An ultrasensitive micropillar-enabled acoustic wave (μPAW) microdevice for real-time viscosity measurement

Viscosity measurement has recently captured considerable attention due to its wide range of applications in fields such as pharmacy, food industry, cosmetic industry, and biomedical diagnostics. Acoustic wave sensors such as quartz crystal microbalance (QCM) are well-known mass sensors that also show their capability in measuring liquid viscosity. However, the challenges for QCM-based viscosity measurement devices lie in their low sensitivity and unstable response. Herein, we report an ultrasensitive micropillar-enabled acoustic wave (μPAW) viscometer by fabricating well-defined polymethyl methacrylate (PMMA) micropillars on a QCM substrate to achieve ultrahigh sensitivity for liquid viscosity with a stable response thanks to a unique vibration coupling between the micropillar and QCM substrate. The μPAW based viscometer shows a 20-fold improvement in the measurement sensitivity over traditional QCM viscometers and achieved an excellent limit of detection (LOD) while measuring the viscosity of sucrose liquid as low as 0.054 wt%. The microdevice developed in this work is a promising tool for the viscosity measurement of liquids.


Introduction
Viscosity is one of the fundamental properties of liquids and gases.Viscosity measurement has recently captured considerable attention due to its wide range of applications in fields such as pharmacy (Puneeth et al. 2021), food industry (Cullen et al. 2000), cosmetic industry (Tadros 1992), and biomedical diagnostics (Vahid et al. 2019).For example, the viscosity of the drug should be comparable to that of blood in drug delivery applications (Akyazi et al. 2018).In addition, viscosity is an important parameter in biomedical diagnostics for biofluids such as urine (Inman et al. 2013) and saliva (Farsaeivahid et al. 2022).Similarly, the food industry applies viscosity to ensure that the flow rate in pipes is sufficient to fill the packets (Tabilo-Munizaga and Barbosa-Ca ´novas 2005).In addition, it is crucial to develop a device capable of measuring and analyzing viscosity with high precision while requiring a small sample volume (microliter or less) (Arosio et al. 2016).
The elementary viscosity measurement relies on pouring a fluid and calculating its time to empty or fill a vessel.
Traditional viscometers are classified into four broad categories: U-tube (Grattoni et al. 1993), falling/rising objects (Brizard et al. 2005), rotational (Cullen et al. 2003) and vibrational viscometers (Yabuno 2021).U-tube Viscometers include a U-shaped glass tube, where the viscosity is determined by the time required for the fluid to fill the tube.The working principle of the falling ball viscometer is based on stokes' law and the measurement of the time required for the object to fall due to the fluid's resistance.Rotational viscometers evaluate the viscosity by turning a spindle in the solution and measuring the required torque.Vibrational viscometers, which are the most common among traditional viscometers, determine viscosity based on the induced viscous drag on a vibrating blade.Recently, microfluidic channels and devices have been developed as a result of advancements in micro-nanofabrication technologies.Microfluidic viscometers are classified into five broad categories: Pressure sensing (Pipe et al. 2008), Flow rate sensing (Solomon et al. 2016), Microfluidic Comparator (Kang et al. 2010), Droplet-based (Li et al. 2017) and Surface Tension viscometers (Srivastava and Burns 2006).
Quartz crystal microbalance (QCM) device is a bulk acoustic wave (BAW) piezoelectric sensor oscillating in thickness-shear mode (TSM) (Ji et al. 2021).The sensing mechanism of a QCM is based on detecting the resonance frequency shift resulting from surface mass loading and near-surface liquid layer viscoelastic properties.The typical sensing resolution of a QCM device operating in a gas phase is approximately 1 ng/cm 2 per Hz, while the reliable measurement for a mass accumulation is up to 100 lg/cm 2 (O'sullivan and Guilbault 1999).The sensing capacity of QCM devices can be versatile as the sensor surface can be easily functionalized with chemical sensing materials.In addition, the QCMs can operate in liquids where part of the shear vibration is transferred to the liquid, causing elastic energy dissipation in the surrounding liquid medium (Yang and Thompson 1993;Ash et al. 2003).This interaction results in the frequency shift, which is described by the Kanazawa and Gordon model and given by Kanazawa and Gordon (1985): where q L is the density and g L is the viscosity of the fluid.Z q and f o represent the mechanical impedance and the natural frequency of the quartz substrate.As can be seen, the change in q L g L leads to the frequency shift (Df).For example, Table 1 presents the frequency shifts of the 10 MHz QCM in responding to the viscosity of the aqueous solutions (Wang et al. 2014a).
Recently, a novel micropillar-enhanced acoustic wave (lPAW) was enabled by fabricating micropillars on a QCM substrate, resulting in orders of magnitude higher mass sensitivity than traditional QCM devices, thanks to a unique coupling between micropillars and QCM (Wang et al. 2014a;Esfahani and Sun 2023).
For instance, the lPAW device improved the mass sensitivity of conventional QCM by three times in detecting acrylic acid grafting and twenty times in measuring bovine serum albumin (BSA) adsorption (Wang et al. 2015;Esmaeilzadeh et al. 2019).In addition, the lPAW devices was used for humidity detection (Wang et al. 2014b).The results showed that the lPAW can enhance resonant frequency shift up to 27 times compared to conventional film based QCM.Su et al. evaluated ligand-analyte binding interactions between anti-human immunoglobulin G (anti hIgG) and human immunoglobulin G (hIgG) using lPAW devices (Su et al. 2018).The lPAW devices demonstrated a detection limit of 80 nM.
Although lPAW devices have been used to detect adsorbed mass on the surface, little study has been conducted to measure the effect of the near-surface liquid layer.This study reports the effect of liquid viscosity on lPAW devices, exploring the potential of lPAW for viscosity measurement.The paper starts with fabricating a PMMA micropillar array on a QCM using thermal Nanoimprinting Lithography (T-NIL).Then a microfluidic lPAW device is developed by integrating the lPAW sensor with a commercial Discovery-Q (Invetrometrix) platform.The sucrose solutions with different viscosities are measured using the developed lPAW system, and sensitivity enhancement analysis for four micropillar heights is performed.At last, a theoretical model based on the cantilever beam analysis is presented to understand the working principle of lPAW for viscosity measurement.

