Figure 1.(a,b) Scanning-Electron Microscope (SEM) images of single pillars and (c) image of a pillar array. (d) Mechanical model of the pillar sensor.As a consequence of the limited region, in which the linear relation between near-wall velocity gradient and wall-shear stress applies, the sensor length Lp is forced to be completely immersed within the viscous sublayer of the flow. Experimental and numerical results [12, 13] indicate that the velocity profile in the vicinity of the wall can be assumed linear up to y+ = 5��6, where y+ = y��/u�� is the non-dimensional wall-distance in viscous units with �� as the kinematic viscosity of the fluid and u�� as the friction velocity. The kinematic viscosity of water is approximately 10?6m2/s, that of air 1.5 �� 10?5m2/s.

The friction velocity can be expressed as a function of bulk Reynolds number and thereby depends on the large-scale geometry of the flow field and the bulk velocity. Typical pillar lengths of sensors applied in the past measurements range in the order of 150��700 ��m. In liquid medium flow facilities with typical bulk-scale dimensions of 10?2��10?1m and typical values of the friction velocity in the order of 10?2m/s this allows the assessment of wall-shear stress at Reynolds numbers up to Reb = 104��105. In boundary layer facilities with air such as that described in [14, 15] with typical dimensions of 100m measurements at Reynolds numbers up to Re�� = 103��104 could be performed with the aforementioned pillar length. Note that the size Lp = 5 l+ should be considered already an upper limit to the possible pillar length.

Due to the integration of the flow field along the pillar length it would be desirable to protrude as little as possible GSK-3 into the viscous sublayer. However, it goes without saying, that a shorter sensor structure also influences the sensor sensitivity and its static response.The question how far the near-wall velocity field can be considered an adequate representative of the local mean and fluctuating wall-shear stress has been discussed in great detail in [2, 7]. Some further discussion can be found in section 6.1. of this paper. The authors concluded that the measurement of mean wall-shear stress and of its intensity by determining the velocity gradient in the vicinity of the wall is generally possible. That is, the mean velocity and the intensity of velocity fluctuations within the viscous sublayer can be assumed constant enough such that the corresponding wall-shear stress properties can be deduced from the integrative quantity measured by the micro-pillar shear-stress sensor.