Dynamic characterization of a polymer-based microfluidic device for distributed-load detection

Sensors and Actuators A 222 (2015) 102–113

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Dynamic characterization of a polymer-based microfluidic device for distributed-load detection Wenting Gu, Jiayue Shen, Yichao Yang, Zhili Hao ∗ Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA, United States

a r t i c l e

i n f o

Article history: Received 4 September 2014 Received in revised form 24 November 2014 Accepted 27 November 2014 Available online 4 December 2014 Keywords: Natural frequency Damping ratio Microfluidic device Distributed-load detection Dynamic behavior

a b s t r a c t This paper presents an experimental study of the dynamic characteristics of a polymer-based microfluidic device for distributed-load detection. The core of the device is a rectangular polymer microstructure embedded with an electrolyte-filled microchannel. Exerted by a rigid cylinder probe, distributed loads deflect the microstructure and consequently alter the geometry of electrolyte in the microchannel, yielding recordable resistance changes. Using a customized experimental setup, the sinusoidal response of the device is measured with the overall sinusoidal load as the input and the sinusoidal deflection of the device as the output. The recorded data are processed to obtain the amplitude ratio, F0 /z0 , of the load to the device deflection and the phase shift, , between the two signals. These two variables are then utilized to fit the dynamic stiffness and damping of the device for extracting its system-level parameters. Three devices of different designs are fabricated and tested, and best-fit values for the system-level parameters of these devices are extracted. Through comparing the measured results among these devices, non-intuitive insight is shed on how key device design parameters and the probe used affect the dynamic characteristics of the device. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In recent years, polymer-based microfluidic devices have been explored for single-load [1–4] and distributed-load detection [5–9]. Generally speaking, these devices consist of a compliant polymer microstructure and an embedded electrolyte-filled microchannel or microchamber for transduction. Owing to its incompressibility, electrolyte underneath a microstructure needs to flow in/out of a microchannel or a microchamber during operation. Therefore, these polymer-based microfluidic devices are heavily damped mechanical systems, as compared with those under-damped silicon-based physical sensors (e.g., accelerometers, tuning-fork gyroscopes, and mass sensors) [10–13]. A network analyzer is commonly employed to measure the frequency response of a silicon-based sensor, where a resonant peak is readily identified and gives rise to its resonant frequency and mechanical Quality factor (Q) [10–13]. In contrast, a heavily damped load sensor fails to exhibit a noticeable resonant peak in its frequency response and thus its resonant frequency and Q are unattainable through the instrument, as evidenced by a recent study on measuring the frequency response of a load sensor, which contains a

∗ Corresponding author. Tel.: +1 757 683 6734; fax: +1 757 683 5344. . E-mail addresses: [email protected], [email protected] (Z. Hao). http://dx.doi.org/10.1016/j.sna.2014.11.021 0924-4247/© 2014 Elsevier B.V. All rights reserved.

cantilever embedded in a silicone elastomer [14]. Yet, since these polymer-based microfluidic devices function as physical sensors, their dynamic characteristics, including natural frequency and damping ratio, play a critical role in determining their ultimate performance, including response time, load resolution, as well as the maximum detectable frequency of sinusoidal loads [15]. Bearing similar configurations as these microfluidic devices for load detection, micropumps, which incorporate a compliant polymer microstructure above or underneath liquid in a microchamber, have been extensively studied for its dynamic performance [16–22], due to its relevance for determining the maximum amount of transported liquid. In a micropump, liquid in a microchamber flows from an inlet to an outlet. In contrast, electrolyte in a microfluidic device for load detection flows in and out of a microchannel or a microchamber from its two ends simultaneously. Therefore, the experimental technique for measuring the dynamic characteristics of a micropump cannot be adopted for microfluidic devices for load detection. The majority of the studies on microfluidic devices for load detection have focused on experimentally demonstrating their feasibility of detecting dynamic loads [1–9]. However, very little work has been conducted on their dynamic characteristics [4,5,7]. This might be largely due to the fact that the heavily damped nature of these devices makes it extremely difficult to identify a resonant peak in their frequency response. Although a preliminary analysis

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some device design parameters and the probe used. At the end, the concluding remarks are given in Section 6.

on the frequency response of this type of devices was conducted, no experimental study has been followed to validate the analysis [1]. Moreover, this analysis does not take into account the interaction between the structure and electrolyte embedded in the structure, as well as the effect of the inlet/outlet for electrolyte. To address this challenge, this paper presents an experimental study of the dynamic characteristics of a polymer-based microfluidic device for distributed-load detection. Using a custom experimental setup, the frequency response of the device is measured with the sinusoidal load as the input and the sinusoidal deflection of the device as the output. Since a resonant peak of the device is not expected to be readily noticeable and non-intuitive complex interactions among different components of the device may manifest in the frequency response, the measured frequency response is processed into the dynamic stiffness and damping as function of frequency, in order to obtain its natural frequency and damping ratio. As compared with our previous work on this device [5,6] and the related work in the literature [1–4,7–9], the original contributions of this work include: (1) an experimental method is established for measuring the dynamic characteristics of a microfluidic device for load detection; and (2) the complex interactions among different components of the device are identified regarding their effect on the dynamic behavior of the device. It must be pointed out that although the basic concept used in this work, namely, processing the frequency response into the dynamic stiffness and damping as a function of frequency, as will be seen in Sec. 3, has been well established, it has not been utilized to examine a microfluidic device for load detection. To the best knowledge of the authors, this work is believed to be the first of its kind on studying the dynamic characteristics of a microfluidic device for load detection using this concept. The rest of the paper is organized as follows. The design and operation of the polymer-based microfluidic device is presented in Section 2. The theory underlying the experimental method for measuring the dynamic characteristics of the device is described in Section 3. The experimental method and associated data analysis are detailed in Section 4. In Section 5, the measured results on three devices of different designs are processed to obtain the dynamic characteristics of the devices; and the significant insight is shed on how the dynamic characteristics of the device vary with

