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Reduction of Microfluidic Logical Pneumatic Mono Stable-Oscillators’ Reversible Outlet Flow

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29 January 2025

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30 January 2025

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Abstract
Microsystems have been developed for a wide range of applications, including medical, military, and industrial maintenance, driven by advancements in actuating and measuring systems. Fluidic actuators, known for their compactness, low cost, and energy efficiency, are increasingly recognized for their potential in cutting-edge industrial and medical microsystems. This study explores the transition from traditional actuators to innovative mono-stable oscillators designed specifically for flow regulation. Mono-stable oscillators have long been acknowledged as effective tools for controlling fluidic logic. These devices provide a control solution without movable components, though they exhibit non-zero reverse output flow—a limitation consistently observed in prior research. Passive solutions, such as Tesla diodes or convergent-divergent conduits, have proven insufficient to address this issue. In this work, we propose a novel approach to eliminate reverse flow by introducing a moving object within the outlet oscillator. Through simulation, we demonstrate that this method effectively mitigates recirculation, offering a significant improvement over existing designs. This study provides a promising solution to enhance the performance of fluidic actuators in microfluidic systems.
Keywords: 
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1. Introduction

Microfluidic technologies have experienced significant growth and development in recent years, emerging as one of the most rapidly advancing fields in scientific research. Among these technologies, microactuators have garnered considerable attention due to their critical role in regulating and manipulating various processes. The development of microactuators dates back to the late 1970s, and since then, there have been substantial advancements in the field of Micro-Electro-Mechanical Systems (MEMS) actuators, particularly in terms of efficiency, power, and force output. These advancements have made microactuators indispensable in emerging industrial and medical applications, where compact, cost-effective, and high-performance devices are increasingly sought after [1].
Fluidic microactuators, which utilize pressurized fluids—either gases (pneumatic) or liquids (hydraulic)—to induce motion through the deformation of inflatable chambers, have demonstrated exceptional power and force densities at the microscale [2]. Their notable durability and resistance to environmental factors further enhance their appeal. Despite these advantages, fluidic microactuators often receive less attention compared to other MEMS technologies, leaving significant potential for further exploration and innovation.
This study focuses on fluidic actuators, with particular emphasis on their operational principles, classifications, and characteristics. Fluidic actuators enable fluid motion through two primary mechanisms: (1) direct peristaltic motion induced by actuated solid membranes, or (2) indirect motion driven by hydrodynamic or osmotic effects. These mechanisms facilitate rotational, translational, and deflection motions, making fluidic actuators versatile tools for a wide range of applications.
One notable category of fluidic actuators is the amplifier fluidic actuator, which operates based on the Coanda effect. This effect ensures the attachment of the main jet from the supply flow to the wall, producing an output flow at the device's end. By altering the control flow or pressure, the main jet can be redirected to another output, achieving stable functionality. However, the process of jet attachment and switching is complex and has been the subject of extensive research [4,5]. These fluidic elements perform functions analogous to electronic systems, offering unique advantages in microfluidic applications.
Despite their potential, fluidic actuators face challenges, particularly in controlling reversible outlet flow in mono-stable oscillators. This study addresses this issue by proposing a novel approach to reduce reversible outlet flow, thereby enhancing the performance and reliability of microfluidic systems. The general design for a fluidic element from this category is presented in Figure 1
This overview primarily examines fluidic actuators, with a particular emphasis on their operational principles, classifications (see Table 1), and distinguishing features.

