Microscale damper prototype: A preliminary study on suppressing air flow oscillations within microchannels

This research introduces a novel micro-damper designed to mitigate pressure and velocity oscillations from a piezoelectric micropump in microfluidic environments. Unlike existing research focusing on damping in incompressible liquid flows with methods like elastic films and PDMS membranes, this study proposes a novel micro-damper prototype. Integrated into a microdevice for particle granulometric separation and detection, the damper connects to a piezoelectric micropump outlet and to a focusing microchannel inlet, followed by a capacitive sensor for size-based particle counting. Preliminary analysis determined an optimal airflow velocity at w = 0.5 m/s for accurate focusing and counting under laminar conditions. The micro-damper, constrained by the piezoelectric pump’s geometry, features a 27 µm high and 1000 µm wide cross section. Its outlet supports two potential focusing microchannel inlet configurations of 30 µm or 40 µm. Distinctively, it incorporates two symmetrical backward micro-channels connecting to the atmosphere, allowing direct piezometric contact between the main flow and an infinite compliant volume. OpenFOAM simulations confirm the damper’s effectiveness in maintaining laminar outlet flow and suppressing micropump disturbances. Thus, the proposed micro-damper ensures optimal inlet conditions for subsequent microchannel processes, enabling stable particle separation and detection in controlled airflow samples.


Introduction
Microfluidic systems have shown vast potential for applications from biomedical diagnostics to chemical synthesis.Whitesides pioneered in recognizing their significance, setting the stage for a plethora of subsequent research [1].
A primary challenge in microfluidics is oscillations in incompressible fluid flows.Addressing this, Utz et al. [2] used an elastic film to dampen pressure oscillations within micro-channels, exploring how pressure perturbations propagate, and how a channel's damping response can be varied based on its geometry and film elasticity, provided a fundamental understanding of this phenomenon.Yang et al. [3] and Iyer et al. [4] evolved this concept using a PDMS membrane to separate liquid flow from compliant chambers, which compensated for pressure and flowrate perturbations.Their methods were in line with the discussion by Squires and Quake [5], who emphasized the intricacies inherent in microfluidic designs and how subtle alterations could lead to pronounced effects.For gas flows, Zhang et al. [6] compared a damper to an RC low-pass filter, efficiently damping frequencies over 5 Hz.Veenstra et al. [7] introduced a compliant capacitive element.An analytical model was developed and experimentally validated to describe the dynamic damping response.However, their methodology faced the intrinsic limitation of air's low compressibility, leading to the realization that damping capacity is contingent upon the available compliant volume.Merging diverse methodologies, Jiao et al. [8] presented an innovative damper encapsulating a gas volume within an elastic envelope.This approach eliminates the need for a membrane at the interface between the channel and the compliant volume.The dynamic damping response of this system is simulated using a numerical finite element model, complemented by an in-depth description of the chip fabrication process and the measurement instrumentation used in experimental tests.This research is in line with the discussions by Gervais et al. [9] and Tsao et al. [10], who explored flow-induced deformations.Delving into complex flow patterns, Dendukuri et al. [11] and Atencia et al. [12] highlighted the importance of controlled flow in microfluidics.This is paramount, especially when the applications involve tasks like precision particle detection or trapping.
In this context, this study proposes a damper to mitigate oscillations from piezoelectric micropumps in a novel microfluidic system for particulate matter classification and measurement, underlining the need for undisturbed laminar airflow.