2. Device design and operation Fig. 1 shows the schematics of a polymer-based microfluidic device for distributed-load detection [5,6], together with its key design parameters. The device consists of a rectangular polymer microstructure embedded with an electrolyte-filled microchannel and five electrode pairs distributed along the microchannel length. Together with the electrode pairs, one body of electrolyte in the microchannel functions as five distributed resistive transducers. During the device operation, a rigid cylinder probe is utilized to exert distributed loads on the microstructure. Consequently, the portion of the microstructure above the microchannel deflects and alters the geometry of electrolyte in the microchannel. Thus, the deflection of the microstructure registers as resistance changes at the locations of the distributed transducers [23]. Two reservoirs at the ends of the microchannel are utilized to inject electrolyte into the microchannel and provide a conduit for electrolyte in the microchannel to flow in/out. Two plugs are inserted into the reservoirs of the device for preventing electrolyte from spillover. The device is fabricated using a standard polydimethylsiloxane (PDMS) based fabrication process [4]. Fig. 2 shows the fabricated devices of three different designs. Note that the microstructure is much wider than the microchannel (WM  wE ), and the deflection of the microstructure occurs largely in its portion above the microchannel. In this work, the deflection of a device is defined as the deflection at the top surface of the microstructure, which is in contact with a cylinder probe used in the experimental measurement. Thus, the probe displacement is equivalent to the deflection of a device, as will be seen later on. Table 1 summarizes the key design parameters of the three devices, the sizes of the probes used, as well as their static stiffness measured from their static performance characterization [6], as shown in Fig. 3. Owing to the viscoelastic nature of PDMS, these devices exhibit a little hysteresis [24] and experience structural damping. However, as compared with viscous damping caused by the electrolyte in a device, the damping from the PDMS microstructure is completely negligible and thus is believed to have no effect on the dynamic behavior of a device.

Plug

Electrolyte-filled microchannel Microstructure

Reservoir Distributed transducers

Pyrex

(a) LP

o Input: F(t)

Cylinder probe z o

RE x Transducers:

LE dE

hE

hM z o

Cylinder probe Rp WM wE

y

1 2 3 4 5

(b)

(c)

Fig. 1. Schematics of a polymer-based microfluidic device for distributed-load detection (a) 3D view (b) side-view along the device length and (c) side view along the device width (out of proportion for clear illustration).

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Plug

Plug 30mm

6mm 5th transducer

6mm

3mm

Contact pads (a)

(b)

12mm 3mm

(c) Fig. 2. Pictures of three tested polymer-based microfluidic devices for distributed-load detection (a) Device A, (b) Device B, (c) Device C.

Table 1 Key design parameters and their values for the three tested polymer-based microfluidic devices. Key parameters

Device A

Device B

Device C

Microchannel cross-section (wE × hE ) Microchannel length (LE ) Reservoir radius (RE ) Transducer spacing (dE ) Microstructure thickness (hM ) Probe radius (Rp ) Probe length (Lp ) Measured static stiffness (Ks )

1 mm × 80 ␮m 30 mm 3 mm 1.5 mm 1.2 mm 0.8 mm 11 mm 2339 N/m

0.5 mm × 80 ␮m 6 mm 1.5 mm 0.75 mm 0.6 mm 0.4 mm 6 mm 2807 N/m

0.5 mm × 80 ␮m 12 mm 1.5 mm 0.75 mm 1 mm 0.4 mm 6 mm 2043 N/m

3. Theory The underlying theory for measuring the dynamic characteristics of the device in this work is based on the concept presented in [25] and is briefly described here. As depicted in Fig. 4, the device is modeled as a second-order mechanical system and then its dynamic behavior is governed by the following equation: d2 z dz + K · z = F(t) +C · dt dt 2

(1)

F(t) = Finitial + F0 · eiωt

(2)

Owing to damping experienced by the device, the deflection of the device is assumed to be: z(t) = zinitial + z0 ei·(ωt−)

(3)

0.7

where zinitial corresponds to the initial static load; z0 is the amplitude of the sinusoidal deflection; and  is the phase shift between the sinusoidal load and the sinusoidal deflection response of the device.

