## 3 Results and Discussion
The analysed area was 100 \(\upmu\)m long in the radial direction and started 20 \(\upmu\)m from the wall to avoid the effect of the wall depletion layer on the results. The uneven OCT amplitude profile (see Figure 3) was eliminated from the images by scaling individual amplitude A-scans with an averaged A-scan amplitude profile. This correction removes all stationary intensity variations from original A-scans, and the remaining intensity variations are due to temporal differences in the local suspension properties (see Figure 5). A dominant factor causing most of these variations is the local concentration of the suspension. Due to different flow rates and scanning frequencies, the size of the analysed area varied in axial flow direction between 60 \(\upmu\)m and 1.1 mm (pixel sizes in the axial flow direction thus varied between 0.06 \(\upmu\)m and 1.1 \(\upmu\)m). In order to make the analysis of different flow rates and their axial and radial floc sizes commensurate, all images were resized to the pixel size of 1.1 \(\upmu\)m, using MATLAB's (ver. 9.1.0.441655 R2016b, MathWorks, Natick, MA, USA) intresize routine, which performs a bicubic interpolation. The floc size analysis was performed using the method presented in [8]. The OCT structural images were thresholded separately using the median of intensity. The (length-weighted) distribution of floc dimensions, in both radial and axial directions, was then computed for every image in the sequence as the run-length distributions (see Figure 6). The floc size distributions  
Figure 4: Viscosity as a function of shear stress. The viscosities have been calculated with Equation (2). The dashed and solid lines show fits of the power law \(\mu=A\tau^{\frac{h}{2}}\) to the two sets of the pipe flow data. The dash-dotted line shows the yield stress \(\tau_{y}=3.4\) Pa of the MFC. were log-normal, which are typical for fibers [32; 33] and many other flocculating particles [34; 35]. Determined distributions were finally averaged to obtain the length weighted average floc sizes. Figure 7 shows the axial and radial floc size as a function of wall shear stress. Both floc sizes are seen to remain approximately constant below the yield stress of \(\tau_{y}\) = 3.4 Pa. Above the yield stress, the both floc sizes decrease monotonically and become approximately equal at the highest wall shear stress of 15.2 Pa. Furthermore, the radial and axial floc size distributions are almost identical at the  
Figure 5: Intensity-corrected structural OCT images composed of successive A-scans of the suspension with the wall shear stress and scan count of (**a**) 3.8 Pa, 1000, and (**b**) 11.2 Pa, 430, respectively. Bright color indicates high and dark color low MFC consistency. Image size is 120 \(\upmu\)m \(\times\) 290 \(\upmu\)m. The pipe wall is on the top of the image and the flow direction is from left to right. The arrows show the axial and radial directions. Figure 6: (**a**) Radial and (**b**) axial floc size distributions calculated with the run-length method [8]. Both axial and radial floc sizes decrease with an increasing wall shear stress. highest wall shear stress (see Figure 6). The above observations indicate that the suspension is finally well fluidized. There appears to be an abrupt drop (see the arrow in Figure 7) in both radial and axial floc sizes at \(\tau_{w}\) = 10 Pa, after which the floc size remains almost constant up to \(\tau_{w}\) = 12 Pa. This sudden structural change coincides with the sudden drop in the viscosity of the suspension (see Figure 4). The number of data points is, however, rather limited, and additional experiments are needed to verify this interesting behavior. Figure 8 shows the floc aspect ratio \(\alpha\) (axial size/radial size) as the function of the wall shear stress. We see from Figure 8 that the floc aspect ratio \(\alpha\) varies a lot with the smallest wall shear rates, but it appears to stay approximately constant, \(\alpha\) = 1.6, at least until wall shear stress of 6 Pa.