# Study of Mass Transport Limited Corrosion With Rotating Cylinder Electrodes

Last Updated: 12/21/20 by Tim Paschkewitz

##### ARTICLE TAGS
• Electrode,
• Electrode Rotator,
• Corrosion,
• DRA10011,
• flow,
• laminar,
• Mass transport,
• Pipe,
• pipeline,
• Rotating Cylinder,
• Shear Stress,
• turbulent
##### Related Pages
1. Abstract
2. Introduction
3. Tuning Turbulent Flow
4. Mass Transport
5. Wall Shear Stress
6. Electrochemical Measurements
7. Modeling Pipeline Flow
8. Corrosion Instrumentation
9. Appendix
10. References

### 1Abstract

This technical note addresses two aspects of electrochemical testing using the Rotating Cylinder Electrode (RCE).  First, the fundamental hydrodynamic behavior at a rotating cylinder is summarized, including equations that predict the mass transport limited corrosion current at an RCE.  Second, a means of selecting the suitable rotation rate for an RCE test is discussed, with emphasis being placed on matching a particular rotation rate to a particular flow velocity in a smooth pipe.  In addition, a bibliography of significant reports regarding the RCE is provided.

### 2Introduction

Corrosion processes can accelerate significantly under extreme environmental conditions such as high temperature, high pressure, and turbulent fluid flow.  When troubleshooting a field corrosion problem, a researcher often needs to return to the lab and reproduce the same (or similar) harsh conditions in a controlled setting.  While familiar laboratory equipment for temperature control (ovens, water baths) and pressure control (autoclaves) is generally readily available and easy to use, recreating a fluid flow condition generally poses a larger challenge to the researcher.  Laboratory flow loop systems often require complex and expensive plumbing, maintenance, and calibration to reliably and reproducibly move fluid past a metal sample.  The need for this type of large scale laboratory equipment can often be avoided by moving the metal sample with respect to the fluid instead.

Figure 1. Fully Assembled Pine Research 15 mm OD Rotating Cylinder Electrode System

A special tip capable of holding a cylindrical-shaped metal sample is mounted at the lower end of the shaft.  The tip is fashioned primarily from chemically-inert and electrically-insulating materials (such as PTFE, PCTFE, or PEEK), but buried within the tip is a metal shank which provides mechanical stability and also electrical contact with the metal cylinder sample, also called a metal coupon (see Figure 2).

Figure 2. Assembled and Disassembled Views of the 15 mm OD Rotating Cylinder Electrode

### 3Tuning Turbulent Flow

At very slow rotation rates, the solution near a rotating cylinder flows with a regular and smooth motion called laminar flow.  As the rotation rate increases, the solution flow becomes more complex.  While the layer of solution in direct contact with the cylinder continues to cling to the surface, the shear stress between this layer and layers further from the cylinder begins to spin off vortices.  At this point, the solution flow transitions from laminar to turbulent flow, and as the rotation rate increases, the vortices themselves spawn further vortices.

The transition from laminar to turbulent flow is often characterized using the Reynolds Number (RE) to quantify the ratio between inertial forces and viscous forces in a solution.  For a rotating cylinder electrode with outer diameter, dcyl (cm), and radius, dcyl/2, the Reynolds Number is shown in Equation 1:
 $\displaystyle{R_E = U_{cyl} d_{cyl} \frac{\rho}{\mu}}$ (1)
where ρ is the solution density (g/cm3), and μ is the absolute viscosity of the solution (g/cm s).  The linear velocity, Ucyl (cm/s), at the outer surface of the cylinder is given by Equation 2:
 $\displaystyle{U_{cyl} = \omega r_{cyl} = \frac{{\pi}d_{cyl} F}{60}}$ (2)
where the rate can either be expressed as angular rotation rate, ω (rad/s), or as frequency, F (RPM).  In general, for a rotating cylinder, when the Reynolds Number is greater than 200, then the flow is turbulent.