Device A(Experiment) Device B(Experiment) Device C(Experiment) Device A(Curve fit) Device B(Curve fit) Device C(Curve fit)

0.6

0.5

Force [N]

M·

where M, K and C denote the equivalent mass, equivalent stiffness and damping coefficient of the device, respectively; and F(t) is the superposition of an initial static load, Finitial , and a sinusoidal load, F0 · eiωt , acting on the device, which is exerted by a cylinder probe:

0.4

Input: F(t)

0.3

0.2

M

Output: z(t)

0.1

K 0

0

20

40

60

80

100

120

140

160

180

C

200

Deflection [μm] Fig. 3. Measured linear load-deflection relations of the three devices.

Fig. 4. A second-order mechanical system model of a polymer-based microfluidic device for its dynamic behavior.

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By substituting Eqs. (2) and (3) into Eq. (1), the dynamic stiffness and dynamic damping of the device can be expressed as [24]:

105

4. Experimental method and data analysis 4.1. Experimental setup

F0 K −M·ω = · cos  z0

(4a)

F0 sin  z0

(4b)

2

C ·ω =

Accordingly, if the amplitude ratio, F0 /z0 , of the sinusoidal load to the sinusoidal deflection of the device and the phase shift, , between the two signals at different frequencies on the right sides of Eqs. (4a) and (4b) can be experimentally measured, then these measured data can be utilized to obtain the system-level parameters of the device on the left sides of Eqs. (4a) and (4b). It is worth pointing out that the measured amplitude ratio as a function of frequency is just the commonly measured frequency response of a second-order mechanical system: z0 = F0



1 2

(K − M · ω2 ) + C 2 · ω2

1/2

(5)

Eq. (5) serves as the basis for measuring the resonant frequency and damping ratio of those silicon-based physical sensors [10–13]. However, this equation fails to give rise to these parameters of a microfluidic device for load detection, simply because of its heavily damped nature and non-intuitive interactions among its different components, as will be seen later on.

The experimental setup for measuring the dynamic characteristics of the fabricated devices is illustrated in Fig. 5. A fabricated device is fixed on a printed circuit board (PCB) and is bonded with wires for electrical connection. Then, the PCB with a wire-bonded device is mounted on a 5-axis manipulator located on an optical table. A rigid cylinder probe and a piezo-type load cell (Kistler9712B5) are assembled together by probe holders and are mounted on a vibration shaker, which is connected to a power amplifier and then a function generator. The cylinder probe is utilized to exert both an initial static load and a sinusoidal load on the device. The 5-axis manipulator is used to better align the cylinder probe in parallel to the device surface so that the device undergoes the same deflection at the locations of all the transducers. While the initial static load is exerted by the 5-axis manipulator, the sinusoidal load acting on the device is controlled by the function generator connected to the shaker. As depicted in Fig. 5(a), the input signal to the device is a sinusoidal overall load acting on it and is recorded by the load cell. To record the sinusoidal deflection of the device in response to the sinusoidal load, an AC voltage signal at 100 kHz is applied to the electrodes on one side of the device, while the electrodes on the other side of the device are connected to their own dedicated electronics [5] for converting an AC current signal to a DC voltage output, Vout . Both the readout of the load cell and the DC voltage outputs of the electronics feed in a DAQ board and are recorded by

Fig. 5. Experimental setup for measuring the dynamic characteristics of a polymer-based microfluidic device for distributed-load detection (a) schematic (b) and (c) pictures of the setup (d) colored liquid in microchannel in contact with the electrode pairs.

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Fig. 6. Signal flow in a dynamic measurement of the polymer-based microfluidic device for distributed-load detection.

a LabVIEW program. Thus, the recorded signals are the sinusoidal load from the load cell and the DC voltage outputs from the electronics, which are representative of the sinusoidal deflection of the device. The signal flow in the dynamic measurement of the device is illustrated in Fig. 6. The input signal, the overall sinusoidal load, F, is first linearly converted to the sinusoidal deflection, z, of the device through the microstructure. Then, the sinusoidal deflection registers as the resistance, R, of a transducer. The electronics connected to the device further translate the resistance of a transducer to the DC voltage output, Vout . The relations between these signals are summarized as below: F =K ·z

(6a)

R0 R(z) = 1 − (z/hE ) · 

(6b)

Vout (z) =

v2PP RF 8R2 (z)

(6c)

where K denotes the equivalent stiffness of the device, as in Eq. (1); R0 denotes the initial resistance of a transducer;  is a constant accounting for non-uniform deflection across the portion of the microstructure above a transducer [6] and its value is around 0.06 for the devices; hE denotes the microchannel height; vPP denotes the peak-peak value of the AC voltage signal; and RF denotes the feedback resistance of the electronics [5,6]. According to Eqs. (6a)–(6c), both the device and the electronics are essentially nonlinear. The static performance of the three devices is characterized to establish the relations (Vout –z relations) of the DC voltage outputs to the deflection of the device [6], prior to their dynamic characterization. Interestingly, three fabricated devices all exhibit a linear relation between the DC voltage outputs and its deflection at the locations of the five transducers. There is a slight variation in the measured DC voltage outputs among the transducers at the same deflection in the devices, which is believed to result from fabrication variations in the devices and misalignment between a probe and a device. Furthermore, as shown in Fig. 3, a linear relation holds between the overall load and the deflection of the devices. Thus, the recorded DC voltage outputs are converted to the deflection of the devices by using their measured linear Vout –z relations, without introducing extra phase shift. Meanwhile, it is assumed that the electronics introduce the same amount of phase shift to all the transducers of a device over the measured frequency range. 4.2. Experimental method After the static measurement of a device for obtaining the Vout –z relations is finished, the following procedure is implemented to measure the dynamic characteristics of a device.