Mathematical model
In the case of lPAW operating in air or vacuum medium, the damping effect can be neglected and the resonance frequency can be simply analyzed by solving two massspring systems (Wang et al. 2014c).The quartz can be considered as the main resonator (m q , k q ) and the micropillar as the second resonator (m p , k p ).However, the dynamic response of the lPAW system becomes more complicated when the interacting medium is liquid (Wang et al. 2015).For a traditional QCM viscometer device operating in a liquid, the oscillation of quartz results in a shear wave in a thin liquid layer of thickness of nanometerscale (decay length, d) near its surface.The frequency response of QCM can be determined by assuming an effective liquid mass layer moving with the QCM surface (Kanazawa and Gordon 1985).The decay length and effective mass are expressed as (Kanazawa and Gordon 1985): and where Dm is the effective mass and A is the sensing area.Different from traditional QCM, the micropillars of the lPAW device can be analyzed as a microscale cantilever beam vibrating in a liquid where the angular frequency (x) where E is the young modulus, I the momentum of inertia, H is the height, W is the width, and _ m is the mass per unit length of the micropillar.c 1 is the real part of induced hydrodynamic loading on rectangular micropillars.The analytical approximation of c 1 on rectangular micropillars is expressed as (Wang et al. 2014c): where a 1 and a 2 two constants with values of 1.0553 and 3.7997 (Gupta 2014).The value of b can be found by solving the following equation (Su et al. 2019): m t is an additional liquid layer moving at the tip of the micropillar and L is the total length of the micropillar.As a result, the resonant frequency of micropillars in a solution can be calculated by solving Eqs.(4-7) concurrently.At the same time, the frequency response of lPAW can be estimated from the two-degree-of-freedom systems analysis with additional effective masses resulting from the induced hydrodynamic loading (Dm p ) on the QCM and micropillars (see Fig. 1).The quartz substrate is treated as the primary resonator with effective mass (m q;eff ¼ m q þ Dm q ) and force constant k q and the micropillar as the second resonator with effective mass (m p;eff ¼ m p þ Dm p ) and force constant k p .As a result, the resonant frequency of the lPAW sensor can be obtained by solving: Solving Eq. ( 8) show the frequency as: Therefore, the coupled resonance frequencies of lPAW sensors with varying micropillar heights are predicted by solving Eqs. ( 2)-( 9).

