*Article* **A One-Dollar, Disposable, Paper-Based Microfluidic Chip for Real-Time Monitoring of Sweat Rate**

**Hongcheng Wang 1, \*, Kai Xu 1 , Haihao Xu 1 , Along Huang 1 , Zecong Fang 2,3 , Yifan Zhang 1 , Ze'en Wang 1 , Kai Lu 1 , Fei Wan <sup>1</sup> , Zihao Bai 1 , Qiao Wang 4 , Linan Zhang <sup>1</sup> and Liqun Wu 1**


**Abstract:** Collecting sweat and monitoring its rate is important for determining body condition and further sweat analyses, as this provides vital information about physiologic status and fitness level and could become an alternative to invasive blood tests in the future. Presented here is a one-dollar, disposable, paper-based microfluidic chip for real-time monitoring of sweat rate. The chip, pasted on any part of the skin surface, consists of a skin adhesive layer, sweat-proof layer, sweat-sensing layer, and scale layer with a disk-shape from bottom to top. The sweat-sensing layer has an impressed wax micro-channel containing pre-added chromogenic agent to show displacement by sweat, and the sweat volume can be read directly by scale lines without any electronic elements. The diameter and thickness of the complete chip are 25 mm and 0.3 mm, respectively, permitting good flexibility and compactness with the skin surface. Tests of sweat flow rate monitoring on the left forearm, forehead, and nape of the neck of volunteers doing running exercise were conducted. Average sweat rate on left forearm (1156 g·m−<sup>2</sup> ·h −1 ) was much lower than that on the forehead (1710 g·m−<sup>2</sup> ·h −1 ) and greater than that on the nape of the neck (998 g·m−<sup>2</sup> ·h −1 ), in good agreement with rates measured using existing common commercial sweat collectors. The chip, as a very low-cost and convenient wearable device, has wide application prospects in real-time monitoring of sweat loss by body builders, athletes, firefighters, etc., or for further sweat analyses.

**Keywords:** wearable device; microfluidic chip; sweat collecting

#### **1. Introduction**

Sweat is known to contain important information corresponding to the status of an individual's health [1]. Sweat production is related to the stimuli underlying body thermoregulation [2]. Secretion of sweat from eccrine glands on the skin surface is an essential means of heat loss in regulating body temperature and for maintaining homeostasis [3] during heat acclimation [4]. Lost body water must be replaced to maintain normal physiologic processes; this is particularly important for body builders, athletes [5], firefighters, etc. Furthermore, sweat, like saliva and tears [6], is noninvasively induced from deeper in the body and carries a diverse array of biomolecules, ranging from small electrolytes (including Na + , K + , and Ca 2+ ) and metabolites (such as glucose, lactate [7], and ethanol [8]) to hormones and larger proteins [9], which may provide vital information about physiological status and fitness level [10]. Sweat analysis could become an alternative to invasive blood tests in

**Citation:** Wang, H.; Xu, K.; Xu, H.; Huang, A.; Fang, Z.; Zhang, Y.; Wang, Z.; Lu, K.; Wan, F.; Bai, Z.; et al. A One-Dollar, Disposable, Paper-Based Microfluidic Chip for Real-Time Monitoring of Sweat Rate. *Micromachines* **2022**, *13*, 414. https:// doi.org/10.3390/mi13030414

Academic Editor: Khashayar Khoshmanesh

Received: 25 January 2022 Accepted: 4 March 2022 Published: 6 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the future [11,12], as Heikenfeld et al. [13] demonstrated—for the first time in vivo—the complete correlation between continuous sweat data and blood data. Collecting and monitoring the rate of sweat production, which is the primary and key step for sweat research, are important for determining body condition and enabling further sweat analyses.

The whole-body wash-down method [14] is an early sweat-sampling technology and well-known as the gold standard for determining whole-body sweat loss, as all sweat runoff is collected. Subjects wearing minimal clothing ride a cycle ergometer in a plastic box. The subject, box, equipment, clothes, and all objects touched by the subject are thoroughly rinsed with deionized water to determine the whole-body sweat loss. However, this method is limited by the controlled laboratory setting, complexity of steps, and single mode of exercise testing; thus, it is not practical for field studies. Patches, composed of an absorbent material with a hydrophilic and porous structure [15], are used for regional skin surface collection and localized sweat sampling. This enables collection of sweat for hours positioned in a specific location [16] (e.g., forearm, thigh, back, or calf), but the collected sweat patch must be peeled off and carefully weighed to obtain the average sweat flow rate. The error rate is relatively high due to evaporation of sweat during the process, and it cannot show real-time flow rate data [17]. In addition, Zhang et al. [18] designed a microfluidic device with one-way-opening chambers and hydrophobic valves for sweat collection and analysis. Pan et al. [19] presented the first digital droplet flowmetry implemented on existing textile substrates for real-time flow rate measurement by counting the number of droplets. Eliot et al. [20] developed a flow rate sensor that easily couples to the outlet of a microfluidic channel to measure flow rate via periodic temporary shorting caused by droplets passing between two electrodes. The device was tested in a dynamic range as low as 25 nL·min−<sup>1</sup> and as high as 9 <sup>×</sup> <sup>10</sup><sup>5</sup> nL·min−<sup>1</sup> . Lindsay et al. [21] designed a skin-interfaced microfluidic system involving multilayered stacks of thin-film polymers that contain intricate microfluidic channels for personalized sweating rate and sweat chloride analytics for sports science applications.

