Inverse Method Used for the Determination of the Wall Shear Stress in a Sliding Rheometer Using Sandwich Probes

The inverse method, based on a numerical sequential estimation, has been applied for the determination of the wall shear stress of a liquid single phase flow in a sliding rheometer using multi-segment probe. This method requires the inversion of the convection diffusion equation in order to apply it to instantaneous mass transfer measurements. Polarography technique, known as the limiting diffusion current method, has been used. This requires the use of Electro-Diffusion ED probe which allows the determination of the local mass transfer rate for known flow kinematics. In addition, two-segment platinum probe was mounted flush to the inert surface of the upper disk of the sliding rheometer. Hydrodynamic oscillations have been imposed to the torsional flow (type sinusoidal), in order to study the frequency response of the sandwich probe for a fixed polarization voltage. Possible error sources which are likely to affect the interpretation of the results e.g. the directional angle effect, the inertial effect, the diffusion effect and the frequencies of oscillations effect have been studied in order to test the robustness of the inverse method within the presence of such impacts. Furthermore, to demonstrate the possible effect of non-negligible inertia and diffusion, we refer to ED results for both modified Reynolds number defined by [1] and Peclet number ranges as well as for different directional angles. An algorithm has been developed for the numerically filtering of the mass transfer signals, and therefore the wall shear stress signals. It permits to eliminate any possible noise effect due to the imposed vibrations to the torsional flow. The analysis shown that the inverse method is in a good agreement with the ED experimental results for the different cases of study, i.e. for different dimensionless Reynolds numbers, for high and low oscillation frequencies, as well as for different directional angles. The little difference is probably caused by the sensitivity of the double probe to such directional angles or to the neglecting of the insulating gap effect on the inverse method solution as a first step of the study of the inverse method for double probes signals.