Micropillar fabrication
The fabrication process of PMMA micropillar for the lPAW consists of four sequential steps (Fig. 2 The PMMA pillars were characterized using a field emission scanning electron microscope (FE-SEM) and the SEM images are illustrated in Fig. 3.As can be seen, the well-defined PMMA micropillar structures were successfully transferred onto the QCM surface with a thin residual layer by the T-NIL process.

Flow cell assembly
The flow cell unit of the microfluidic lPAW device includes four sensor wells, which are electrically connected to the Discovery-Q platform underneath.Well-known softlithography was employed to fabricate the flow cell unit, where the mold of the flow cell structure was designed in SolidWorks and then printed using a 3D printer (Ultimaker 3). Figure 4a illustrates the exploded-view of the lPAW system, which consists of an electronic oscillator circuit board, interface plate, O-rings, lPAW sensors, flow cell, and cover plate (stainless plate).After micropillars are fabricated on the quartz plate, the sensors are gently placed on the top of conducting O-rings in the sensor wells of the flow cell (Fig. 4b).Then PDMS flow cell is pressed on top of the lPAW sensor and sandwiched between the cover plate and the oscillator circuit board of the Discovery-Q system.The electrical signal of the sensors is transmitted to the DAQ unit of the system and analyzed by the in-house software for display and analysis.The metallic cover plate is used to maintain the surface flatness of the PDMS flow cell and prevent leakage using screw-tightening.

Experimental procedure
Sucrose solutions with different concentrations (0.2-50 wt%) were prepared by adding sucrose.
powder to a glass vial (20 ml) on an electronic scale and then adding DI water into the vial.The vial was heated on a hotplate and stirred with a magnetic stirrer at 60 °C for 30 min, and cooled down to room temperature.The experimental setup for carrying out the test consists of the lPAW system, syringe pump, solution containers, and data acquisition (DAQ) components (Fig. 5).The experimental procedure is as follows: (1) DI water is pumped into the sensor well, and the frequency response of sensors is recorded to obtain the baseline; (2) sucrose solutions at different concentrations are driven into the well, and the response frequencies are recorded.The lPAW device was rinsed with DI water and followed by blowing nitrogen gas to dry to remove the residual after each measurement.
All the experiments in this study were conducted at well-controlled room temperature (20 °C) to exclude the unreliable results induced by temperature variation of the solutions.It is worth noting that all the experiments were repeated three times to ensure the repeatability of the measurement results.1)) that the frequency shift of a traditional QCM is linearly related to the density-viscosity of the Newtonian solution as (Kanazawa and Gordon 1985): Figure 6 presents the frequency shift of conventional QCM-F in the stationary sucrose solutions under different concentrations with respect to ffiffiffiffiffiffiffiffiffiffi q L l L p .As can be seen, the frequency shifts between the experimental measurements agree well with the predictions from the Kanazawa-Gordon equation (R 2 = 0.998).It is worth noting that the residual layer (* 3 lm) is so thin that the effect of the layer on the sensor's sensitivity is negligible (Su et al. 2018).In addition, the results indicate that the effect of particle adsorption on the PMMA surface is negligible.

