Impacts of Liquid Level on Microwave Resonance Sensing with a Flexible Microfluidic Channel

Permittivity sensing based on resonance tracking lays the fundamental principle for a variety of biochemical sensors, which has found vast applications in cancer biomarker detection, antigen‐antibody analysis, and so on. Driven by continuous promotion of the detection limit, precise environmental control highlights its critical importance. Here, the impacts of liquid level on microwave resonance sensing are investigated, in which a flexible polydimethylsiloxane microfluidic channel and soft tubing are employed to control the liquid under test. The hydraulic pressure affects the effective permittivity of the liquid and the channel material, hence causing extra resonance shift signals. Both contactless and contacting sensing scenarios are studied in numerical simulations and experiments. It is demonstrated that the resonance frequency varies sensitively with the liquid level, and a sensitivity of 343 kHz mm−1 is measured. Meanwhile, a spoof localized surface plasmon resonator and its optimized excitation structure are employed and analyzed for a good figure of merit, addressing the detectability difficulties for high‐permittivity and high‐loss aqueous solutions. These results provide general guidelines for understanding and controlling the resonance sensors in aqueous environments and help to realize further lower detection limits.


Introduction
These years have witnessed tremendous progress in the microwave resonance sensing and its vast applications. [1] Compared with optical resonance sensors such as surface plasmons [2,3] and optical microcavities, [4][5][6] microwave resonance sensors which are fabricated on planar printed circuits have shown high robustness to noises and vibrations, and exhibit excellent promises DOI: 10.1002/adsr.202200040 in portable and wearable sensing devices. [1,7] In the booming trend of the Internet of things, the microwave resonance sensors have been investigated to apply in biomedical detection, [8,9] gas concentration sensing, [7] engineering structure monitoring, [10,11] and dielectric material measurements. [12,13] Ultracompact and wireless sensing systems have been constructed and reported, which integrate the microwave resonance sensors with signal detection circuits and Bluetooth modules. [7,14] Both wireless and wired radio-frequency (RF) liquid sensors have been widely investigated. The wireless RF liquid sensors [15][16][17][18] are used for contactless and long-range measurements, but they are susceptible to the spatial electromagnetic wave interferences. The wired RF liquid sensors are more immune to the spatial electromagnetic interferences, [19,20] and more suitable for compact sensing systems.
Among the broad application scenarios, biomedical applications based on the microwave resonance sensors attract the most attention, such as glucose concentration sensing, [8,9,21,22] antigen-antibody analysis, [23,24] single-cell detection, [25] etc. These sensing signals originate from the permittivity changes of the solutions under test, which are caused by the concentration variations of the target biomedical quantities. However, there are some principal difficulties in microwave resonance sensing in aqueous solutions. The relative permittivity of water is extremely high at these low frequencies (80 around 1 GHz at room temperature [26] ), while the refractive index is only around 1.3 at optical frequencies. [27] The relative permittivity values of circuit board substrates at microwave frequencies are commonly between 2 to 5 (for example, 2.2 for Rogers RT 5880, 3.38 for Rogers RO4003C). The large contrast of the permittivity usually weakens the resonance intensities and leads to very shallow peaks. If increasing the resonance intensity with an over-coupled excitation structure, the quality factor (Q-factor) will be lowered. [28][29][30] Meanwhile, the Q-factor and sensitivity of microwave resonance sensors are still unsatisfactory compared with optical resonance sensors. [1,10] In recent years, the concept of spoof localized surface plasmon (SLSP) cuts a good figure in the microwave resonance sensing field. [1] This concept was first proposed by Garcia-Vidal et al. in 2012, which resembles the modal profiles and physical properties of optical localized surface plasmons at microwave and terahertz bands using artificial metallic structures. [31] In 2014, Cui et al. demonstrated that SLSPs can be sustained by ultrathin metallic patterns and made this concept compatible with printed circuit board (PCB) technologies. [1,30,[32][33][34] The features of deepsubwavelength confinement, excellent Q-factors, and high local sensitivity make SLSPs competitive candidates for trace-amount biomedical sensing. [8,9,22,28,[35][36][37][38][39] In 2022, Zhang and Cui reported sub-micromole glucose sensing using an SLSP resonator with an electrical size smaller than 1/40 wavelength and a high Q-factor of 187. [8] With the continuous promotion of sensitivities and detection limits, these sensors can also respond to the environmental distractions sensitively. Hence, precise environmental control highlights its critically important roles. Microfluidic channels are commonly employed to control the inlet and outlet of the solution to build a more controllable environment. [40][41][42][43] Even though, resonance shifts have been reported to present reverse trends varying with the glucose concentration, when the detection limits approach the mg mL −1 level. [9,[44][45][46] These phenomena are inexplicable and indicate that there must be some issues to be addressed to lower any possible signal disturbances or null shifts.