For all but the very slowest rotation rates, the turbulent condition is expected and desired.  So, for a typical Pine Research RCE (15 mm OD, see Figure 2), rotation rates between 5 and 4000 RPM correspond to a range of Reynolds Numbers spanning several orders of magnitude (see Table 1 in Section 9.1).  The transition from laminar to turbulent flow occurs just above 20 RPM, when the Reynolds Number exceeds 200.  It is worth noting that this transition occurs at a relatively small rotation rate, making the RCE an ideal tool for studying turbulent flow at low velocity—precisely the condition frequently found in pipeline infrastructures.  Higher turbulent velocities are also easily accessible at higher rotation rates.

### 4Mass Transport

The turbulent flow at the RCE can bring material from the solution to the surface of the cylinder, and it can also carry material away from the surface.  In the context of a corrosion study, the rate of mass transport to and from the metal surface is often the factor which governs the rate of corrosion.  A familiar example would be a corrosion process which is limited by how fast oxygen can be transported from the solution to the metal surface.

Early reports by Eisenberg provide the most commonly accepted description for RCE mass transport. In particular, the mass transfer coefficient, KM (cm/s), to a rotating cylinder is given by the following relationship:
 $\displaystyle{K_M = S_H \frac{D}{d_{cyl}} = [0.0791 {R_E}^{0.7} {Sc}^{0.356}]\left(\frac{D}{d_{cyl}}\right) }$ (3)
where the diffusion coefficient, D (cm2/s), is usually taken as the diffusion coefficient for the molecule or ion undergoing mass transport, and where SH and RE are the dimensionless Sherwood and Reynolds Numbers, respectively.  The Schmidt Number, SC = μ/ρD, is also a dimensionless number.

Combining Equations 1 - 3, the overall mass transfer coefficient to an RCE can be expressed in one of three forms, as shown in Equations 4a - 4c:
 $\displaystyle{K_M = 0.0791 {d_{cyl}}^{-0.3} \left(\frac{\mu}{\rho}\right)^{-0.344} D^{0.644} {U_{cyl}}^{0.7}}$ (4a) $\displaystyle{K_M = 0.0487 {d_{cyl}}^{0.4} \left(\frac{\mu}{\rho}\right)^{-0.344} D^{0.644} \omega^{0.7}}$ (4b) $\displaystyle{K_M = 0.0100 {d_{cyl}}^{0.4} \left(\frac{\mu}{\rho}\right)^{-0.344} D^{0.644} F^{0.7}}$ (4c)
The exact form depends upon whether the rotation rate is expressed in terms of linear surface velocity (Ucyl), angular rotation rate (ω), or rotations per minute (F).  Note that the form shown in Equation 4a is that which is most often found in the literature.

### 5Wall Shear Stress

The turbulent flow at the RCE induces a wall shear stress on the surface of the cylinder.  Again, Eisenberg’s original reports offer a well accepted equation for the wall stress, τcyl (g/cm s):
 $\displaystyle{\tau}_{cyl} = 0.0791 {\rho} {R_E}^{-0.3} {U_{cyl}}^{2}$ (5)
The wall shear stress for a typical Pine Research RCE tip (dcyl = 1.5 cm) over a range of rotation rates is listed in Table 1 in Section 9.1.

### 6Electrochemical Measurements

When a rotating cylinder is used as the working electrode in a traditional three-electrode cell configuration, the corrosion behavior can be monitored by measuring the electric current at the cylinder. Electrical connection to the metal cylinder is accomplished by means of a brush contact on the rotating shaft.  A potentiostat is employed to impose various potentials on the cylinder electrode while simultaneously measuring the current.  The potential signal applied to the cylinder may be a very slow voltage sweep (e.g., Linear Polarization Resistance, LPR), or it may involve a high frequency sinusoidal signal (i.e., Electrochemical Impedance Spectroscopy, EIS).

