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3D Suspended Polymeric Microfluidics (SPMF^{3}) with Flow Orthogonal to Bending (FOB) for Fluid Analysis through Kinematic Viscosity

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## Abstract

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^{3}), with flow plane orthogonal to the bending plane of the structure, along with tested results of various fluids covering a wide range of engineering applications. Kinematic viscosity, also called momentum diffusivity, considers changes in both fluid intermolecular forces and molecular inertia that define dynamic viscosity and fluid density, respectively. In this study a 3D suspended polymeric microfluidic system (SPMF

^{3}) was employed to detect changes in fluid parameters such as dynamic viscosity and density during fluid processes. Using this innovative design along with theoretical and experimental results, it is shown that, in fluids, the variations of fluid density and dynamic viscosity are not easily comprehensible due to their interconnectivity. Since any change in a fluid will affect both density and dynamic viscosity, measuring both of them is necessary to identify the fluid or process status. Finally, changes in fluid properties were analyzed using simulation and experiments. The experimental results with salt-DI water solution and milk with different fat concentrations as a colloidal fluid show that kinematic viscosity is a comprehensive parameter that can identify the fluids in a unique way using the proposed microplatform.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. 3D Suspended Polymeric Microfluidics

^{3}. Following are the equations of both systems and their relation to kinematic viscosity. On substituting for $\mathrm{\Delta}P$ from Equation (5) into Equation (6), one can obtain the relation to kinematic viscosity, υ.

#### 2.2. Fabrication of the Device

## 3. Results and Discussion

^{3}using a syringe pump at a flow rate of 50 μL/min and the cantilever deflection was recorded. According to the salt-water solutions in Table 1, kinematic viscosity variations through the addition of salt could be detected by the SPMF

^{3}using tip deflection. However, both density and viscosity increased when salt was added to the DI water. As such, Table 1 summarizes the microcantilever deflections against changes with fat contents of milk. Milk viscosity increased with fat concentration while its density decreased [38].

^{−7}kg/s at ρ = 10

^{3}kg/m

^{3}, and the fluid was water. This analysis has been done using two ANSYS modules, namely CFX and Static (2017, ANSYS, Pittsburgh, PA, USA), to solve the Navier–Stockes equations of steady state fluid dynamics and structural behaviors in order to predict the resultant deflections due to applied flow forces on the microcantilever.

^{3}deflections. However, the FEA results have confirmed that the viscosity and density effects are opposite to each other.

^{3}, the theoretical prediction (Equation (7)) is compared with FEA results and shown in Figure 5c. These parameters are microchannel hydraulic diameter, (a = 133 μm), velocity difference at nozzle sides, ($\mathrm{\Delta}V$ = 0.002 m/s), microcantilever stiffness, (${k}_{m}$ = 0.035 N/m) which is calculated based on E = 700 kPa [34], mass flow rate, ($\dot{m}$ = 8.33 × 10

^{−7}kg/s), and nozzle length, (l = 300 µm). The parameters are substituted into the derived theoretical formula which can be simplified as $\upsilon =k\delta -S$ where k is the resultant cantilever stiffness. The theoretical formulation can be used to design any SPMF

^{3}for required kinematic viscosity measurements. In other words, any variation in fluid concentration cannot exactly be predicted with only density or dynamic viscosity since both are changing and each parameter has a different effect on the static behavior of suspended microfluidics. The proposed suspended microcantilever has a unique response to changes in kinematic viscosity as is shown here, thus validating the SPMF

^{3}as an appropriate tool for measuring fluid property through kinematic viscosity.

^{3}platform for kinematic viscosity measurements, the experimental results with water-salt solutions and milk, in Table 1, are compared with finite element analysis and simplified prediction formulation in Figure 6. As is shown here, there is a good agreement among the theoretical, finite element and experimental results. These results are shown in the logarithmic format in order to represent fluid properties in equally expanded regions. As is shown, kinematic viscosity can be employed for studying variation in fluid properties specifically in a more comprehensive way.