In this paper, we investigate the impacts of liquid level on the microwave resonance sensing with polydimethylsiloxane (PDMS) microfluidic channel, using an elaborately designed SLSP resonator and its excitation structure. Both contactless and contacting sensing scenarios are studied. The permittivity changes of both the liquid and the channel materials responding to the hydraulic pressure will contribute to the resonance shifts of signals. The liquid level can cause the resonance shifts in a sensitivity value as high as 343 kHz mm −1 . The detectability difficulties in aqueous environments caused by the high-permittivity and high-loss water are also addressed, based on the optimized figure of merit (FoM) of the resonances. This paper provides general guides for the basic and important issues of solution controls in resonance sensing and helps to achieve further lower detection limits.

Conceptual Illustration
It is experimentally demonstrated that the microwave resonator can respond sensitively to the liquid level inside a container, where the flexible tubing pumps liquids from or exhausts liquids to. Such an experimental setup was common for resonance sensing working with a microfluidic channel, [47,48] as shown in Figure 1a. A rigid substrate was used in the resonator, which was fastened flat on the table to avoid possible resonance-frequency shifts due to bending. The microfluidic channel attached above the resonator was made of PDMS, which was the most common material for constructing microfluidic channels. A soft tubing was used to connect the inlet and outlet of the microfluidic channel to the syringe and the container to form an enclosed space. The syringe was controlled by a syringe pump to draw water from the container so that the soft tubing and the microfluidic channel were all filled with water. The pump was kept still during measurements to avoid any possible disturbances, and the liquid level was changed using a pipette to draw water from or add water to the container. The two ports of the microstrip line which excited the resonator were connected to a vector network analyzer (VNA) via coaxial cables, to measure the transmittance (S 21 ) spectrum. The resonance frequency can be obtained from the S 21 spectrum, and its shift reflected the effective permittivity around the resonator surface. The pressure at the bottom of the microfluidic channel was related to the pressure at the bottom of the container and varies with the liquid level in the container. (These two pressures were equal in ideal conditions assuming all joints were sealed well.) Increasing the liquid level led to higher pressure on the flexible PDMS microfluidic channel, which simultaneously resulted in smaller volumes and higher densities of both the PDMS substrate and the internal liquid. Both volume and density perturbation effects will cause resonant frequency shifts, and were jointly considered as effective permittivity changes. The illustration of the pressure transmission is shown in Figure 1b. The effects of the liquid level on the resonance frequency via systematic simulations and measurements will be investigated. The results will supply a clear guideline for solution control in similar liquid sensing cases and help to lower the possible distracting signals for further lower detection limits.

Mode Analysis of the Spoof Localized Surface Plasmon Resonator
A spiral-shaped SLSP resonator and its elaborately designed excitation structure were used, which had been proposed to achieve a high Q-factor and enough resonance intensity in ref. [8]. The SLSP resonator was composed of two Archimedean spiral arms of 16 rounds and a central disk with a diameter of 1 mm, as shown in Figure 2a. The width of the spiral arm and the slit between the two arms were both 0.15 mm. The diameter of the whole SLSP structure was around 11.15 mm. It was made up of copper and its thickness was 0.018 mm. Here, the simulated extinction cross section (ECS) of the proposed SLSP resonator is demonstrated in Figure 2b, which was equal to the addition of the scattering cross section and the absorption cross section. The time domain solver of the CST Microwave Studio was employed for the full-wave electromagnetic simulations. In the simulation, the horizontally y-polarized electromagnetic wave was incident along the x-axis. The results showed 5 equally-spaced resonance peaks in the range from 0 to 5 GHz. Figure 2c illustrates the vector magnetic field distributions of the first five modes. These modes were magnetic plasmonic resonances, [8] and were also known as magnetic plasmonic skyrmions. [49,50] Among them, the fundamental resonance frequency was 740 MHz. Figure 2d shows the field distributions of all electric and magnetic components for Mode 1. For Mode 1, the Q-factor calculated from the ECS spectrum was 173.7.

