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A revisit of the electro-diffusional theory for the wall shear stress measurement

The Department of Multiphase Reactors has been working with the measurement of shear stresses on the wall for a long time, typically using a non-invasion electrodiffusion method. Although this primarily constitutes basic research, the results of measurements using this method allow a description of the system’s hydrodynamic behavior near solid surfaces. To interpret the obtained data, it is necessary to use the correct theory capable of connecting the measured electric current with the desired result in the form of the shear rate vector magnitude. The article by Associate Professor Jaromír Havlica deals with the generalization of the classical Lévêque’s theory, commonly used to interpret data obtained using the electrodiffusion method. It was published in the prestigious chemical engineering journal International Journal of Heat and Mass Transfer (Impact Factor = 4.947). The publication was published in collaboration with scientists from the Jan Evangelista Purkyně University in Ústí nad Labem and Gustav Eiffel University in France.

This work aimed to generalize the electrodiffusion theory for measuring the shear stress on the wall using rectangular electrodes. The given generalization of the theory consisted of introducing the assumption of two components of the shear flow velocity near the wall (i.e., axial and transverse). The general analytical formulas for the effective mass transfer length and the dimensionless mass transfer coefficient were derived as a function of two parameters: the dimensionless angle of the liquid flow direction concerning the leading edge of the electrode and the aspect ratio of the rectangular electrode. A numerical solution convection-diffusion transport equation confirmed the accuracy of analytical relations for any flow direction and electrode aspect ratio. It has also been shown that differences between Lévêque’s solution (classical theory) and our general analytical formula can show a significant deviation for a certain range of parameters. In the case of three-dimensional boundary layers, in addition to the magnitude of the shear stress on the wall, the direction of fluid flow near the wall is crucial. Therefore, a measurement methodology was proposed using two probes with different aspect ratios, based on which both of these quantities can be obtained. The resulting equations needed to quantify the shear rate vector’s magnitude on the wall and the dimensionless fluid flow angle were also derived.



Figure: Generalized Lévêque’s solution for calculating the dimensionless mass transfer coefficient on a rectangular electrode as a function of the dimensionless angle of the liquid flow direction and the aspect ratio.

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