Two other electrodes are also required to make an electrochemical measurement, a reference electrode (such as a silver/silver-chloride electrode) and a counter electrode. The counter electrode is often an even larger diameter cylinder, rod, wire loop, or flag placed in the solution so that it surrounds the rotating cylinder.  This helps to assure uniform current density at the RCE during the test.

In general, the mass transport limited current density, jlim (A/cm2), observed in an electrochemical experiment is related to the mass transfer coefficient by the following relationship:
 $\displaystyle{j_{lim} = \frac{i_{lim}}{A} = zFCK_m}$ (6)
where F is Faraday’s constant (96485 C/mol), ilim (A) is the limiting current, and A (cm2) is the area of the electrode.  To make full quantitative use of this relationship, both the number of electrons exchanged, z, and the bulk concentration of the ion or molecule involved in the electrochemical process, C (mol/cm3), must be known.

Combining equations (4) and (6), the mass transport-limited current density can be expressed as follows:
 $\displaystyle{j_{lim} = 0.0791zFC {d_{cyl}}^{-0.3} \left(\frac{\mu}{\rho}\right)^{-0.344} D^{0.644} {U_{cyl}}^{0.7}}$ (7a) $\displaystyle{j_{lim} = 0.0487zFC {d_{cyl}}^{0.4} \left(\frac{\mu}{\rho}\right)^{-0.344} D^{0.644} \omega^{0.7}}$ (7b)
Thus, if a corrosion process is limited by mass transport, it is expected that the limiting current (or limiting current density) will vary linearly with the rotation rate raised to the 0.7 power (ω0.7).  Note that this behavior can be verified even without explicit knowledge of z and C simply by conducting a set of measurements at several different rotation rates.

For example, consider a series of LPR scans performed over a range of rotation rates (see Figure 3).  As the rotation rate increases, so does the observed current.  A log/log plot of the limiting current (or limiting current density) versus the rotation rate will reveal whether or not the observed current is mass transport-limited (see Figure 4).  If the slope of a line drawn through the points on this plot is near 0.7, then this is good evidence that the corrosion process is limited by mass transport.

Figure 3. Example of a Series of LPR Scans Recorded at Various Rotation Rates

Figure 4. Logarithmic Plot to Test for Mass Transport-Limited Corrosion Process

### 7Modeling Pipeline Flow

The discussion here will be limited to the latter case, but at the outset, it is important to note that modeling a field corrosion situation in the laboratory involves some compromise and some assumptions.  When an RCE is operated at a rotation rate that produces similar mass transport conditions to those found in the field, it is assumed that the corrosion mechanism occurring in the field will be reproduced in the laboratory. However, it is not expected that the actual corrosion rate at the RCE will match that found in the field.  There have been specific cases where the RCE failed to reproduce the field corrosion condition. Particular attention is required when surface roughness influences mass transport. And lastly, there are practical limitations on the range of pipe diameters accessible with the RCE method.

 $\displaystyle{U_{cyl} = 0.1185 \left(\frac{\rho}{\mu}\right)^{1/4}\left(\frac{{d_{cyl}}^{3/7}}{{d_{p}}^{5/28}}\right) S_C^{-0.0857} {U_{p}}^{5/4}}$ (8)
where dp (cm) is the diameter of the pipe.  Using this relationship together with Equation 2, it is possible to compute a target rotation rate for the RCE.

Equation 8 has too many parameters to plot convenient working curves on a graph.  To convey some idea of the type of results produced using this equation, Table 2 in Section 9.1 lists the pipe velocity/rotation rate relationships for a typical Pine Research RCE (dcyl = 1.5 cm and A = 3.0 cm2) operating in pure water.  As an example, if water is flowing through a smooth 10 in Schedule 40 pipe at 1.0 ft/s, an RCE should be operated at about 131 RPM to match the conditions in the pipe.