2. Simulation of Fluidic Actuation with Mobile Object

The increasing demand for microsystems in medical and military applications has driven the development of advanced actuation systems. In this study, we simulate mono-stable fluidic systems incorporating mobile components to manipulate the shape and output chamber of the moving object, thereby optimizing actuator performance.
Description of the Geometrical Model (Combination of Oscillator and Actuator)
A fluidic actuator measuring 5 × 15 mm² was designed for numerical simulation using FLUENT. The actuator features a moving part with two inlets and one outlet. To evaluate the system's behavior and optimize performance, the moving part was modeled in three distinct shapes: sphere, square, and H-shaped, each with dimensions of 4.8 mm.
The simulation process involved the following steps:
1-Geometrical Modeling: The actuator and oscillator were combined into a single model.
2-Mesh Generation: A triangular mesh was created, consisting of 166,782 nodes, to ensure accurate simulation results.
3-Dynamic Mesh Model: A dynamic mesh model was employed to track the movement of the mobile object under fluid forces.
4-The geometry of the actuator was modified to ensure convergence at the two inlets, aligning with the oscillator's outlet dimensions. This configuration is illustrated in Figure 2
The second part of this study constitutes its core contribution. It involves the integration of the ball actuator with the fluidic oscillator to enhance the oscillator's performance by minimizing reverse fluid flow through the right and left outlet holes, as well as the oscillator itself. To achieve this, the actuator's geometry was modified to ensure convergence at the two inlets, aligning it with the oscillator's outlet dimensions. This modified geometry is illustrated in Figure 3
To accommodate the new geometry, several modifications were made to the mesh. The primary objective was to achieve a mesh with a low maximum aspect ratio and minimal asymmetry. The final mesh used in the FLUENT simulations, presented in Figure 4, consists of a triangular structure comprising 166,782 nodes. To ensure optimal balance between result accuracy and computational efficiency, additional meshes with varying densities (41,000 nodes and 442,986 nodes) were also generated and evaluated.
As the moving part (the sphere) shifts in response to fluid forces acting on its boundaries, the mesh boundaries must adapt accordingly. To address this, a dynamic mesh model was employed. The dynamic mesh capabilities of FLUENT, combined with a user-defined function, were utilized to accurately track the movement of the sphere throughout the simulation.

3. Simulation Results

The mass flow rate at the exit of the actuator, corresponding to the geometry of case (b), is depicted in Figure 5. This figure illustrates the mass flow rate under a pressure variation of P = 3 bar during both the forward and return motion of the spherical mobile object Figure 6..
Mobile Forward phase
Mobile return phase

3.1. Evolution of Mass Flow at the Left and Right Outputs of the Oscillator-Actuator Combination

Figure 7 depicts the mass flow rate as a function of time at the actuator's output under applied pressures of 2 bar and 2.5 bar, respectively. The results indicate that the return flow at both the left and right outputs of the oscillator is nearly negligible.

3.2. Evolution of Mobile Velocity

Figure 8 illustrates the axial velocity profiles of the sphere's motion for supply pressures of P=1.5 bar and P=2 bar at the oscillator inlet. The profiles exhibit a distinct sawtooth pattern, with the velocity reaching a peak of 10 m/s at a pressure of 2 bar.

3.3. Trend Curve

The fluid oscillator frequency at the millimeter scale was simulated using CFD. The initial numerical results indicate that the fluid oscillator frequency increases with an increasing ΔP/P ratio, within a pressure range of 1.5 to 3 bars Figure 9.

5. Conclusions

The performance and compactness of microfluidic actuators have been significantly enhanced through the implementation of various mechanisms and innovative combinations. High-performance actuators, characterized by their elevated force and power density alongside minimal power consumption, are in great demand for a wide range of applications, including minimally invasive surgical procedures and micro-robotic systems.
Numerical simulations have been conducted to assess the efficiency of these microactuators, with particular attention given to the internal channel length scale and the diameter of the digital flow. However, accurately modeling the complexity of the diode geometry remains challenging due to the involvement of high-pressure conditions.
This study has proven to be instrumental in addressing several challenges faced by our team. Notably, it has provided effective solutions to the backflow issues encountered with mini-injectors, as reported in previous works in literature.

