**Figure 1.**
Schematic illustration of the velocity profile in a parallel-plate system (gap height $H$, plate radius $R$); (**a**) showing wall slip (slip velocity ${u}_{S}$) with the particle-depleted area $\epsilon $; (**b**) with grooved surface to prevent wall slip.

**Figure 1.**
Schematic illustration of the velocity profile in a parallel-plate system (gap height $H$, plate radius $R$); (**a**) showing wall slip (slip velocity ${u}_{S}$) with the particle-depleted area $\epsilon $; (**b**) with grooved surface to prevent wall slip.

**Figure 2.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip.

**Figure 2.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip.

**Figure 3.**
CAD construction of the modified parallel-plate systems with pyramidal structure (**a**), columnar structure (**b**), and longwise bars (**c**).

**Figure 3.**
CAD construction of the modified parallel-plate systems with pyramidal structure (**a**), columnar structure (**b**), and longwise bars (**c**).

**Figure 4.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip, measured with columns (system 6), bars (system 12), and pyramids (system 2).

**Figure 4.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip, measured with columns (system 6), bars (system 12), and pyramids (system 2).

**Figure 5.**
Apparent viscosity of silicon oil AK 5000 as a function of shear rate using bars (system 13) at a gap height of $H=1.2\text{}\mathrm{mm}$ and reference viscosity determined with smooth plates.

**Figure 5.**
Apparent viscosity of silicon oil AK 5000 as a function of shear rate using bars (system 13) at a gap height of $H=1.2\text{}\mathrm{mm}$ and reference viscosity determined with smooth plates.

**Figure 6.**
Effective gap extension $\delta $ dependent on shear rate for AK 5000, measured with different pyramidal structures (systems 1–3).

**Figure 6.**
Effective gap extension $\delta $ dependent on shear rate for AK 5000, measured with different pyramidal structures (systems 1–3).

**Figure 7.**
Uncorrected, corrected, and reference viscosity from silicon oil AK 5000, measured with pyramids (system 2).

**Figure 7.**
Uncorrected, corrected, and reference viscosity from silicon oil AK 5000, measured with pyramids (system 2).

**Figure 8.**
Correction function for the silicon oils AK 5000 and AK 12,500, measured with pyramids (systems 2) and columns (system 6).

**Figure 8.**
Correction function for the silicon oils AK 5000 and AK 12,500, measured with pyramids (systems 2) and columns (system 6).

**Figure 9.**
Uncorrected, corrected, and mean correction functions of AK 5000 viscosities, measured with pyramids (system 2).

**Figure 9.**
Uncorrected, corrected, and mean correction functions of AK 5000 viscosities, measured with pyramids (system 2).

**Figure 10.**
Effective gap extension $\delta $ (gap- and material-averaged) dependent on structure depth, measured with pyramidal structure (system 1–4), columnar structure (systems 5, 8, 10, 11) and bars (system 12–15) for $\dot{\gamma}=5{\text{}\mathrm{s}}^{-1}$.

**Figure 10.**
Effective gap extension $\delta $ (gap- and material-averaged) dependent on structure depth, measured with pyramidal structure (system 1–4), columnar structure (systems 5, 8, 10, 11) and bars (system 12–15) for $\dot{\gamma}=5{\text{}\mathrm{s}}^{-1}$.

**Figure 11.**
Effective gap extension $\mathsf{\delta}$ (gap- and material-averaged) dependent on column distance (**a**) (systems 6–9, $L=0.5\mathrm{mm}$) and number of bars (**b**) (systems 15–18, $L=1.0\mathrm{mm}$) for $\dot{\gamma}=5{\text{}\mathrm{s}}^{-1}$.

**Figure 11.**
Effective gap extension $\mathsf{\delta}$ (gap- and material-averaged) dependent on column distance (**a**) (systems 6–9, $L=0.5\mathrm{mm}$) and number of bars (**b**) (systems 15–18, $L=1.0\mathrm{mm}$) for $\dot{\gamma}=5{\text{}\mathrm{s}}^{-1}$.

