## Materials and Methods  
### Materials and Apparatus  
A high precision 3536 LCR meter (Hioki, Japan) was employed to conduct EIS experiments. An LCR meter is a type of electronic test equipment used to measure the inductance (L), capacitance (C), and resistance (R) of an electronic component. An Uno Wifi board (Arduino, Australia), AD5933 impedance analyzer chip (Analog Devices, Norwood, MA, USA), and an ADG849 switch chip (Analog Devices, Norwood, MA, USA) were used. Form 2 Desktop Stereolithography (SLA) 3D printer (Formlabs, Somerville, MA, USA) was used. Materials of Sylgard 184 Polydimethylsiloxane (PDMS, Dow Corning Corporation, Midland, MI, USA) and calcium calibration buffer kit (Biotium, Fremont, CA, USA) were used. Multi-Sensing Electrode Interdigital Sensor and Electrochemical Impedance Spectroscopy (EIS) Measurement  
In interdigital sensors, the penetration depth of the electric field corresponds to the spatial wavelength of the interdigital sensor [33; 34]. To enhance the penetration depth, interdigitated Micro-electrodes (IDuE) can be fabricated directly on a thin layer of poly(N-isopropylacrylamide) polymer (PNIPAm)-graphene nanoplatelet (GR) composite using a shadow mask with a pre-defined pattern [35]. In this article, planar interdigital sensors with multi-sensing electrodes have been designed and fabricated [36]. Figure 1 shows the configuration of the interdigital sensor. On the top of a single 525 um thick crystal silicon wafer, an over native silicon dioxide (SiO\({}_{2}\)) insulative layer, and a 500 nm gold (Au) layer were sputtered on top of a 22.5 nm Chromium seed layer to provide defect-free adhesion of thin film gold sensors. The dimension of each sensor is 10 mm \(\times\) 10 mm (Figure 1a) with a sensing surface of 2.5 mm \(\times\) 2.5 mm (Figure 1b). The zoom view of the sensing pad shows that electrodes and the gaps between electrodesare all 25-um wide (Figure 1c). Due to the interdigitated nature of the sensors, their working principle was based on capacitive principle. Figure 2a,b show the schematic diagram of the operating principle. The interdigitated electrodes of the silicon sensor were planar in nature to operate in a single-sided and non-invasive manner. Because of this design, when a potential difference as a function of time is applied across the electrodes, the electric field lines would bulge from one electrode to another of opposite polarity. The impedance \(Z\) consists of a real part (resistance, R) and an imaginary part (reactance, \(X\)) that can be written as below:  
\[Z=\mathrm{R}+\mathrm{j}\;X \tag{1}\]  
\(X\) can also be explained based on the capacitance (C) and frequency (\(f\)) as follows:  
\[X=\frac{1}{2\pi fC} \tag{2}\]  
where,  
\[C=\frac{\epsilon_{0}\epsilon_{r}A}{d} \tag{3}\]  
\(A\) is the area of each plate, \(d\) is the distance between the plates, \(\epsilon_{0}\) and \(\epsilon_{r}\) are the dielectric constant of free space and the relative dielectric constant of the material, respectively. If any material was kept in contact or proximity to the electrodes, the field lines penetrate through it. This changes the characteristics of the field lines, which can be studied to simultaneously determine the attributes of the material under test (MUT). In these sensors, the electric field lines penetrate through the liquid flowing through the PDMS-based microfluidic system embedded above the sensing area. Figure 1: The configuration of the interdigital sensor. (**a**) The configuration of the whole sensor with 2 connect pads and one sending pad. (**b**) The configuration of the sensing pad with an area of 2.5 mm \(\times\) 2.5 mm. (**c**) The zoom view on the sensing pad, showing the widths of the electrodes and the gaps between the electrodes are all 25 \(\upmu\)m.  
Figure 2: The schematic diagram of the working principle of the developed sensor prototypes.