Viscosity measurement of lPAW
Figure 7 presents the responses of lPAW sensors (pillar heights: 6.4 mm, 10.3 mm, 13.9 mm, and 18.1 mm) and QCM-F sensors to sucrose solutions with a concentration range of 10 to 50 wt%.The viscosity and density data of sucrose solutions corresponding to these concentrations are shown in Table 2 (Swindells et al. 1958).As can be seen, all the lPAW sensors show much higher frequency shifts  toward the variations of sucrose solution properties (viscosity and density) than the QCM-F.For instance, QCM-F shows a maximum frequency shift of 11 kHz at 50 wt% sucrose solution, while the shifts of lPAW with a micropillar height of 13.9 mm reached 102 kHz.On the other hand, we also notice that the noise level of the 13.9 mm sensor is higher for the 50 wt% sucrose solution.This is believed to be caused by the low quality factor (Q-factor) and damping of the lPAW near the critical height.The response of lPAW sensors is prone to the effect of nonspecific physical adsorption of particles on the surface.To exclude the impact of particle attachment, a control experiment based on the steady flow (100 ll/min) is conducted for the sensor with a micropillar height of 18.1 mm (Fig. 8a).In this experiment, DI water is injected into the flow cell to obtain the baseline.The sucrose solutions (10-50 wt%) are then flowed through the sensors, and the resonance frequency of lPAW sensors is recorded.At last, DI water is driven to flow over the sensor surface again.It is clear that if there exists a resonant frequency difference between the first and second DI water flows, some particles in the sucrose solutions must attach to the lPAW sensor surface.Figure 8a shows that the frequency shift of the lPAW sensor returned to baseline, which indicates that the

Limit of detection (LOD)
The LOD of lPAW devices was determined by evaluating the response of the sensor at various concentrations near the LOD value and constructing a linear calibration curve (Loock and Wentzell 2012).A series of experiments are conducted to determine the response of QCM-F and lPAW in sucrose solutions with concentrations ranging from 0.2 to 1.2 wt%, and the results are shown in Fig. 9.
The results show that as sucrose concentration decreases, the frequency shifts of the lPAW and QCM-F decrease accordingly.Both lPAW and QCM-F sensors are capable of detecting variations of the solution properties up to 1.2 wt%.The lPAW with 13.9 lm micropillar height shows a frequency shift of 2657 Hz for the 1.2 wt% sucrose concentration, compared to only 32 Hz measured from QCM-F (Fig. 9b).The lPAW is able to measure the variation at sucrose concentration as low as 0.2 wt%, while there is almost no response from QCM-F for sucrose concentration below 0.6 wt%.The obtained analytical LODs based on the linear calibration curve for lPAW and QCM-F sensors are shown in Table 3. Decreasing LOD is achieved by embedding micropillars with QCM compared to QCM-F.It is obtained that the lPAW with 13.9 lm micropillar height has a LOD of 0.054 wt%, compared to 0.54 wt% measured from QCM-F.In addition, lPAW sensors close to critical height can achieve minimum LOD compared to the lPAW sensors out of the ultra-sensitive zone.