**Figure 12.**
Comparison between normalised viscosities of xanthan gum solution and silicon oils dependent on gap height, measured with pyramids (system 2, $L=0.5\mathrm{mm}$), columns (system 6, $L=0.5\mathrm{mm}$), and bars (system 12, $L=0.3\mathrm{mm})$ at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 12.**
Comparison between normalised viscosities of xanthan gum solution and silicon oils dependent on gap height, measured with pyramids (system 2, $L=0.5\mathrm{mm}$), columns (system 6, $L=0.5\mathrm{mm}$), and bars (system 12, $L=0.3\mathrm{mm})$ at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 13.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip, measured with pyramids (system 2) at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 13.**
Comparison between apparent shear rate ${\dot{\mathsf{\gamma}}}_{\mathrm{a}}$ and true shear rate $\dot{\mathsf{\gamma}}$ in the velocity profile between two parallel plates showing wall slip, measured with pyramids (system 2) at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 14.**
Comparison between viscosity values of $1\mathrm{wt}.\text{}\%$ xanthan gum solution obtained for columns (system 6) and reference system at $H=1\mathrm{mm}$.

**Figure 14.**
Comparison between viscosity values of $1\mathrm{wt}.\text{}\%$ xanthan gum solution obtained for columns (system 6) and reference system at $H=1\mathrm{mm}$.

**Figure 15.**
Effective gap extension $\delta $ (gap- and material-averaged) dependent on the shear rate of $1\text{}\mathrm{wt}.\text{}\%$ xanthan gum solution obtained for columns (system 6, $H=1\text{}\mathrm{mm}$).

**Figure 15.**
Effective gap extension $\delta $ (gap- and material-averaged) dependent on the shear rate of $1\text{}\mathrm{wt}.\text{}\%$ xanthan gum solution obtained for columns (system 6, $H=1\text{}\mathrm{mm}$).

**Figure 16.**
Correction of viscosity values obtained for columns (system 6) at $H=1.4\text{}\mathrm{mm}$ and $H=1.0\text{}\mathrm{mm}$.

**Figure 16.**
Correction of viscosity values obtained for columns (system 6) at $H=1.4\text{}\mathrm{mm}$ and $H=1.0\text{}\mathrm{mm}$.

**Figure 17.**
Influence of structure depth $L$ on $\delta $ measured at $\dot{\mathsf{\gamma}}=5.05\text{}1/\mathrm{s}$.

**Figure 17.**
Influence of structure depth $L$ on $\delta $ measured at $\dot{\mathsf{\gamma}}=5.05\text{}1/\mathrm{s}$.

**Figure 18.**
Influence of number of bars (systems 15, 17, and 18) on $\delta $, measured at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 18.**
Influence of number of bars (systems 15, 17, and 18) on $\delta $, measured at $\dot{\gamma}=5.05\text{}1/\mathrm{s}$.

**Figure 19.**
Normalised viscosities of silicon oils and $25\text{}\mathrm{wt}.\text{}\%$ suspension dependent on the measuring gap, measured with columns (system 2), bars (system 6), and pyramids (system 9) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Figure 19.**
Normalised viscosities of silicon oils and $25\text{}\mathrm{wt}.\text{}\%$ suspension dependent on the measuring gap, measured with columns (system 2), bars (system 6), and pyramids (system 9) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Figure 20.**
Normalised viscosities of suspensions for different concentrations, measured with pyramidal structure (system 1) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Figure 20.**
Normalised viscosities of suspensions for different concentrations, measured with pyramidal structure (system 1) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Figure 21.**
Flow curves of silicon oil AK 5000, $1\text{}\mathrm{wt}.\text{}\%$ xanthan gum solution, and $25\text{}\mathrm{wt}.\text{}\%$ suspension, measured with reference system.

**Figure 21.**
Flow curves of silicon oil AK 5000, $1\text{}\mathrm{wt}.\text{}\%$ xanthan gum solution, and $25\text{}\mathrm{wt}.\text{}\%$ suspension, measured with reference system.

**Figure 22.**
Uncorrected, corrected, and reference viscosities of $25\text{}\mathrm{wt}.\text{}\%$ suspension, measured with columns (system 5).

**Figure 22.**
Uncorrected, corrected, and reference viscosities of $25\text{}\mathrm{wt}.\text{}\%$ suspension, measured with columns (system 5).