back by 50 ␮m. At the point, the probe is assumed to be in contact with the device surface, while without deforming the device. Thus, there might be a distance of <50 ␮m between the probe and the device. Step 2: Exertion of an initial static deflection on a device By manually adjusting the z-axis of the 5-axis manipulator, the device is moved upward by a pre-defined displacement, which is equivalent to an initial deflection, zinitial , acting on the device. Since the load cell is a piezotype, its charge decays away in a short time. The DC voltage outputs of the device before and after this initial static deflection are recorded for obtaining the initial static load. These DC voltage outputs and zinitial are used for the data analysis later on. Step 3: Dynamic characterization of a device The function generator connected to the vibration shaker is first turned on to exert a sinusoidal input on the device through the probe. After the device reaches its steady state, a LabVIEW program is turned on to record the readout of the load cell and the DC voltage outputs of the device for 10 s at a sampling rate of 5 kHz for Devices A and C and 500 Hz for Device B. This procedure is repeated for the sinusoidal inputs over a frequency range of about 5–100 Hz. The frequency interval is arbitrarily chosen to be 5 Hz for Device A and 10 Hz for Devices B and C. While the signals at low frequencies bear severe environmental noise, the signals at frequencies close to the resonant frequency of a device vary considerably. As will be seen later on, the resonant frequency of the three devices is a little bit over 100 Hz. Another concern is that crosstalk (i.e., other vibration modes) might kick in and cause an abrupt drop in the phase shift in the measurement. As such, 5–100 Hz is chosen as the frequency range for all the devices. The recorded data for the dynamic characterization of a device are the sinusoidal overall load and DC voltage outputs as a function of time at different frequencies. 4.3. Data analysis The recorded readout of the load cell is converted to the overall sinusoidal load, and the DC voltage outputs are converted to the deflection of a device by using the measured Vout –z relations. Fig. 7 shows part of the recorded sinusoidal overall load and the sinusoidal deflection of the devices at two different frequencies: 10 Hz and 80 Hz. Note that the recorded data for Device B at 80 Hz is heavily distorted, due to a low sampling rate. As can be seen in these figures, with a reasonably high sampling rate, these devices are capable of clearly capturing distributed sinusoidal loads at both relatively low frequency and high frequency. Under the same sinusoidal load, different deflection amplitudes among the transducers of a device simply indicate misalignment between a device and a probe. The initial deflections of the three devices are all fixed at zinitial = 500 ␮m. The recorded data are analyzed in the frequency domain to obtain the amplitude ratio, F0 /z0 , using Fast Fourier Transform (FFT) analysis and to obtain the phase shift, , between the two signals using Cross Spectrum analysis. All the data analysis is implemented in Matlab. 5. Results and discussion

Step 1: Determination of contact point The probe is brought down to a certain visible distance above the device. Then, the PCB with the device is moved upward by controlling the 5-axis manipulator by an interval of 50 ␮m at a time until a noticeable change is observed in the readout of the load cell. Then, the device is brought

5.1. Measured results Fig. 8 plots the measured phase shift and amplitude ratio of the sinusoidal overall load versus the sinusoidal deflection of the three devices as a function of frequency. The phase shift goes up with

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Fig. 7. Recorded steady-state sinusoidal overall load and the sinusoidal deflection of the three devices at 10 Hz and 80 Hz: Device A at (a) 10 Hz and (b) 80 Hz recorded at a sampling rate of 5 kHz, Device B at (c) 10 Hz and (d) 80 Hz recorded at a sampling rate of 500 Hz, Device C at (e) 10 Hz and (f) 80 Hz recorded at a sampling rate of 5 kHz (Dashed lines represent the time delay between the load and the voltage output of one of the transducers, the 2nd transducer for Device A, the 5th transducer for Device B and the 2nd transducer for Device C.).

frequency for all the devices. While the amplitude ratio of Device B increases with frequency, the amplitude ratio of Device C drops with frequency. This can be explained by the over-damped nature of Device B and the under-damped nature of Device C, as will be seen in later on. As to Device A, its amplitude ratio goes up with frequency at low frequencies (<50 Hz), but drops with frequency at high frequency (>50 Hz). Since Device A is under-damped, the measured data at low frequencies may carry relatively large errors. Fig. 9 illustrates how the dynamic stiffness and damping of the devices vary with frequency. Since the sudden drop below zero in dynamic stiffness indicates the location of the natural frequency of a device [24], Fig. 9(a) and (e) indicates that the natural frequencies, fn , of Devices A and C are above 100 Hz. Fig. 9(c) indicates that the natural frequency of Device B is below100 Hz at the locations of the 4th and 5th transducers, and the results of the 1st, 2nd and 3rd transducers suggest a higher frequency at their locations. As shown in Fig. 9(b), (d) and (f), damping of all the devices goes up with

frequency. Since the measured data on these devices have been characterized by their static counterparts, the variations among the transducers in a device are believed to be a combination of misalignment between a device and a probe used and experimental noise. According to Eqs. (4a) and (4b), Fig. 10 plots the measured dynamic stiffness of the devices as a function of squared angular frequency and the measured damping of the devices as a function of angular frequency, using the experimental data from the 3rd transducer of Devices A and B. The experimental data from all the transducers of Device C are plotted in Fig. 10(c), owing to its relatively uniform performance across the transducers. Consequently, a linear relation for the dynamic stiffness fits the experimental data for extracting their equivalent mass and equivalent stiffness. Similarly, another linear relation for the damping fits the experimental data for obtaining their damping coefficient. The best-fit values for the system-level parameters, K, M, and C, of the three devices are

