter being present in the fluid. That effect is usually caused by the corrosion reaction being limited by the rate of mass transfer to or from the surface by one or more constituents important to the corrosion reaction. Fluid velocity can sometimes decrease corrosion relative to that in a static environment. That effect is usually caused by an increase in mass transfer of a constituent that increases surface passivity. Particulates present in the fluid can also increase corrosion. That form of corrosion is usually called erosion corrosion which results from the combined action of both the fluid and the particles impinging on the surface.

Mass Transfer Influenced Corrosion

When fluid flows past a stationary surface, the fluid velocity at the surface is assumed to be zero. This assumption is often called no slip at the wall. The fluid velocity increases with distance from the wall until the free stream velocity is reached. This distance is referred to as the boundary layer. When the fluid flow is turbulent which is often the case, the boundary layer is often pictured as having two regions, an inner laminar sublayer close to the wall and a turbulent region farther into the fluid. If mass (molecules or ions) are being transported to or from the surface, a concentration profile also develops. This profile reflects the change in concentration between that at the wall and that in the free stream. If mass is being transferred from the wall to the fluid, the profile shows a decrease with distance from the wall. If mass is being transferred from the fluid to the wall, the profile shows an increase with distance from the wall. In liquids, the concentration profile is much shorter than the velocity profile and the mass transfer boundary layer lies well within the velocity boundary layer. These relationships are shown in the figure below for turbulent flow conditions on a hydraulically smooth surface. The term hydraulically smooth surface means that all protuberances on the surface caused by non-uniformity are smaller than the thickness of the laminar sublayer immediately adjacent to the wall.

Mass transfer rates are usually expressed as a mass transfer coefficient times the difference in concentration between that in the bulk fluid far from the wall and that in the fluid immediately adjacent to the wall. If the corrosion rate is limited by the rate of mass transfer, then the corrosion rate is equal to the mass transfer rate. These relationships are usually written mathematically as:

This equation corresponds to the rate of mass transfer from the bulk fluid to that at the surface. An example of this situation is the corrosion of steel in water containing dissolved oxygen. The corrosion rate is limited by the rate at which oxygen migrates to the wall and reacts with iron. For this situation, the concentration of oxygen at the surface is assumed to be zero.

Under turbulent flow conditions, the mass transfer coefficient cannot be calculated analytically. It is usually measured by experiment. The mass transfer coefficient is usually expressed as the non-dimensional Sherwood number (written as Sh):

This quantity expresses the ratio of convective mass transport to diffusive mass transport between the bulk fluid and the surface. The characteristic dimension depends on the geometry being considered. For example, the characteristic dimension in a pipe is the pipe diameter.

In the literature the Sherwood number is usually expressed as a function of the product of the Reynolds number (written as Re) and the Schmidt number (written as Sc) as:

In the above equation a, b, and c are constants. This equation is actually a straight line approximation (in log-log coordinates) of the relationship as determined by experimentation. The Reynolds number is:
This quantity expresses the ratio of convective forces to diffusive forces in the fluid. The characteristic dimension again depends on the geometry being considered. For example, the characteristic dimension in a pipe is the pipe diameter. The Schmidt number is:
This quantity expresses the relative thickness of the hydrodynamic boundary layer to the mass transfer boundary layer. For liquids, this quantity is very large expressing the fact the that mass transfer boundary layer is much narrower than the hydrodynamic boundary layer. An excellent discussion of turbulence and boundary layer theory can be found in H. Schlichting, Boundary-Layer Theory, McGraw-Hill Book Co., New York, 1979. The discussion includes an analysis of pipe flow under both laminar and turbulent conditions. A lengthy discussion of these relationships with respect to the rotating cylinder electrode and how mass transfer control can be assessed by this device can be found at (http://www.argentumsolutions.com/tutorials/cylexpert_tutorialpg4.html).

Mass Transfer and Polarization

As mentioned above, the rate of corrosion in some corroding systems depends on the rate of mass transfer of a component to or from the surface. Either the anodic reaction (oxidation of the metal which releases electrons into the metal) or the cathodic reaction (reduction of a species that reacts with the released electrons) could be under mass transfer control. Such control is sometimes called diffusion control by electrochemists. In either case, the rate of mass transfer (convective diffusion) increases with fluid velocity.

Reduction Process Under Mass Transfer Control

In some corroding systems, the corrosion rate is controlled by the rate at which the species being reduced is transferred from the bulk medium to the surface. An example is any corrosion reaction in which dissolved oxygen is the species being reduced (e.g. corrosion of carbon steel in water). Shown in the figure below is the polarization behavior of the anodic (metal to metal ion) and cathodic (oxidant to reduced species) reactions that might occur.