High Figure of Merit for Aqueous Solution Sensing
The SLSP resonator was placed on an F4B dielectric substrate of 0.5 mm thick and integrated with a microstrip transmission line to form an integratable microwave sensor, [8] as demonstrated in Figure 3. The SLSP resonator coupled with a 50 Ω microstrip line to form the top layer of the resonator. A hole was placed on the bottom plane, the radius of which was R. The thicknesses of both the top and the bottom copper layers were 0.018 mm. The relative permittivity of the F4B substrate was 2.65, and the F4B thickness was chosen to be 0.5 mm. Its excitation structure, that is, the hole on the bottom ground plane, had been elaborately designed. The FoM was defined to simultaneously evaluate the resonance bandwidth and the excitation in which Q is the Q-factor, and I is the resonance intensity, that is, the amplitude of the S 21 dip in the linear scale. The optimization of the FoM can be interpreted via the temporal coupled-mode theory (CMT). [12,51] For a resonance mode coupled with two ports as shown in Figure 3, the CMT equation describing the dynamics is where a is the amplitude of the resonance mode, 0 is its eigenfrequency, 1/ 0 is the decay rate caused by the internal loss of the mode, while 1/ 1 and 1/ 2 describe the decay due to power escaping from Ports 1 and 2 respectively. The last two terms in Equation (2) represent the energy that the waveguide can carry into the mode with the traveling wave, and n measures the coupling from Port n to the resonant mode (n = 1 or 2). The power transmits from Port 1 to Port 2 is Thus, the transmittance (S 21 ) is in which 1 = 2 for symmetric resonators and ports.  The R = 0 and R = 7.5 mm cases were analyzed by full-wave simulations and CMT fittings as shown in Figure 3b,c. The parameters were modified from the simulation results. 0 can be considered at the resonance dips, and can be calculated from the bandwidth of the resonances as = 1/2 Δf FWHM . (Δf FWHM is the full width at half maximum calculated from the spectra in the linear scale, which is equivalent to the 3 dB bandwidth but more universal for those cases with resonance intensities smaller than 3 dB.) 0 is achieved by increasing until the CMT fitting curve coincides with the simulated curve. 1 and 2 are fitted from the S 21 curves. The fitted 0 is smaller in the R = 0 case, which means a higher loss. Meanwhile, the simulated power loss den- sity distributions confirm that the internal loss was greater in the R = 0 case than in the R = 7.5 mm case (as shown in the insets of Figure 3b,c). In addition, the lower power loss leads to a higher Q-factor, which is also confirmed by the simulation results. The hole on the ground leads to an efficient excitation of the resonance, that is, a higher resonance intensity. (It is noticeable that the y-axis scales are different in Figure 3b,c, to present both resonances clearly.) The total Q-factor was 157.6 with a resonance intensity of 6.1% for the R = 0 case, while the total Q-factor was 228.7 with a resonance intensity of 68.5% for the R = 7.5 mm case. The parameters used in CMT analysis for both R = 0 and R = 7.5 mm cases are listed in Table 1. The S 21 curves calculated by simulation and fitted by CMT coincided with each other well. The transmittance (S 21 ) spectra under different hole radii were simulated and illustrated in Figure 3d. Figure 3e presents the Q-factors and resonance intensities varying with R. The R = 7.5 mm case was the optimal one which led to the highest FoM. Figure 4 presents the resonances when the SLSP resonator works with the microfluidic channels filled with water, which highlighted the importance of the resonance intensity (i.e., the FoM) in sensing. Figure 4a illustrates the schematic of the resonator with a microfluidic channel adhered to its upper surface. Two sensing cases were considered: One is contactless sensing with an enclosed microfluidic channel, and the other is contacting sensing using an open channel attached to the resonator surface. The geometry of the microfluidic channel of the contactless case is illustrated in Figure 4b. The overall length of the microfluidic channel was 17 mm and the width was 11 mm. It consisted of three parts, of which the base was 0.5 mm thick, the cover was 1 mm thick, and the channel was 0.3 mm thick. The microfluidic channel was made of PDMS, and the substrate separated the liquid to be measured from the resonator surface, to avoid polluting the resonator during the sensing process. In the contacting sensing case, the microfluidic channel was made up of only the cover and the channel layers, without the substrate (as shown in the inset of Figure 4e). The wall of the channel adhered to the resonator surface and the liquid under test will contact the resonator surface. Figure 4c-f show the simulated transmittance (S 21 ) spectra of the SLSP resonator in air and in presence of the PDMS microfluidic channels filled with water, for both contactless and contacting cases when R = 0 and R = 7.5 mm. The permittivity and loss tangent values of PDMS (the relative permittivity PDMS = 2.7, the loss tangent tan PDMS = 0.012) are taken from ref. [52]. The complex permittivity values of water ( liquid = 80, tan liquid = 0.025) are adopted from ref. [53]. The data was interpolated at 400 MHz from the curve figure. The high loss of water and PDMS made the resonances shallow. For the R = 0 cases, the resonances almost disappeared even in simulations. In experiments, such resonances will be smeared in signal ripples. For the R = 7.5 mm cases, the optimized FoM maintained the resonances well when loading high index and high loss liquids. Thus the resonance intensities can be well maintained in real experiments.