### 8Corrosion Instrumentation

Pine Research offers specialized tools for the study of mass transport-limited corrosion.  In addition to our potentiostats for measuring corrosion current and potential, we design and manufacture complete corrosion cell kits.  These laboratory corrosion cells have been designed based on input we have received from researchers and practitioners in the corrosion community.  The corrosion cell is designed to be sturdy, long-lasting, and easily integrated with other Pine Research products.

The Pine Research classic RCE system was based on a 12 mm OD RCE (see Table 3 in Section 9.2), but an improved system based on a 15 mm OD RCE is now available (see Table 1 in Section 9.1). The Pine Research 15 mm OD Rotating Cylinder Electrode System has many features listed below.  Additionally, Figures 5 and 6 show the components of the 15 mm OD RCE system.

• Reliable electrical contact between the shaft and the replaceable cylinder insert is accomplished using a spring-loaded ball plunger that pushes against the inside diameter of the cylinder insert.
• All shaft components are fabricated from a chemically-resistant polymer, polyether ether ketone (PEEK), to protect the shaft from corrosive attack during testing.  PEEK has good mechanical stability at elevated temperatures (up to 80°C).
• The 15 mm OD allows for greater wall shear at the cylinder surface for a given rotation rate (as compared to the traditional 12 mm OD design).
• The OpenTop cell features a removable lid for easy cleaning.  The chemically-resistant PTFE lid has six easily configurable cell ports with standard taper adapters for either 14/20 or 24/25 accessories.  With these cell ports, the cell can be configured with a variety of accessories (condenser, pH measurement, thermowell, each sold separately) while still having enough ports for the reference and counter electrodes.
• The OpenTop cell features a special recess in the bottom of the cell into which the lower end of the RCE shaft is inserted.  This recess assists with aligning the shaft along the axis of the glass cell.
• Achievement of finer temperature control with a jacketed cell design.
• The one liter cell allows for larger solution volumes.
• A dual port purge accessory included with the cell permits the solution to be sparged and/or blanketed with a purge gas.  In addition, the gas-purged bearing assembly (through which the rotating shaft enters the cell) has a separate purge port to allow a positive purge pressure to be maintained within the void space of the bearing itself.

Figure 5. Components of the 15 mm OD RCE System

Figure 6. Assembled 15 mm OD RCE System with MSR Rotator

The following additional items are necessary to perform corrosion-based measurements:

• A potentiostat to measure corrosion current (e.g., Pine Research WaveDriver 100)
• An electrode rotator to achieve the desired wall shear stress (e.g., Pine Research MSR Electrode Rotator, see Figure 7)
• Metal sample inserts for the RCE electrode (see Figure 2)
• A reference electrode for potentiostat control (e.g., Ag/AgCl, Saturated Calomel, Hg/Hg2SO4, or Hg/HgO)

Figure 7. Pine Research MSR Rotator

### 9Appendix

#### 9.1Appendix A - 15 mm OD RCE Technical Information and Data

The 15 mm OD RCE System uses a specially-designed RCE shaft and metals inserts.  As shown in Figure 8, the shaft length is insulated with PEEK for higher temperature tolerance (up to 80°C).  The metal cylinder insert fits onto the shaft between rubber O-ring seals and is secured with a screw cap.  The black rubber O-rings ensure a tight seal to prevent solution leakage.  The RCE shaft (15 mm OD) fits directly into a Pine Research MSR rotator.

Figure 8. Assembled and Disassembled Views of the 15 mm OD Rotating Cylinder Electrode

The electrode shaft should never be cleaned or treated with acid.  The shaft and internal hardware may corrode if exposed to corrosive solutions.  Only use the RCE when fully assembled with seals, metal insert, and cap.