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Figure 1. geometrical form of micro actuators.
Figure 1. geometrical form of micro actuators.
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Figure 2. Geometrical form and meshing prototype.
Figure 2. Geometrical form and meshing prototype.
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Figure 3. The geometry representing the combination of the actuator and the oscillator.
Figure 3. The geometry representing the combination of the actuator and the oscillator.
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Figure 4. The mesh used for the simulations of geometry in Fluent.
Figure 4. The mesh used for the simulations of geometry in Fluent.
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Figure 5. Mass flow rate signal as a function of time (s) at the output and for a ΔP = 3 bar at the output of the actuator for the circular-shaped mobile.
Figure 5. Mass flow rate signal as a function of time (s) at the output and for a ΔP = 3 bar at the output of the actuator for the circular-shaped mobile.
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Figure 6. Contour plots of the velocity Position of the ball at different times.
Figure 6. Contour plots of the velocity Position of the ball at different times.
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Figure 7. Mass Flow Rate Signal as a Function of Time at the Right and Left Outlets for the Oscillator-Actuator Combination Subjected to Pressures of 2 Bars and 2.5 Bars.
Figure 7. Mass Flow Rate Signal as a Function of Time at the Right and Left Outlets for the Oscillator-Actuator Combination Subjected to Pressures of 2 Bars and 2.5 Bars.
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Figure 8. Axial Velocity Profile as a Function of Time for Pressures P=1.5 barP = 1.5 \, \text{bar}.
Figure 9. Trend Curve Representing the Oscillation Frequency as a Function of the (ΔP/P).
Figure 9. Trend Curve Representing the Oscillation Frequency as a Function of the (ΔP/P).
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Table 1. Relevant work on micro actuators.
Table 1. Relevant work on micro actuators.
reference First Author Year Actuation
Type
Size L*w*h
(in µm)
Operating
Conditions
[36] Chi S.P. 1997 Electro thermal 1000*700*3 15V    2,8µN
[37] Neils T. 1998 Electrostatic 200*100*0,5 40V
[38] Just E. 1999 SMA 2000*3900*100 22mW    17mN
[39] Bhailis D. 2000 Electromagnetic 5000*5000*2000 1A     15mN
[05] Volland B.E. 2001 Electrostatic 3300*1250*5 80V   170µm Ø
[40] Fuller, S.B. 2002 Electro thermal / 300 °C     5V
[41] Abadie J. 2002 SMA 3000*800*200 0,8A       68°
[25] Bordatchev E.V. 2003 Electro thermal 2800*1400*12,5 1,9V
[42] Olivier. M 2004 Electrostatic 1200*800*10 75V
[43] Yang J. 2004 Piezoelectric 1200*320*1,5 15V   16,67kHz
[44] Vitorio. A 2004 Electrostatic / 400V
[33] Zhang H. 2004 SMA 4000*3000*290 1A      81µm Ø
[45] Ahn 2004 Electromagnetic 3500*3500 20mA     920Hz
[46] Fu 2004 SMA 2200*2200 5V       30mA
[02] D.Piyabongkarn 2005 Electrostatic 3200*3000*50 10V
[29] C.T. Pan 2005 Electromagnetic 1000*1000*10 5V       17,5°
[31] D.H. Kim 2005 Electromagnetic 15500*5220*500 8V       18mN
[47] Mitsui 2006 Electromagnetic 7400*9800 4.6mA   80,5Hz
[13] S.K.Nah 2007 Piezoelectric 36000*30000*3 0-100V
[06] Felix. B 2007 Electrostatic 7700*5600*50 150V  100µm Ø
[48] Liu X. 2007 Electrostatic 4000*4000 30V
[49] Young-ho C. 2007 Electromagnetic 4000*4000*570 27mA     11kHz
[50] Andrew C. 2007 Electromagnetic 200*2*3.5 4V       200µN
[51] Kim 2007 Electromagnetic 2400*2900 3V       350Hz
[52] Vagia. M 2008 Electrostatic 400*400 /
[07] Chen. T 2008 Electrostatic 6200*3500*50 30V    150µm Ø
[53] Gustavo.A. 2008 Electro thermal 500*500*30
1000*1000*30
70mW
79mW
[54] Guo S. 2008 SMA 45000*30000*30000 1000µL   50 Hz
[55] P. M. Nieva 2008 Electro thermal 200*25*2 10V 3.7-13.3µm
[08] Varona. J 2009 Electrostatic 100*100*3,5 45V
[56] Jia 2009 Electro thermal 1000*1000 8V       336Hz
[57] Micky.R. 2010 Piezoelectric 15000*2000*300 100V      15mN
[58] Zhu 2011 Piezoelectric 2000*2000 2V       316Hz
[16] Koh 2011 Piezoelectric 5000*5000 9V        30Hz
[59] Lan C.C. 2011 SMA 45000*70000*20500 3.6 V     490mN
[60] Liu 2012 Electro thermal 2000*2000 0,6V     197Hz
[09] Jia. Y 2013 Electrostatic 6900*6500*50 120V
[61] Q. Xu 2013 Piezoelectric 26000*5000*860 2V        500Hz
[62] Park, E.S. 2013 Electrostatic 650*90*2.25 200°C      10Ω
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[73] Yingxiang Liu 2018 Piezoelectric 80800*48000*24000 427 mm/s
[27] Marija Cauchi 2018 Electro thermal 606*169*28 3V     (5-9)µm
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[76] Fan, J. 2020 Pneumatic actuator 175000 × 100000 × 60000 0.01 to 0.09
[77] Nader A. Mansour 2021 Electromagnetic Actuator 15000 × 15000 × 40 000 0 to 100 mA
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[79] Saurabh .Jadhav 2023 Pneumatic actuators 60000 x60000
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