The sensing performances of the SLSP resonator (R = 7.5 mm) were simulated for both the contactless and contacting cases, as demonstrated in Figure 5. Permittivity changes of the PDMS and the liquid were considered, both of which responded to the pressure, that is, the liquid level. These simulations lay the theoretical foundations for the experiments in the next section. For the contactless case, the resonance frequency decreased from 423.6 to 422.4 MHz when the liquid permittivity increased from 72 to 80, which meant a frequency shift of 0.28% when the liquid permittivity changed by 10.5%. The resonance frequency decreased from 431 to 414 MHz when the PDMS permittivity increased from 2.5 to 2.9, which meant a frequency shift of 4% when the PDMS permittivity changed by 15%. Hence, the resonator will be more sensitive to the PDMS permittivity rather than the liquid permittivity in contactless sensing. For the contacting case, the resonance frequency decreased from 305 to 294 MHz when the liquid permittivity increased from 72 to 80, which meant a frequency shift of 3.67% when the liquid permittivity changed by 10.5%. For the sensing of liquid, the contacting sensitivity was much larger than the contactless one, since the liquid contacts the resonator directly.

Experiments and Discussion
The experimental setups and measured spectra are shown in Figure 6, in which Figure 6a-c demonstrate the experimental setups. The optimal R = 7.5 mm structure is fabricated and measured. The experimental setup is described in Section 2.1. A soft ruler is used to measure the liquid level in the beaker, sticking it along the wall of the beaker. During measurements, the liquid level is changed using a pipette to draw water from or inject water into the beaker. Other parts of the whole setup are kept still to avoid any possible disturbances and to make the liquid level the only changing factor. The intermediate frequency (IF) bandwidth of the VNA is set to 5 kHz to lower the signal jittering. After preparing the experimental setup, it is crucial to wait for several minutes until the resonance is stable.
The transmittance (S 21 ) spectra measured by the VNA are demonstrated in Figure 6d. For the bare SLSP resonator in air, the measured Q-factor is 187, and the measured resonance intensity is 3.65 dB, which indicates a measured FoM of 72. Attributed to the optimized FoM, these resonances are still well detectable working with the microfluidic channels filled with water, although they deteriorate a lot from those working in air. For the contactless case, a double-sided adhesive tape is used to fix the three-layer PDMS microfluidic (as shown in the inset of Figure 4c) channel on the PCB, and the resonance frequency and the excitation efficiency resemble the simulated results well. For the contacting case, silicone adhesive glue is used to bond the double-layer PDMS microfluidic channel (as shown in the inset of Figure 4e) and PCB. The glue inevitably occupies part of the microfluidic channel (as shown in Figure 6a), the permittivity of which is around 4 and much lower than that of the water. [54] Hence, the measured resonance frequency and measured resonance intensity are much higher than the simulated results. Bonding techniques [55,56] can be used to bond the PDMS mi- Figure 4. The resonances when the SLSP resonator works with microfluidic channels. a) Schematic of the SLSP resonator working in a microfluidic channel. b) Schematic of the three-layer microfluidic channel. Simulated transmittance (S 21 ) spectra of the SLSP resonators working in air and working with a water-filled microfluidic channel, for the c,e) R = 0 and d,f) R = 7.5 mm cases. A three-layer, that is, contactless microfluidic channel is employed in (c) and (d); while a two-layer, that is, contacting microfluidic channel is employed in (e) and (f).
crofluidic channels to the PCB surface and improve the deviations. In the contactless case, the measured Q-factor is 69, the measured resonance intensity is 8.9%, hence the measured FoM is 6.14. In the contacting case, the measured Q-factor is 61.5, the measured resonance intensity is 7.3%, hence the measured FoM is 4.5.