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7000

5000

Phase shift[degree]

6000 F0/z0 (N/m)

100

1st 2nd 3rd 4th 5th Theory

4000 3000 2000 0

50 Frequency [Hz]

80 60 40 20 0 0

100

1st 2nd 3rd 4th 5th Theory

20

(a)

F0/z0 (N/m)

15000

Phase shift[degree]

1st 2nd 3rd 4th 5th Theory

20000

10000 5000 0

0

100

50 Frequency [Hz]

100

50

0 0

100

1st 2nd 3rd 4th 5th Theory

20

(c)

40 60 Frequency [Hz]

80

100

(d) 100

4000

3000

Phase shift[degree]

1st 2nd 3rd 4th 5th Theory

3500 F0/z0 (N/m)

80

(b)

150

25000

40 60 Frequency [Hz]

2500 2000 1500 0

50 Frequency [Hz]

100

(e)

80 60

1st 2nd 3rd 4th 5th Theory

40 20 0 0

20

40 60 Frequency [Hz]

80

100

(f)

Fig. 8. Measured results of the devices on the amplitude ratio and phase shift of the sinusoidal overall load and the sinusoidal deflection as a function of frequency (a) amplitude ratio and (b) phase shift of Device A, (c) amplitude ratio and (d) phase shift of Device B, (e) amplitude ratio and (f) phase shift of Device C.

summarized in Table 2. The extracted natural frequency, fn , and the damping ratio, , are also included in the table. Defined as the ratio of the actual damping coefficient to critical damping coefficient, the damping ratio is calculated here for its ease to identify whether a device is an over-damped or under-damped mechanical system. It is worth mentioning that the extracted equivalent stiffness of the three devices is all higher than their static counterpart, since it is obtained at an initial static deflection, as listed in Tables 1 and 2. Based on the best-fit values from the 3rd transducer of the devices, their phase shift and amplitude ratio can be calculated using the following expressions and are further plotted into Fig. 8 for comparison:  = tan−1 F0 = z0





C ·ω K − M · ω2 2



(K − M · ω2 ) + C 2 · ω2

(7a)

1/2 (7b)

Meanwhile, the dynamic stiffness and damping are also calculated using these best-fit values and are plotted in Fig. 9. According to Eq. (7a), the phase shift of the devices should be very small at low frequencies. However, as shown in Fig. 8, a phase shift of 10–20◦ is observed at a frequency as low as a few Hz in the measurements of the devices. This explains the non-zero damping at 0 Hz frequency in Fig. 10. This initial phase shift is believed to be largely due to the electronics connected to the devices for recording the output signals of the devices. 5.2. Validity of the system-level model with the ratio of the probe length to the microchannel length As shown in Figs. 8 and 9, a large difference exists between their theoretical results and their experimental counterparts for Device A. In contrast, the theoretical results of Devices B and C match the experimental results very well, particularly with Device C demonstrating the best agreement. While dynamic motion of the device

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Table 2 Best-fit values for the system-level parameters of the three polymer-based microfluidic devices extracted from the experimental data (a) Device A, (b) Device B, (c) Device C. 1

2

3

4

5

(a) K (N/m) M (kg) C (N s/m)  fn (Hz)

4126 0.0044 1.32 0.15 154

4088 0.0054 1.13 0.12 138

3819 0.0038 0.90 0.12 160

3552 0.0028 0.77 0.12 179

3121 0.0019 0.47 0.10 204

(b) K (N/m) M (kg) C (N s/m)  fn (Hz)

3514 0.0004 4.24 1.77 468

3869 0.0014 8.53 1.84 265

3974 0.0067 14.92 1.45 123

5139 0.0283 21.01 0.87 68

5650 0.0284 30.90 1.22 71

(c) K (N/m) M (kg) C (N s/m)  fn (Hz)

3064 0.0060 2.54 0.30 113

2854 0.0056 2.42 0.30 113

3026 0.0059 2.50 0.30 114

2627 0.0050 2.15 0.30 115

2716 0.0049 2.21 0.30 118

4000

8000

1st 2nd 3rd 4th 5th Theory

3500 3000

Damping C ω (N/m)

2

Dynamic stiffness K-m ω (N/m)

Parameter

2500 2000 1500 0 10

1

10 10 Frequency [Hz]

1st 2nd 3rd 4th 5th Theory

6000 4000 2000 0 0 10

2

1

10 10 Frequency [Hz]

2.5 1st 2nd 3rd 4th 5th Theory

0.5 0

Damping C ω (N/m)