The rate of an electrochemical reaction not under mass transfer control increases with polarization. In this case the anodic reaction or reaction of the species being oxidized is not under mass transfer control and its rate increases with polarization of the surface. The species being reduced reacts at a faster rate. At some point, the rate of the anodic reaction equals the rate of mass transfer of the species being reduced. At that point, the reaction rate can no longer increase with polarization because the rate of mass transfer of the species being reduced cannot increase. The corrosion rate which is denoted by the intersection of the anodic and cathodic reactions becomes independent of potential. That behavior is represented by the vertical lines in the plot. As the velocity is increased, the rate of mass transfer increases and the reduction reaction can reach higher rates. The overall corrosion rate is marked by the intersection of the cathodic and anodic curves (points A, B, and C). The result is that the overall corrosion rate increases with fluid velocity. Situations can arise that the velocity is so high that the reduced species is replenished fast enough that the reaction can come under activation control. That point is indicated by point D and beyond.

Oxidation Process Under Mass Transfer Control

In some corroding systems, the corrosion rate is controlled by the rate at which the product of metal ion oxidation is transferred from the surface to the bulk medium. An example is the corrosion of steel in concentrated sulfuric acid (e.g. > 90 wt% sulfuric acid, balance water). In that case, the corrosion rate of iron being oxidized to Fe+2 is limited by the rate at which a saturated salt of FeSO4 is tranferred from the surface to the bulk. Shown in the figure below is the polarization behavior of the anodic reaction as a function of velocity.

The rate of oxidation of the metal increases with potential. At some potential, the rate of formation of a salt containing the metal ion becomes equal to the rate at which it migrates from the surface. At that point, the corrosion rate becomes equal to the rate of mass transfer of the salt from the surface to the bulk medium. Once this point is reached, the current density becomes independent of potential. If the velocity is increased, the mass transfer rate is increased and the maximum corrosion rate is increased until it equals the new, higher corrosion rate of mass transfer. This behavior is marked by points A, B, C, and D. In many instances, at some higher potential a new oxidation reaction becomes dominant and the current is no longer independent of potential. For iron in sulfuric acid when the potential increases above a certain value, iron is oxidized to another form, e.g. Fe+3, which imparts greater passivity to the surface resulting in a decrease in corrosion current. The plot depicts this type of behavior at higher potentials.

Erosion Corrosion Caused by Particulate Impingement

Erosion corrosion is often caused by the joint action of molecular corrosion and solid particulate impingement. The rate of such erosion tends to vary with the fluid velocity raised to a power that is above 1, often between values of 2 and 4. Some studies have shown this exponent to be about 3. These values are much higher than mass transfer influenced corrosion under turbulent flow conditions without particulates which tends to vary with velocity raised to a power between about 0.6 and 1 depending on geometry. Thus, the presence of particulates can, in many instances, accelerate corrosion well above the rate attributable to mass transfer alone. Unfortunately, the exponent can sometimes be close to 1 depending on the alloy and particle. But, examining erosion as a function of fluid flow rate (Reynolds number) can often serve as a first-pass evaluation of the relative effects of corrosion and particulate erosion.

Unlike mass transfer influenced corrosion, well-defined correlations do not exist for particulate influenced corrosion even in the absence of molecular corrosion. The phenomenon is a complex function of the following variables:

  • fluid velocity especially that impacting the alloy surface
  • average particle size
  • average particle shape
  • average particle microroughness
  • average particle density (especially relative to the fluid)
  • particle concentration
  • particle material
  • particle hardness relative to the alloy
  • alloy being affected
  • fluid environment
  • equipment geometry (affects impact angle and flux of particles)
  • particle distribution in fluid

The velocity component normal to the surface can (but not always) play a major role in erosion corrosion. The variables of impact velocity, impact angle, relative density between particle and fluid, and particle size are the main determinants of the kinetic energy of the particles as measured normal to the surface. Erosion rates can increase significantly if the flow is disturbed, e.g. suffers boundary layer separation as would be found immediately downstream of an expansion joint or at an elbow.

Erosion corrosion caused by suspended particles is more difficult to analyze than mass transfer influenced corrosion. Each system has to be analyzed individually. The relative contributions to overall corrosion by molecular corrosion and erosion corrosion caused by the joint action of molecular corrosion and suspended particles can be assessed individually in the geometry. Information on possible test techniques can be found in ASTM Annual Book of Standards, Volume 03.02, Corrosion of Metals; Wear and Erosion (available at http://www.astm.org.

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