**Figure 23.**
Flow curves of suspensions containing different particle volume fractions ϕ.

**Figure 23.**
Flow curves of suspensions containing different particle volume fractions ϕ.

**Table 1.**
Geometric dimensions of the pyramidal structure, $R=12.5\mathrm{mm}$.

**Table 1.**
Geometric dimensions of the pyramidal structure, $R=12.5\mathrm{mm}$.

Measuring System No. | $\mathbf{Structure}\text{}\mathbf{Depth}\text{}\left(\mathbf{Pyramid}\text{}\mathbf{Height}\right)\text{}\mathit{L}/\mathbf{mm}$ | $\mathbf{Side}\text{}\mathbf{Length}\text{}\mathbf{of}\text{}\mathbf{Base}\text{}\mathbf{Area}\text{}\mathit{b}/\mathbf{mm}$ |
---|

$1$ | 0.3 | 0.6 |

$2$ | 0.5 | 1.0 |

$3$ | 0.7 | 1.4 |

$4$ | 1.0 | 2.0 |

**Table 2.**
Geometric dimensions of the columnar structure, $R=12.5\mathrm{mm}$.

**Table 2.**
Geometric dimensions of the columnar structure, $R=12.5\mathrm{mm}$.

Measuring System No. | $\mathbf{Structure}\text{}\mathbf{Depth}\text{}\left(\mathbf{Column}\text{}\mathbf{Height}\right)\text{}\mathit{L}/\mathbf{mm}$ | $\mathbf{Distance}\text{}\mathbf{Between}\text{}\mathbf{Columns}\text{}\mathit{a}/\mathbf{mm}$ |
---|

5 | 0.1 | 1.0 |

6 | 0.5 | 0.5 |

7 | 0.5 | 0.8 |

8 | 0.5 | 1.0 |

9 | 0.5 | 1.2 |

10 | 0.7 | 1.0 |

11 | 1.0 | 1.0 |

**Table 3.**
Geometric dimensions of the bars, $R=15\mathrm{mm}$.

**Table 3.**
Geometric dimensions of the bars, $R=15\mathrm{mm}$.

Measuring System No. | $\mathbf{Structure}\text{}\mathbf{Depth}\text{}\left(\mathbf{Bar}\text{}\mathbf{Height}\right)\text{}\mathit{L}/\mathbf{mm}$ | $\mathbf{Number}\text{}\mathbf{of}\text{}\mathbf{Bars}\text{}\mathit{N}/-$ |
---|

12 | 0.3 | 20 |

13 | 0.5 | 20 |

14 | 0.7 | 20 |

15 | 1.0 | 20 |

16 | 1.0 | 19 |

17 | 1.0 | 18 |

18 | 1.0 | 16 |

**Table 4.**
Values for $\delta $ for different measuring systems at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Table 4.**
Values for $\delta $ for different measuring systems at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

Measuring System | $\mathbf{Effective}\text{}\mathbf{Gap}\text{}\mathbf{Extension}\text{}\mathit{\delta}/\mathbf{mm}$ |
---|

Silicon Oil AK 5000 | Silicon Oil AK 12,500 | $25\mathbf{wt}.\mathit{\%}\text{}\mathbf{Suspension}$ (AK 5000) |
---|

1 (pyramids) | $0.23\pm 0.006$ | $0.25\pm 0.004$ | $0.22\pm 0.011$ |

4 (pyramids) | $0.91\pm 0.040$ | $0.83\pm 0.032$ | $0.86\pm 0.071$ |

5 (pyramids) | $0.44\pm 0.023$ | $0.49\pm 0.016$ | $0.48\pm 0.029$ |

8 (columns) | $0.20\pm 0.003$ | $0.22\pm 0.009$ | $0.19\pm 0.014$ |

12 (bars) | $0.35\pm 0.009$ | $0.37\pm 0.004$ | $0.35\pm 0.009$ |

17 (bars) | $0.73\pm 0.068$ | $0.71\pm 0.072$ | $0.70\pm 0.089$ |

**Table 5.**
Values for $\mathsf{\delta}$ for suspensions of different concentrations, measured with pyramidal structure (system 1) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

**Table 5.**
Values for $\mathsf{\delta}$ for suspensions of different concentrations, measured with pyramidal structure (system 1) at $\dot{\gamma}=5.05{\text{}\mathrm{s}}^{-1}$.

AK 5000 | AK 12,500 | $5\mathbf{wt}.\mathbf{\%}$ | $25\mathbf{wt}.\%$ | $35\mathbf{wt}.\%$ |
---|

$0.23\pm 0.006$ | $0.25\pm 0.004$ | $0.23\pm 0.007$ | $0.22\pm 0.011$ | $0.22\pm 0.015$ |