 Rotation Rate F (RPM) Rotation Rate ω (rad/s) Surface Velocity* Ucyl (cm/s) Wall Sheer Stress* τcyl (g/cm s2) Reynolds Number* RE (unitless) 5 0.524 0.39 0.0035 66 10 1.047 0.79 0.0113 131 20 2.094 1.57 0.0366 263 50 5.236 3.93 0.1737 657 100 10.47 7.85 0.5642 1315 200 20.94 15.7 1.8332 2629 250 26.18 19.6 2.6789 3287 500 52.36 39.3 8.7039 6573 1000 104.7 78.5 28.279 13146 2000 209.4 157 91.879 26293 3000 314.2 236 183.05 39439 4000 418.9 314 298.52 52586
Table 1. Hydrodynamic Computations for a Typical* 15 mm OD Pine Research Rotating Cylinder Electrode in Water

* These quantities assume a typical Pine Research 15 mm OD RCE tip with outer diameter 1.5 cm rotating in water at 25°C.  For pure water at 25°C, the density is 0.997 g/cmand the absolute viscosity is 0.00891 g/cm s.

 Pipe Velocity Standard Schedule 40 Pipe Sizes (actual ID in cm) (ft/s) (cm/s) (mi/hr) 2 in (5.25 cm) 4 in (10.23 cm) 6 in (15.41 cm) 8 in (20.27 cm) 10 in (25.45 cm) 12 in (30.32 cm) 16 in (38.1 cm) 18 in (42.88 cm) 24 in (57.48 cm) 0.1 3.0 0.07 0.2 6.1 0.14 23 21 19 18 18 17 16 16 0.3 9.1 0.2 39 34 32 30 29 28 27 26 25 0.4 12.2 0.27 55 49 46 43 42 40 39 38 36 0.5 15.2 0.34 73 65 60 57 55 53 51 50 48 0.6 18.3 0.41 92 81 76 72 69 67 64 63 60 0.7 21.3 0.48 111 99 92 87 84 81 78 76 72 0.8 24.4 0.55 131 117 108 103 99 96 92 90 86 0.9 27.4 0.61 152 135 126 120 115 111 107 105 99 1.0 30.5 0.68 174 154 143 136 131 127 122 119 113 2.0 61.0 1.36 413 366 341 324 311 302 290 284 269 3.0 91.4 2.05 685 608 565 538 517 501 481 471 447 4.0 122 2.73 982 871 810 771 741 718 689 675 640 5.0 152 3.41 1298 1152 1071 1019 979 949 911 892 846 6.0 183 4.09 1630 1447 1345 1280 1229 1192 1144 1120 1063 7.0 213 4.77 1976 1754 1630 1552 1491 1445 1387 1358 1289 8.0 244 5.45 2335 2073 1926 1834 1761 1707 1639 1605 1523 9.0 274 6.14 2705 2401 2232 2125 2041 1978 1899 1859 1764 10.0 305 6.82 3086 2739 2546 2425 2328 2256 2166 2121 2013 11.0 335 7.50 3477 3086 2868 2731 2623 2542 2440 2389 2267 12.0 366 8.18 3876 3441 3198 3045 2924 2834 2721 2664 2528 13.0 396 8.86 3803 3534 3366 3232 3132 3007 2944 2794 14.0 427 9.55 3878 3692 3545 3436 3299 3230 3065 15.0 457 10.23 3865 3746 3596 3521 3341 16.0 488 5.45 3898 3817 3622 17.0 518 11.59 3907 18.0 549 12.27
Table 2. Rotation Rate Correlation for Water between a Typical* 15 mm Pine Research Rotating Cylinder Electrode and Smooth, Straight Pipe Flow.

* These quantities assume a typical Pine Research 15 mm OD RCE tip with outer diameter 1.5 cm rotating in water at 25°C.  For pure water at 25°C, the density is 0.997 g/cmand the absolute viscosity is 0.00891 g/cm s.  Values that appear grayed out indicate this rotation rate is incompatible with the maximum or minimum rotation rates.

