# Optimizing Sensitivity in a Fluid-Structure Interaction-Based Microfluidic Viscometer: A Multiphysics Simulation Study

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## Abstract

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## 1. Introduction

## 2. Device Design

## 3. Materials and Methods

#### 3.1. Multiphysics Modelling

#### 3.2. Simulation Parameters

## 4. Results and Discussion

#### 4.1. Pillar Aspect Ratio ($AR$)

#### 4.2. Gap between the Pillar Tip and Channel Ceiling ($g$)

#### 4.3. Channel Width ($CW$)

#### 4.4. Pillar Spacing ($d$)

#### 4.5. Young’s Modulus ($E$)

## 5. Conclusions

- Aspect Ratio Enhancement: Our study demonstrated a substantial increase in sensitivity with aspect ratio. Consider employing micropillars with aspect ratios of 4:1 or higher, as these configurations exhibited notable sensitivity gains.
- Optimal gap between the micropillar tip and the channel ceiling: Maintaining a gap-to-pillar height ratio within $g/H=0.125\u20130.166$ not only maximizes sensitivity, but also ensures an accommodating gap size for facile and consistent device fabrication.
- Young’s modulus: While a low Young’s modulus enhances sensitivity, it is essential to consider the structural integrity of the micropillars and potential fabrication challenges when dealing with excessively low values.
- Channel Width Reduction: Decreasing the channel width enhances the sensitivity of the viscometer. Narrowing the cross-sectional area of the microchannel intensifies fluid-micropillar interactions.
- Pillar Spacing Expansion: Increasing the space between micropillars mitigates the shielding effect, fostering stronger fluid-micropillar interactions. Our investigation revealed a consistent sensitivity enhancement with increased pillar spacing.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geometric design parameters utilized in the FSI-based microfluidic viscometer. $D$: pillar diameter, $H$: pillar height, $g$: gap between micropillar tip and channel ceiling, $d$: pillar spacing, $CW$: channel width, $CH$: channel height.

**Figure 2.**The impact of aspect ratio on FSI-based microfluidic viscometer sensitivity: (

**a**–

**c**) Micropillar displacement as a function of fluid viscosity at various flow rates for three different micropillar aspect ratios. (

**d**) Sensitivity ($s$) of the viscometer as a function of aspect ratio. The sensitivity of the viscometer increases with aspect ratio.

**Figure 3.**The impact of gap ($g$) between the micropillar tip and channel ceiling on FSI-based microfluidic viscometer sensitivity. The sensitivity ($s$) of the viscometer as a function of the normalized gap ($g/H)$ for three different micropillar aspect ratios: (

**a**) $AR=3:1$, (

**b**) $AR=4:1$, and (

**c**) $AR=5:1$. The sensitivity reaches a maximum at normalized gap values of $g/H=0.1667$, $g/H=0.125$, and $g/H=0.1333$ for $AR=3:1$, $AR=4:1$, and $AR=5:1$, respectively. Flow rates (${Q}_{1}-{Q}_{7})$ are provided in Figures S3–S5.

**Figure 4.**The impact of channel width ($CW$) on FSI-based microfluidic viscometer sensitivity: (

**a**–

**c**) The sensitivity ($s$) of the viscometer as a function of the channel width ($CW)$ for three different micropillar aspect ratios. The sensitivity increases with decreasing channel width for all aspect ratios. Flow rates (${Q}_{1}-{Q}_{7})$ are provided in Figures S6–S8.

**Figure 5.**The impact of pillar spacing ($d$) on FSI-based microfluidic viscometer sensitivity. The sensitivity ($s$) of the viscometer as a function of the pillar spacing ($d)$ for flow rates between 15 and 105 mL/h. The sensitivity moderately increases with pillar spacing.

**Figure 6.**The impact of Young’s modulus ($E$) on FSI-based microfluidic viscometer sensitivity. The sensitivity ($s$) of the viscometer as a function of the Young’s modulus ($E)$ for flow rates between 15 and 105 mL/h. The sensitivity decreases with Young’s modulus.

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**MDPI and ACS Style**

Mustafa, A.; Ertas Uslu, M.; Tanyeri, M.
Optimizing Sensitivity in a Fluid-Structure Interaction-Based Microfluidic Viscometer: A Multiphysics Simulation Study. *Sensors* **2023**, *23*, 9265.
https://doi.org/10.3390/s23229265

**AMA Style**

Mustafa A, Ertas Uslu M, Tanyeri M.
Optimizing Sensitivity in a Fluid-Structure Interaction-Based Microfluidic Viscometer: A Multiphysics Simulation Study. *Sensors*. 2023; 23(22):9265.
https://doi.org/10.3390/s23229265

**Chicago/Turabian Style**

Mustafa, Adil, Merve Ertas Uslu, and Melikhan Tanyeri.
2023. "Optimizing Sensitivity in a Fluid-Structure Interaction-Based Microfluidic Viscometer: A Multiphysics Simulation Study" *Sensors* 23, no. 22: 9265.
https://doi.org/10.3390/s23229265