1

(b)

4

2

-0.5

1

10 10 Frequency [Hz] (c)

4000

2

Dynamic stiffness K-m ω (N/m)

-1 0 10

3000 2000

1 0.5 0 0 10

2500

1st 2nd 3rd 4th 5th Theory

1

10 10 Frequency [Hz]

(e)

2

4

1st 2nd 3rd 4th 5th Theory

1.5

2

1000 0 0 10

x 10

2

Damping C ω (N/m)

Dynamic stiffness K-m ω (N/m)

(a)

x 10

2

2000 1500

1

10 10 Frequency [Hz] (d)

2

1st 2nd 3rd 4th 5th Theory

1000 500 0 0 10

1

10 10 Frequency [Hz]

2

(f)

Fig. 9. Dynamic stiffness and damping of the devices as a function of frequency (a) dynamic stiffness and (b) damping of Device A, (c) dynamic stiffness and (d) damping of Device B, (e) dynamic stiffness and (f) damping of Device C.

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4000

4000 Damping C ω (N/m)

Experiment 3rd transducer Curve fit

2

Dynamic stiffness, K-mω (N/m)

110

3500 3000 2500 2000 0

1

2 2 2 2 ω (rad /s )

3

4 x 10

5

Experiment 3rd transducer Curve fit

3500

3000

2500 200

400 600 ω (rad/s)

4000

(b)

10000

Experiment 3rd transducer Curve fit

3500

Damping C ω (N/m)

2

Dynamic stiffness, K-mω (N/m)

(a)

3000 2500 2000 1500 0

1

2 ω2 (rad2/s2)

3

6000 4000 2000 0 0

4 x 10

Experiment 3rd transducer Curve fit

8000

5

200 400 ω (rad/s)

4000

1st Curve fit 1st 2nd Curve fit 2nd 3rd Curve fit 3rd 4th Curve fit 4th 5th Curve fit 5th

2000

2500 Damping C ω (N/m)

3000

1000

1

2 2 2 2 ω (rad /s )

600

(d)

2

Dynamic stiffness, K-mω (N/m)

(c)

0 0

800

3

4 x 10

5

(e)

2000 1500

1st Curve fit 1st 2nd Curve fit 2nd 3rd Curve fit 3rd 4th Curve fit 4th 5th Curve fit 5th

1000 500 0 0

200

400 ω (rad/s)

600

800

(f)

Fig. 10. Dynamic stiffness of the devices as a function of squared angular frequency and damping of the devices as a function of angular frequency for extracting the values for their system-level parameters (a) dynamic stiffness and (b) damping of Device A, (c) dynamic stiffness and (d) damping of Device B, (e) dynamic stiffness and (f) damping of Device C.

is dominated by the portion of the microchannel (including the microstructure and electrolyte) underneath the probe, the portion of the microchannel outside the probe also affects the dynamic motion of the device, because the microstructure in this portion deforms and electrolyte in this portion flows during device operation. Since the portion of the microchannel outside the probe in Device A is much longer than the portion of the microchannel underneath the probe (30 mm versus 11 mm), it affects the validity of treating the device as a second-order mechanical system. As to Device C, the portion of its microchannel outside the probe is short, as compared with its portion underneath the probe (12 mm versus 6 mm), its effect on the validity of the assumed mechanical system model is quite trivial. In contrast, the probe spans across the whole microchannel in Device B. Thus, electrolyte interaction between the microchannel and reservoirs dramatically affects its dynamic performance, as will be detailed in Section 5.3. Thus, Device B exhibits the largest variation in dynamic behavior among the transducers. Taken together, there is a tradeoff on the ratio of the probe length

to the microchannel length to validate the device as a second-order mechanical system. 5.3. Electrolyte in the microchannel and reservoirs Electrolyte in the microchannel and reservoirs play a critical role in viscous damping in a device. Generally speaking, viscous damping in a device includes z-axis squeezing in the microchannel portion underneath the probe and x-axis oscillatory flow in the microchannel portion outside the probe, as well as electrolyte interaction between the microchannel and reservoirs, as depicted in Fig. 11. Note that since the probe covers its whole microchannel, Device B does not experience oscillatory flow. Comparison in damping ratio of the 3rd transducer among the three devices indicate that Devices A and C are both under-damped, while Device B is over-damped and experiences much larger damping. Since the microchannel cross-section of Device A doubles its counterpart of Device B, it is reasonable to observe that damping ratio of Device A is

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Fig. 11. Viscous damping from electrolyte in the microchannel and reservoirs in the polymer-based microfluidic device for distributed-load detection.