#### 9.2Appendix B - 12 mm OD RCE Technical Information and Data

Our classic 12 mm OD rotating cylinder electrodes have been used in oilfield corrosion inhibitor studies and other high velocity (high shear) corrosion experiments.  While Pine Research will continue to support the 12 mm OD rotating cylinder electrode, new customers are encouraged to consider our integrated 15 mm OD RCE system instead.  The 12 mm RCE design features a PTFE electrode shroud around the shaft connector with PTFE washers as shown in Figure 9.  The 12 mm RCE tip fits an E3 series shaft for the MSR rotator or the permanently-installed shaft on the discontinued Pine Research CPR rotator.  The 12 mm RCE tip is not compatible with the 15 mm RCE shaft.

Figure 9. Assembled and Disassembled Views of the 12 mm OD Rotating Cylinder Electrode

The electrode shaft should never be cleaned or treated with acid.  The shaft and internal hardware may corrode if exposed to corrosive solutions.  Only use the RCE when fully assembled with seals, metal insert, and cap.

 Rotation Rate F (RPM) Rotation Rate ω (rad/s) Surface Velocity* Ucyl (cm/s) Wall Sheer Stress* τcyl (g/cm s2) Reynolds Number* RE (unitless) 5 0.524 0.31 0.0025 42 10 1.047 0.63 0.0082 84 20 2.094 1.26 0.0267 169 50 5.236 3.14 0.1270 422 100 10.47 6.28 0.4125 844 200 20.94 12.6 1.3402 1688 500 52.36 31.4 6.3631 4219 1000 104.7 62.8 20.674 8438 2000 209.4 125.7 67.169 16876
Table 3. Hydrodynamic Computations for a Typical* 12 mm OD Pine Research Rotating Cylinder Electrode in Water

* These quantities assume a typical Pine Research 12 mm OD RCE tip with outer diameter 1.2 cm rotating in water at 25°C.  For pure water at 25°C, the density is 0.997 g/cmand the absolute viscosity is 0.00891 g/cm s.

 Pipe Velocity Standard Schedule 40 Pipe Sizes (actual ID in cm) (ft/s) (cm/s) (mi/hr) 2 in (5.25 cm) 4 in (10.23 cm) 6 in (15.41 cm) 8 in (20.27 cm) 10 in (25.45 cm) 12 in (30.32 cm) 16 in (38.1 cm) 18 in (42.88 cm) 24 in (57.48 cm) 0.1 3.0 0.07 0.2 6.1 0.14 26 0.3 9.1 0.2 44 39 36 34 33 32 31 30 29 0.4 12.2 0.27 63 56 52 49 47 46 44 43 41 0.5 15.2 0.34 83 74 68 65 63 61 58 57 54 0.6 18.3 0.41 104 92 86 82 79 76 73 72 68 0.7 21.3 0.48 126 112 104 99 95 92 89 87 82 0.8 24.4 0.55 149 132 123 117 113 109 105 103 97 0.9 27.4 0.61 173 153 143 136 130 126 121 119 113 1.0 30.5 0.68 197 175 163 155 149 144 138 135 129 2.0 61.0 1.36 469 416 387 368 354 343 329 322 306 3.0 91.4 2.05 778 691 642 612 587 569 546 535 508 4.0 122 2.73 1115 990 920 876 841 815 783 766 727 5.0 152 3.41 1474 1308 1216 1158 1112 1078 1035 1013 961 6.0 183 4.09 1851 1643 1527 1454 1397 1354 1299 1272 1207 7.0 213 4.77 1993 1852 1764 1693 1641 1576 1543 1464 8.0 244 5.45 1939 1862 1823 1730 9.0 274 6.14 10.0 305 6.82
Table 4. Rotation Rate Correlation for Water between a Typical* 12 mm Pine Research Rotating Cylinder Electrode and Smooth, Straight Pipe Flow

* These quantities assume a typical Pine Research 12 mm OD RCE tip with outer diameter 1.2 cm rotating in water at 25°C.  For pure water at 25°C, the density is 0.997 g/cmand the absolute viscosity is 0.00891 g/cm s.  Values that appear grayed out indicate this rotation rate is incompatible with the maximum or minimum rotation rates.

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