Microscale damper design for the suppression of flow perturbations
The micro-scale damper described in this study is part of an advanced microscale particulate detection system, aiming to characterize airborne particulate matter within a controlled airflow sample.This process involves a focusing channel for spatial separation based on particle diameter and an array of capacitive sensors for precise particle counting.Preliminary analysis suggested an optimal average airflow of w = 0.5 m/s for the device's operation, highlighting the need for laminar and steady flow.The damper, placed between the piezoelectric micropump and the focusing microchannel, ensures laminarity at the inlet by suppressing flow disturbances.It has a transversal section height of 27 µm and an inlet of 1000 µm, aligning with the pump's outlet for consistent flow.The outlet section width accommodates two configurations of 30 µm and 40 µm.Multiple damper configurations have been developed with distinct features, as depicted in figure 1.The entry region maintains a constant rectangular inlet cross-section of 1000 µm x 27 µm; a converging section following the entry region, with an axial length L_α defined by a convergence angle α of either 45° or 30°; the outlet micro-channel, interfacing with the external environment, can have cross-section dimensions of either 40 µm x 27 µm or 30 µm x 27 µm.This section has an axial length, L out , strategically designed to be L out > 10 L DH , i.e. ten times greater than the equivalent hydraulic diameter D H , to ensure flow's re-laminarization before reaching the focusing channel; two IOP Publishing doi:10.1088/1742-6596/2685/1/0120223 backward micro-channels connect directly to the atmosphere, facilitating direct communication between the primary flow in the main micro-channel and an infinite compliant volume, crucial for damping perturbations from the piezoelectric micropump.Consequently, the micro-damper's design not only meets the operational constraints but also introduces novel features that actively dampen disturbances.This stabilization is critical for ensuring that downstream components, such as the focusing channel, receive a steady flow crucial for precise analysis.Further details on the various design configurations are provided in Table 1.  1 presents four distinct damper configurations (A1, A2, B1, B2), each with unique convergence angles, outlet dimensions, and lengths, impacting fluid dynamics and performance characteristics.All configurations share a standardized inlet of 1000 µm x 27 µm for uniform flow entry.The axial length of the entry region L in varies with A1 and B1 shorter length than A2 and B2, affecting initial flow distribution.The convergence angle α is steeper (45°) in A1 and B1 for rapid convergence, while A2 and B2 have an angle of 30° for gradual narrowing.Outlet dimensions differ; A1 and A2 have 30 µm x 27 µm outlets, and B1 and B2 have wider 40 µm x 27 µm outlets, influencing flow rate and distribution.The equivalent hydraulic diameter D H is consistent with A1 and A2, and slightly larger in B1 and B2, potentially affecting flow rates and fluid dynamics.The axial length of the converging section, L α , is uniform across configurations.L out , the axial length of the outlet section, is consistent in both A and B configurations to ensure steady flow into subsequent channels.Finally, L tot represents the total axial length of the damper, with variations across configurations.

Numerical modelling of the microscale damper
The fluid dynamics within the micro-damper were simulated using OpenFOAM.

Model assumptions
The micro-damper simulations assume incompressible and predominantly laminar flow, with the icoFoam solver selected for its appropriateness for incompressible fluids with mainly laminar motion.The pulsatile behavior of the piezoelectric micropump, manifesting as sinusoidal flow variations, is an essential factor considered in the simulations.

Geometry and mesh generation
The geometry of the micro-damper has been accurately meshed, as illustrated in figure 2, ensuring that the flow domain is precisely resolved.

Boundary conditions
The employment of the "uniformTotalPressure" inlet boundary condition has been chosen to maintain a consistent total pressure (encompassing both static and dynamic components) across the inlet.This selection is particularly appropriate for incompressible flows.Concurrently, the utilization of the "pressureInletVelocity" for velocity coupling at the inlet refers to a system where the velocity field is derived based on the prescribed total pressure and internal field metrics, ensuring an equilibrium in the

Input parameters
The following specific pressure conditions at the inlet and outlet sections have been applied: (a) imposed normalized pressure at the input section; (b) imposed normalized pressure at the main outlet section, given as p out / air = const: (c) imposed constant normalized (relative) atmospheric pressure at the outlets of the side compensation channels, i.e., p atm / air = 0.One important aspect that must be considered is the dampening effect of flow perturbations caused by the pulsatile behavior of the piezoelectric micropump.These pulsations typically manifest as sinusoidally pulsating flow variations.Therefore, to simulate such a condition, a second set of simulations have been performed with the following imposed values: 1. at the inlet section: a) the normalized pressure is expressed as: in norm air air p t p ft Here, the pressure pulsates at a frequency  with both an oscillation amplitude and a mean pressure value equivalent to p nom /r air ; a) the velocity field is derived from the pressure-velocity coupling by imposing only inflow at the inlet section.2. at the outlet of the main channel (intended for connection to the focusing channel): a) an imposed constant normalized pressure is defined as p out / air ; b) the velocity field emerges from the pressure-velocity coupling, both outflow and inflow; 3. at the side channels' outlet (compensation channels): a) a set constant (relative) atmospheric pressure is established, denoted as p atm / air = 0; the same condition used for the main outlet section.