^{3}which is designed for kinematic viscosity measurement addresses the interconnectivity of density and viscosity.

## 4. Conclusions

^{3}shows different behaviors of a microcantilever against fluid density and dynamic viscosity variations. Using kinematic viscosity as a comprehensive parameter, both Newtonian and non-Newtonian fluids were studied and tested in a less complicated manner.

^{3}deflections against kinematic viscosity variations were studied.

^{3}platform shows promising results as a microsystem for kinematic viscosity measurements for Newtonian and non-Newtonian fluids, and biological and non-biological fluids in a unique way.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Capillary kinematic viscosity measurement system, (

**b**) Microfluidic system designed based on the capillary system, (

**c**) Suspended microchannel designed to transduce and measure fluid forces.

**Figure 2.**(

**a**) 2D suspended microfluidics with the flow plane parallel to the bending (neutral) plane, (

**b**) 3D suspended polymeric microfluidics with the flow plane orthogonal to the bending plane.

**Figure 3.**(

**a**) Microchannel and nozzle molds for PDMS microfabrication, (

**b**) Fabricated 3D suspended polymeric microfluidic system (

**c**) Detailed view of the SPMF

^{3}.

**Figure 5.**Finite element analysis results of microcantilever deflection when fluid density or viscosity was changed, (

**a**) against density at constant viscosity, μ = 0.89 cP, (

**b**) against viscosity at constant density, ρ = 997 kg/m

^{3}, (

**c**) finite element analysis (FEA) and theoretical results of microcantilever deflection against kinematic viscosity.

**Figure 6.**Prediction and experiment comparison of deflection behavior for various fluids; different ranges of fluids are indicated with colorful hatching and the cantilever deflection is shown with colorful dots.

**Table 1.**Changes in DI water-salt solution and milk with different fat content properties and experimental deflection results; both density and viscosity varied with salt and fat concentrations.

Fluid | Concentration | Density (kg/m^{3}) | Dynamic Viscosity (cP) | Kinematic Viscosity (cSt) | Tip Deflection (μm) |
---|---|---|---|---|---|

Water-Salt wt % | 0% | 999 | 1.002 | 1.00 | 2.51 |

10% | 1070 | 1.193 | 1.11 | 2.75 | |

15% | 1110 | 1.350 | 1.21 | 3.08 | |

Milk-Fat wt % | 0% | 1033 | 3.594 | 3.48 | 10.48 |

3.25% | 1030 | 4.192 | 4.07 | 11.90 | |

10% | 1025 | 4.797 | 4.68 | 14.85 | |

20% | 1012 | 6.598 | 6.52 | 20.80 | |

35% | 994 | 11.391 | 11.46 | 36.21 |

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**MDPI and ACS Style**

Marzban, M.; Packirisamy, M.; Dargahi, J. 3D Suspended Polymeric Microfluidics (SPMF^{3}) with Flow Orthogonal to Bending (FOB) for Fluid Analysis through Kinematic Viscosity. *Appl. Sci.* **2017**, *7*, 1048.
https://doi.org/10.3390/app7101048

**AMA Style**

Marzban M, Packirisamy M, Dargahi J. 3D Suspended Polymeric Microfluidics (SPMF^{3}) with Flow Orthogonal to Bending (FOB) for Fluid Analysis through Kinematic Viscosity. *Applied Sciences*. 2017; 7(10):1048.
https://doi.org/10.3390/app7101048

**Chicago/Turabian Style**

Marzban, Mostapha, Muthukumaran Packirisamy, and Javad Dargahi. 2017. "3D Suspended Polymeric Microfluidics (SPMF^{3}) with Flow Orthogonal to Bending (FOB) for Fluid Analysis through Kinematic Viscosity" *Applied Sciences* 7, no. 10: 1048.
https://doi.org/10.3390/app7101048