lower than that of Device C. Devices B and C have the same dimension, except that Device B has a much shorter microchannel and a thicker microstructure, as listed in Table 1. The measured large damping in Device B is believed to be from electrolyte interaction between the microchannel and reservoirs. Since electrolyte in the microchannel flows in and out of the reservoirs during operation, electrolyte interaction arises between the microchannel and the reservoirs. Consequently, the distance between a reservoir and the probe affects to what extent this interaction contributes to viscous damping. The reservoirs are 9 mm and 3 mm away from a probe in Devices A and C, respectively, and thus the interaction is not expected to be severe. In contrast, the probe is next to the reservoirs of Device B, the electrolyte interaction between the microchannel and reservoirs becomes significant. This can be evidenced by significant variation in the measured damping ratio among the transducers, as shown in Table 2(b). As illustrated in Fig. 2(b), owing to fabrication misalignment, the 5th transducer of Device B is next to the reservoir, as compared with the 1st transducer. Therefore, the interaction gives rise to a much larger damping. Meanwhile, the equivalent stiffness and equivalent mass measured at the locations of the 4th and 5th transducers in Device B are also much higher than those measured from the rest transducers, as listed in Table 2(b). This is also believed to result from the severe electrolyte interaction between the microchannel and reservoirs. Therefore, an optimized distance between the probe and the reservoir is desired so as to validate the device as a second-order mechanical system and minimize the effect of electrolyte interaction between the microchannel and reservoirs on the dynamic behavior of the device. 5.4. Variations in the measured system-level parameters among different transducers in a device As shown in Table 2(a), the equivalent stiffness and equivalent mass of Device A decreases along the device length from the 1st transducer to the 5th transducers (except that the equivalent mass and natural frequency measured from the 1st transducer does not follow the trend). Meanwhile, the damping ratio exhibits the same trend. These variations in the system-level parameters are consistent with the variations among the transducers shown in Figs. 8 and 9, since both the phase shift and damping, an indicator of the damping ratio, go up from the 1st transducer to the 5th transducer, and the amplitude ratio of F0 /z0 , an indicator of the equivalent stiffness, go up from the 1st transducer to 5th transducer. This variation trend is believed to be caused by the misalignment between the probe used and the device: the probe is tilt toward the 1st transducer. Owing to this tilt, the portion of the microstructure above the 1st transducer deflects more, and then electrolyte in this portion experiences a larger viscous damping. This tilt also causes the natural frequency of the device going up from the 1st transducer to the 5th transducer. In contrast, there is a slight variation among the transducers in Device C. It is believed that the misalignment between the probe and the device is trivial and the variation is mainly from experimental noise. As pointed out in Section 5.3, the measured large variation among the transducers

in Device B is due to the severe electrolyte interaction between the microchannel and reservoirs. 5.5. Factors affecting the natural frequency of a device Table 3 compares the system-level parameters of the three devices using the results from the 3rd transducer, since the result from this transducer is relatively immune to misalignment and electrolyte interaction mentioned above. Since a probe is utilized to exert distributed loads on a device, the measured natural frequency of a device is a combination of the device and the probe used. As pointed out in the literature [26], the size and weight of a probe affect the measured frequency of a cantilever. In this work, both the probe size and the PDMS microstructure contribute to the equivalent stiffness of a device. Owing to the larger probe used, the equivalent stiffness of Device A is higher than that of Device C, although Device C has a narrower portion of the microstructure above the microchannel. The contribution of electrolyte to the equivalent stiffness is negligible in Devices A and C, but is significant in Device B, due to its severe electrolyte interaction. Although Device A is much larger than the other two devices, the equivalent mass of Device A is much lower than the other devices. This is believed to result from the fact that the probe covers only one third of the microchannel in Device A, while the probe covers the whole microchannel in Device B and half of the microchannel in Device C. Thus, the equivalent mass of a device is determined by the size and weight of the probe relative to the PDMS microstructure [26]. It is counter-intuitive to note that Device A having a large dimension exhibits a higher natural frequency than the other two devices having a small dimension. 5.6. Significance of the experimental method Polymer-based microfluidic devices are typically used for biological and chemical analysis, where a polymer microstructure is used to confine liquid into certain dimensions, while without experiencing deformation. In contrast, when a microfluidic device is used for load detection, its dynamic characteristics need to be examined for determining its response time, load resolution and the maximum detectable frequency of sinusoidal loads. The experimental method employed h ere can be extended to characterize similar microfluidic devices for load detection. In essence, this experimental method requires: (1) the collection of the sinusoidal load-deflection relations of a device at different frequencies; (2) data analysis of obtaining the amplitude ratio and phase shift of Table 3 Comparison of the system-level parameters of the three devices extracted from the 3rd transducer. Parameter

Device A

Device B

Device C

K (N/m) M (kg) C (N s/m)  fn (Hz)