Preliminary results
To assess the damper's capability to ensure laminar flow at the focusing channel inlet, simulations were executed under steady flow conditions.The outcomes of these simulations are depicted in figure 3, highlighting the pressure field and of the axial component of the velocity field.
In the configuration with the angle α = 45°, although the flow remains laminar throughout, the pronounced narrowing induces a local detachment of the flow streamlines.Consequently, this leads to Hence, the criterion selected for determining the length of the straight outlet channel ensures that flow re-lamination is achieved before reaching the focusing channel.The laminarity of the flow at the outlet of the damper is ensured also when the pulsatile nature of the piezoelectric micropump is considered, i.e., the imposed inlet pressure is given as in equation ( 1).This is demonstrated by the laminar structure of the pressure and velocity fields reported in figure 4 for p in /ρ air = 40 m 2 /s 2 and f = 10 Hz.For all the reported cases the detail of the velocity field is reported on a cross-section situated in the re-laminated zone, chosen at the abscissa that corresponds to the middle third of the outlet channel.To characterize the behavior of the damper, it is not only crucial to consider the re-lamination of the flow, but also to gauge the amplitude of residual pulsations which might disturb the stationarity of the flow at the outlet section.Figure 6 provides insight into the residual velocity pulsations of the axial component u max , evaluated at the center of a cross-section in the re-laminated zone.The simulations were based on an inlet pressure characterized by an amplitude and mean value both equivalent to p in /ρ air = 40 m 2 /s 2 at a pulsation frequency of 50 Hz.As they refer to the center of the cross section, the data reported correspond to the residual perturbation of the local maximum of the parabolic velocity profile.Leveraging the Poiseuille relation: allows for the deviation of the average velocity u av based on the maximum value u max identified along the duct's axis.Consequently, the residual pulsation within the average velocity can be discerned from the residual pulsation in u max .Table 2 summarizes the average velocity values alongside the amplitude of the residual fluctuations at the cross section of the damper outlet channel for a triad of benchmark frequencies.It's imperative to note that, for comparative consistency across all conditions, the inlet pressure pulsation was standardized to an amplitude and mean value both equal to p in /ρ air =40 m 2 /s 2 .Reported results highlight that across the spectrum of assessed pulsation frequencies, the residual pulsation remains sufficiently low.This confirms the efficacy of the proposed damper in ensuring optimal inlet conditions for the subsequent focusing channel.

Conclusions
The objective of this study was to conceptualize, simulate, and analyse a micro-scale damper that ensures the laminarity of the input flow to a focusing channel, specifically designed to detect particulate matter.Air is introduced inside the damper by a piezoelectric micropump, known to introduce time-dependent flow perturbations.By using OpenFOAM, a preliminary study delineated the behaviour of the fluid under various condition.In particular, several damper designs were evaluated in the context of their geometrical and operational constraints.The study demonstrated that, even under laminar conditions, certain damper configurations could introduce localized vortices, especially when a narrowing is encountered in the damper's geometry.However, these vortices were found to dissipate rapidly, ensuring a relatively smooth flow downstream.The criterion for selecting the length of the straight output channel proved effective in achieving flow re-laminarization before introducing the fluid to the subsequent focusing channel.In light of the discussed results, the proposed damper stands as a robust solution, proficient in mitigating the challenges posed by the piezoelectric micropump.It not only ensures the laminarity of the flow, but also minimizes the residual pulsations to a negligible extent.This accomplishment is of paramount importance for the subsequent focusing channel, which is integral to the accurate detection of particulate matter.Future research will consist in the validation of the obtained numerical results with a properly built experimental setup.

Figure 2 .
40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012022 flow dynamics representation.The "pressureNormalInletOutletVelocity" function, designated for the outlet, caters to scenarios with potential flow direction reversals.Essentially, this condition enforces a zero-gradient when the flow is outgoing and transitions to the "pressureInletOutletVelocity" paradigm upon ingoing flow.Schematic of the mesh (a) plan view; (b) 3D view on a cross section.

Figure 3 .
40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012022 a transient generation of vorticity.Nevertheless, this localized vortex is quickly attenuated within the initial segment of the outlet channels.The rapid damping of this vorticity is further corroborated by the distribution of the axial velocity component presented in figure 3(c), taken at two-thirds the length of the outlet channel.Simulation result for steady state flow supply condition, p in /ρ air = 40 m 2 /s 2 : detail of the pressure field (a) and of the flow field (b) in the convergent section and in the outlet channel; (c) velocity field on a cross-section in the re-laminated region in proximity of the outlet

Figure 4 .Figure 5 .
Inlet pressure with amplitude and average value both equal to p in /ρ air = 40 m 2 /s 2 and pulsation frequency Inlet pressure with amplitude and average value equal to p in /ρ air = 40 m 2 /s 2 and pulsation frequency 100 Hz: (a) pressure field throughout the convergent section and the damper outlet channel; (b) velocity field on a cross section in the re-laminated region of the damper outlet channel; (c) parabolic velocity profile along the y-direction passing by the centroid of the cross section.umax(t)40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012022

Table 1 .
Different design configuration

Table 2 .
Average axial velocity and maximum amplitude of residual perturbation