Shear stress
Shear stress (often denoted by τ, Greek: tau) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.
Further information: Shear forceMeasurement with sensors[edit]
Diverging fringe shear stress sensor[edit]
This relationship can be exploited to measure the wall shear stress. If a sensor could directly measure the gradient of the velocity profile at the wall, then multiplying by the dynamic viscosity would yield the shear stress. Such a sensor was demonstrated by A. A. Naqwi and W. C. Reynolds.[7] The interference pattern generated by sending a beam of light through two parallel slits forms a network of linearly diverging fringes that seem to originate from the plane of the two slits (see double-slit experiment). As a particle in a fluid passes through the fringes, a receiver detects the reflection of the fringe pattern. The signal can be processed, and knowing the fringe angle, the height and velocity of the particle can be extrapolated. The measured value of wall velocity gradient is independent of the fluid properties and as a result does not require calibration. Recent advancements in the micro-optic fabrication technologies have made it possible to use integrated diffractive optical element to fabricate diverging fringe shear stress sensors usable both in air and liquid.[8]
Micro-pillar shear-stress sensor[edit]
A further measurement technique is that of slender wall-mounted micro-pillars made of the flexible polymer PDMS, which bend in reaction to the applying drag forces in the vicinity of the wall. The sensor thereby belongs to the indirect measurement principles relying on the relationship between near-wall velocity gradients and the local wall-shear stress.[9][10]
Electro-diffusional method[edit]
The electro-diffusional method measures the wall shear rate in the liquid phase from microelectrode under limiting diffusion current condition. A potential difference between an anode of a broad surface (usually located far from the measuring area) and the small working electrode acting as a cathode leads to a fast redox reaction. The ion disappearance occurs only on the microprobe active surface, causing the development of the diffusion boundary layer, in which the fast electro-diffusion reaction rate is controlled only by diffusion. The resolution of the convective-diffusive equation in the near wall region of the microelectrode lead to analytical solutions relying the characteristics length of the micro-probes, the diffusional properties of the electrochemical solution and the wall shear rate.[11]