Relative frequency shifts are calculated for further analysis, which can demonstrate the response to the liquid level more clearly than the absolute resonance frequency. Three sets of continuously measured data are analyzed, to avoid distractions during too-long measurement processes. Range error bars are adopted for the data analyses in Figures 7 and 8, which indicate the mean values, the lowest values, and the highest values. [57] MATLAB is used for the data analyses and plotting.
For the contactless case, four sets of experiments are conducted as shown in Figure 7, increasing or decreasing the liquid level in the height range of 1.4-1.9 cm and 6.2-6.7 cm respectively. The resonance frequency increases with the decreas-  ing liquid level, and the SLSP resonator can sense a height variation smaller than 1 mm. Relative frequency shifts subtracting the initial resonance frequencies are used in Figure 7e,f. The relative frequency shifts present good repeatability as indicated by the error bars, although some random factors may change the initial resonance frequencies within a certain range, e.g., the relative position of the microfluidic channel to the resonator center, small bubbles in the channel, etc. Four coefficients of determination (R 2 ) are all greater than 0.96, which indicate good linearities. In the range of 1.4-1.9 cm, the sensitivity is calculated to be 343 kHz mm −1 for the falling case and 336 kHz mm −1 for the rising case using the means of three groups of data. In the range of 6.2-6.7 cm, the sensitivity is calculated to be 137 kHz mm −1 for the falling case and 127 kHz mm −1 for the rising case using the Impacts of the liquid level in the contactless sensing case. Transmittance (S 21 ) spectra are measured when the liquid level a) falls from 1.9 to 1.4 cm, b) rises from 1.4 to 1.9 cm, c) falls from 6.7 to 6.2 cm, d) rises from 6.2 to 6.7 cm, respectively. Fitted lines of the resonance frequency shifts varying with liquid levels e) within 1.4-1.9 cm and f) within 6.2-6.7 cm. The solid lines are fitting results, and the range error bars indicate the means, the lowest values, and the highest values.
means of three groups of data. The sensitivities measured with falling liquid levels are slightly higher than those measured with rising liquid levels. This is attributed to the null blue shifts of this setup. When the liquid level is higher, the sensitivity responding to the liquid level is lower, which is coincident with the common saturation phenomena in resonance sensing. [8,58,59] In the contacting sensing experiment, the pressure can only change the permittivity of the liquid and the PDMS channel walls. The PDMS substrate is removed, which contributes mostly to the sensitivity in the contactless case. Hence, the sensitivity is much lower (as predicted by simulations in Figure 5) and the measurements are conducted in steps of 5 mm as presented  in Figure 8. The linearity is also good and the R 2 values equal 0.9986 and 0.9926 for the falling and rising cases respectively. The sensitivity is 51 and 34 kHz mm −1 for the falling and rising cases using the means of three groups of data respectively. From a large number of repeated experiments, it can be concluded that the effect of pressure on the permittivity of PDMS is greater than that on the permittivity of the liquid. Therefore, the contactless case is more sensitive to the liquid level changes. Meanwhile, the glue occupies part of the microfluidic channel, which further lowers the sensitivity of contacting sensing case to the liquid level. Due to the less sensitivity and smaller frequency shifts in the contacting case, the differences between the falling curve and the rising curve are more obvious. All sensitivities in both contactless and contacting cases are summarized in Table 2.

Conclusion
An SLSP resonator with an elaborately designed excitation structure has been systematically analyzed, which achieves high FoM values when it works with PDMS microfluidic channels filled with water. Full-wave electromagnetic simulations and temporal CMT analysis are used to interpret the mechanism to enhance the FoM for aqueous solution sensing. Both contactless and contacting sensing experiments are carried out to investigate the impacts of liquid level during resonance sensing measurements. We demonstrate that the liquid level greatly affects the resonance frequency, and the highest sensitivity of 343 kHz mm −1 has been measured. These results provide general guides for environment control in resonance sensing with a microfluidic channel, and can help to realize further lower detection limits.