Comparison with model prediction
To validate the developed model in Sects.2-3 (Eqs.(2-9)), the predicted frequency shifts of lPAW sensors in air and DI water were compared with experimental measurements (Fig. 10).Overall, the prediction results agree well with the measured values.As can be seen, the critical height of lPAW sensors becomes smaller (13 lm) when the sensors operate in DI water instead of air (15 lm).This is believed to be caused by the induced hydrodynamic loading and the additional mass on the micropillars and QCM surface.In addition, the frequency shift of sensors shows a sudden ''drop and jump'' near the micropillar's critical height due to the coupling of the vibrations of quartz substrate and micropillars.The analytical model successfully captures nonlinear frequency responses with the change of micropillar heights.
Figure 11 shows the model prediction for the frequency shift of lPAW devices in sucrose solutions with concentrations of 10 wt%, 30 wt%, and 50 wt%.As can be seen, the model can successfully capture the dynamics of lPAW operating in viscous solutions.The viscosity of the sucrose solutions can be easily calculated based on the frequency shift of lPAW with the developed model and the density of the solutions.The prediction results agree well with the experimental observations except for the micropillar with 13.9 lm height.This deviation is mainly due to the relatively low quality factor of the micropillar vibration near the critical height resulting in higher measurement errors.Figure 12 presents sensitivity enhancements of lPAW devices (micropillar heights: 6.4 lm, 10.3 lm, 13.9 lm, and 18.1 lm) over traditional QCM-F.The results show that lPAW demonstrates a 20-fold improvement in viscosity measurement due to the resonant coupling between the micropillar and QCM substrate.

Conclusions
A new micropillar-enabled acoustic wave (lPAW) device was developed by fabricating a QCM PMMA micropillars on a QCM substrate to achieve ultrahigh sensitivity for viscosity measurement.Square cross-section micropillars were fabricated on QCM substrates with micropillar heights of 6.4 lm, 10.3 lm, 13.9 lm, and 18.1 lm and tested for measuring the viscosity of sucrose solutions.The results show that the lPAW is able to enhance the sensitivity of traditional QCM as much as 20-fold for viscosity measurement applications.Analyzing the LOD of lPAW and QCM-F reveals that the minimum detectable sucrose concentration using lPAW was 0.054 wt% compared to the traditional QCM, which was 0.54 wt%.The effect of flow conditions on the viscosity measurement of the lPAW device indicated that the frequency response of lPAW is independent of the flow conditions.At last, a theoretical model was developed to analyze the behavior of lPAW in viscous solutions.It is concluded that the viscosity effect on the lPAW devices can be analyzed by a modified twodegree-of-freedom model with additional effective masses.As the viscosity of the solution increases, the mass that is moving by the micropillar increases, leading to a frequency shift of the lPAW device.

Fig. 1
Fig. 1 Modified two-degree-of-freedom model with additional effective masses for lPAW in a viscous solution plate and electronic scale (PM-100, resolution: 0.001g) were purchased from Barnstead Thermolyne Corp. (Ramsey, MN) and Intelligent Weighing Technology (Port Townsend, WA).A frequency measurement system (Discovery-Q) was purchased from Invitrometrix (Lowell, MA).The flow cell of the lPAW system was fabricated by soft lithography.SYLGARD TM 184 Silicone Elastomer Kit was purchased from Dow Inc. (Midland, MI).

Fig. 2
Fig. 2 Flow chart of fabricating PMMA micropillars on QCM quartz substrate )(Wang et al. 2014a;Esmaeilzadeh et al. 2021): (A) preparation of SU-8 mother mold; (B) replica of polydimethylsiloxane (PDMS) transfer mold; (C) filling PDMS mold with PMMA by spin coating; (D) thermal nanoimprinting lithography (T-NIL) to fabricate PMMA micropillars on QCM.After nanoimprinting, a thin residual layer (* 3 lm) was produced between micropillars and the QCM substrate.In addition, a QCM sensor having a PMMA residual layer of the same thickness (* 3 lm) (QCM-F) was fabricated for the purpose of comparison.The micropillars used in this study have a square cross-section with a 10 lm diameter and a 21 lm center-to-center spacing.

Fig. 4 a
Fig. 4 a Exploded view of the lPAW device assembly and b schematic of the flow cell; c actual lPAW device

Fig. 5
Fig. 5 Experimental setup for measuring viscosity using lPAW devices

Fig. 6
Fig. 6 Comparison of experimental results of QCM-F and Bare QCM with the prediction of the Kanazawa-Gordon model

Table 3
LOD of lPAW and QCM-F sensors Fig. 10 Comparison of Frequency shifts of lPAW operating in air and DI with model prediction