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Diagnostics of the fluctuating wall shear rate components using an uncalibrated three-segment electrodiffusion sensor


An inverse problem is used to significantly improve the frequency response of a three-segment electrodiffusion (ED) sensor subjected to strong inertial effects in high-amplitude unsteady flows. It is shown that the fluctuating component of the wall shear rate’s magnitude and direction can be accurately determined when both variables exhibit simultaneous large-amplitude variations, even when using an uncalibrated probe. Measurements are performed in the vicinity of a rotating cylinder in motion in a highly viscous fluid with poor electrochemical diffusivity, thus establishing a harsh environment for an ED sensor. Results using the inverse problem showed strong concordance with PIV complementary measurements in most cases and further expose the potential of this non-intrusive technique for thorough wall shear stress diagnostics.

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  1. One can show that \(k^*=\sum {\textit{Sh}}^*_{\text {num},\,m}\) when \({\textit{Pe}}\rightarrow \infty\), but \(k^*\) can vary when dealing with experimental signals (cf. Sect. 2.2).

  2. While no simulation was performed for the OC motion, one can expect similar conclusions as velocities and frequencies are comparable, except for case OC2.

  3. Especially on A, as the active area of a probe can be altered during measurements by probe poisoning (Sobolík et al. 1998; Bard and Faulkner 2001).

  4. Based on errors of \(\sim 2\%\) and \(\sim 3\%\) on A and D, respectively (cf. Sect. 2.1).

  5. Such a motion could be achieved by disabling smoothing parameters in the motor drive.


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The authors would like to acknowledge the financial support of the Canadian Foundation for Innovation (CFI), the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de recherche du Québec—Nature et technologies (FRQNT). We also acknowledge the technical support of T. Lafrance from MËKANIC and J.-M. Béland for their cooperation in the design and fabrication of the experimental setup and the reviewers for valuable recommendations in the revision process.

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Lamarche-Gagnon, MÉ., Sobolík, V. & Vétel, J. Diagnostics of the fluctuating wall shear rate components using an uncalibrated three-segment electrodiffusion sensor. Exp Fluids 59, 168 (2018).

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