3819 0.0038 0.90 0.12 160

3974 0.0067 14.92 1.45 123

3026 0.0059 2.50 0.30 114

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the load versus the deflection as a function of frequency: F0 /z0 (␻) and ␾(␻); and (3) consequently, plotting the amplitude ratio and phase shift based on Eqs. (4a) and (4b) will give rise to the systemlevel parameters of a device. As described above, because of the structure-electrolyte interaction in the device, the effect of the probe size and weight on its dynamic behavior, as well as unavoidable fabrication variations of the device, an experimental study perhaps offers a relatively simple, accurate method to obtaining the natural frequency and damping ratio of a microfluidic device for load detection. 6. Conclusion An experimental study has been presented on the dynamic characteristics of a polymer-based microfluidic device for distributedload detection. By treating the device as a second-order mechanical system, its dynamic characteristics can be expressed in terms of the amplitude ratio of the sinusoidal load to the sinusoidal deflection of the device and the phase shift between these two signals at different frequencies. These two variables on a device are measured using a custom experimental setup and fitted into the dynamic stiffness and damping of the device for extracting its system-level parameters. By examining the obtained dynamic characteristics of three devices of different designs, it has been found that (1) the ratio of the probe length to the microchannel length affects the validity of treating the device as a second-order mechanical system; (2) electrolyte interaction between the microchannel and reservoirs can severely affect the dynamic behavior of a device, depending on the distance between the probe used and a reservoir; and (3) the size and weight of a probe play an important role in determining the measured natural frequency of a device. Overall, the experimental method and the associated data analysis presented here provide a generalized approach to measure the dynamic characteristics of a microfluidic device for load detection. In the future, the dynamic characteristics of this device will be systematically characterized for its application in measuring the viscoelasticity of soft materials [27,28]. Acknowledgement The authors wish to acknowledge the financial support from the National Science Foundation CMMI under grant no. 1265785. References [1] C.A. Gutierrez, E. Meng, Impedance-based force transduction within fluidfilled parylene microstructures, J. Microelectromech. Syst. 20 (2011) 1098–1108. [2] W.Y. Tseng, J.S. Fisher, J.L. Prieto, K. Rinaldi, G. Alapati, A.P. Lee, A slow-adapting microfluidic-based tactile sensor, J. Micromech. Microeng. 19 (2009) 085002. [3] B. Nie, S. Xing, J.D. Brandt, T. Pan, Droplet-based interfacial capacitive sensing, Lab Chip 12 (2012) 1110–1118. [4] B. Nie, R. Li, J.D. Brandt, T. Pan, Iontronic microdroplet array for flexible ultrasensitive tactile sensing, Lab Chip 14 (2014) 1107–1116. [5] W. Gu, P. Cheng, A. Ghosh, Y. Liao, B. Liao, A. Beskok, Z. Hao, Detection of distributed static and dynamic loads with electrolyte-enabled distributed transducers in a polymer-based microfluidic device, J. Micromech. Microeng. 23 (3) (2013) 035015. [6] P. Cheng, W. Gu, J. Shen, A. Ghosh, A. Beskok, Z. Hao, Performance study of a PDMS-based microfluidic device for detection of continuous distributed static and dynamic loads, J. Micromech. Microeng. 23 (8) (2013) 085007. [7] C.Y. Wu, W.H. Liao, Y.C. Tung, Integrated ionic liquid-based electrofluidic circuits for pressure sensing within polydimethylsiloxane microfluidic systems, Lab Chip 11 (10) (2011) 1740–1746. [8] Y.L. Park, C. Majidi, R. Kramer, P. Bérard, R.J. Wood, Hyperelastic pressure sensing with a liquid-embedded elastomer, J. Micromech. Microeng. 20 (12) (2010) 125029. [9] R.D. Ponce Wong, J.D. Posner, V.J. Santos, Flexible microfluidic normal force sensor skin for tactile feedback, Sens. Actuators A: Phys. 179 (2012) 62–69.

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Biographies

Wenting Gu received the B.S. degree from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2009. She joined the MEMS group at Old Dominion University in 2010 and worked on silicon-based MEMS inertial sensors and polymer-based microfluidic force sensors. She received the M.E. degree in mechanical engineering from Old Dominion University, US, in 2013. She is currently a Ph.D. candidate in Department of Mechanical and Aerospace Engineering at Old Dominion University. Her dissertation topic is concurrent spatial mapping of the viscoelastic behavior of heterogeneous soft materials via a polymer-based microfluidic device.

Jiayue Shen obtained B.S. degree in Zhejiang University (China) in 2009 and M.S. degree in Lanzhou University of Technology (China) in 2012. Currently, she is a third-year doctoral student at Mechanical and Aerospace Department from Old Dominion University (USA). Her research interests include the design, characterization and application of polymer based microfluidic sensors.

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Yichao Yang received his B.S. in Measurement Control Technology and Instruments from Yantai University, Yantai, People’s Republic of China (2009) and his M.S. in Control Engineering from University of Electronic Science and Technology of China, Chengdu, People’s Republic of China (2013). He is currently pursuing his Ph.D. degree in Mechanical and Aerospace Engineering at Old Dominion University, Norfolk, Virginia. His doctoral research focuses on design, fabrication, and testing of polymerbased microfluidic tactile sensors as well as applications of these tactile sensors, such as tissue palpation during Minimally Invasive Surgery and tactile sensing for robotic fingers.

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Zhili Hao received the B.S and M.S. degrees in Mechanical Engineering from Shanghai Jiao Tong University, Shanghai, P.R. China, in 1994 and 1997, respectively. She received her Ph.D. degree from the University of Central Florida, Department of Mechanical, Materials and Aerospace Engineering, in 2000. After graduation, Dr. Hao worked as a MEMS Engineer in industry for two years. In July 2006, she joined the Department of Mechanical and Aerospace Engineering at Old Dominion University as an assistant professor and is currently an associate professor. Her research interests include developing various MEMS/microfluidics-based sensors, investigating their applications in biomedical and robotics fields, as well as studying micromechanics critical for performance improvement of micro-sensors.