One of the most common current commercial samplers is the Macroduct [22], which consists of a concave disk and a spiral plastic tube that collects sweat. Compared with patches, Macroducts avoid sweat leakage, contamination, and potential hydromeiosis, because the sweat is almost immediately removed from the skin. However, the device cannot be positioned on any position of the human body, so the popularity of Macroducts remains limited. A variety of modified absorbent materials, such as paper [23,24], nonwoven fabrics, textiles [25], cellulosic materials, hydrogels [26,27], and rayon pads [28] are widely used as sweat-collecting carriers. Among these materials, filter paper composed of disorderly stacked cellulose fibers with abundant hydroxyl (-OH) active groups provides high porosity, thus facilitating rapid imbibition of fluid and rendering it a very promising substrate for the immobilization of bioactive substances. Filter paper-based sweat-collecting chips are paper-based microfluidic analytical devices [29] that have generated great interest among researchers due to their portability, low cost [30], versatility, and ease of results interpretation in the analytical area due to their attractive passive movement properties (capillary phenomenon [31]) of analytes without any external forces. These chips show great promise for applications in point-of-care health systems [32], environmental monitoring [33], and food safety.

Most of the above systems, however, have complex structures or require an external collection mechanism, which is not suitable for widespread application or batch production. Paper-based microfluidic chips, which are presented in this article for the first time, can be used for real-time monitoring of sweat secretion rate. The chips, which can be pasted on any part of the skin surface, are low cost and disposable, consisting mainly of filter paper and adhesive tape with a disk shape. Sweat volume can be read directly by scale lines without any electronic elements.

#### **2. Materials and Methods**

#### *2.1. Structure of Paper-Based Sweat Rate Monitoring Chips*

Paper-based sweat rate monitoring chips (P-SRMCs) consist of a skin adhesive layer, a sweat-proof layer, a sweat-sensing layer, and a scale layer from the bottom to top, as shown in Figure 1a. The skin adhesive layer on the bottom, made of medical-grade double-sided adhesive tape (PICARO), is used to attach the chip to the skin surface. A small hole with a diameter of 2 mm in the center serves as the inlet for sweat secreted from the skin. The sweat-proof layer with a center hole the same size as that of the bottom layer hole is made of single-sided transparent adhesive tape (202102022207, DELE) and prevents sweat from penetrating through the double-sided adhesive material to the sweat-sensing layer and ensures that sweat flows through the center hole.

**Figure 1.** Structure of the paper-based sweat rate monitoring chip: (**a**) exploded view showing all layers of the whole chip, including the skin adhesive layer, sweat-proof layer, sweat-sensing layer, and scale layer; (**b**) method for fabrication of the sweat-sensing layer using a 3D-printed mold with a double-spiral structure.

μ The sweat-sensing layer, as the core layer, is used to determine sweat volume. A schematic illustration of its fabrication process is shown in Figure 1b. Paraffin wax (58#, Jinmen Weijia Industro Co., Ltd., Jinmen, China) is heated using a constant-temperature heating device (ET-200, ETOOL) to the melting state of 72 ◦C on a section of glass slide. A mold with two parallel spiral structures 1.5 mm high is printed using a 3D printer (Pro2, Raise3D) with white polylactate as the material. The double spiral structure has a smooth flow path, can form longer channel per area than other designs, and is suitable for a disc-shape sensing chip. The parallel spiral structure is dipped into melted paraffin and then transferred onto a piece of filter paper (102, Aoke, maximum void in the range of 15–20 µm) to form paraffin wax lines (marked in yellow). The two parallel spiral wax lines constitute a micro-channel through which collected sweat travels, because the wax material is incompatible with aqueous sweat and functions as a boundary. The waximpressed, paper-based microfluidic chip is thus one of the most promising methods for future applications because it is inexpensive, easy to use, provides rapid and robust results, and is harmless to human skin [34].

Cobalt chloride solution (AR grade, Chengdu Huaze Cobalt and Nickel Material Co., Ltd., Chengdu, China) with a mass fraction of 0.157 g/mL (0.65 mol/L), which is a good chromogenic agent to H2O molecules, is used as a precursor for the sweat chromogenic agent. The color of anhydrous CoCl<sup>2</sup> changes from blue to red when it absorbs H2O molecules, forming CoCl2·6H2O. Cobalt chloride solution is harmless to human skin surface and the color of CoCl2·6H2O turns back to blue when H2O molecules are removed, which makes the chip possible to be reused if necessary. Cobalt chloride is slowly added to the sweat flow micro-channel using a pipettor. Then the filter paper with CoCl<sup>2</sup> solution

and wax lines is dried for 90 min in a vacuum drying oven (ZKXF-1, Shanghai Shuli Yiqi Yibiao Co., Ltd., Shanghai, China) set at 45 ◦C to remove H2O molecules.

The scale layer, as the top layer, is also made of single-sided transparent adhesive tape. A small hole with a diameter of 2 mm is punched and aligned to the end of the sweat flow channel in the sensing layer. The hole exposed to air is used for releasing increased air pressure caused by the entry of sweat and continuously draws sweat through the micro-channel [35]. In addition to the higher flow rate, the biggest advantage of the small hole for evaporation is that it enables convenient control of the flow rate [36]. By changing the size of the small hole, the flow rate can be easily regulated. The scale, made of red stamp ink (YY01, GSD), is impressed on the reverse side using a mold to avoid the possibility of being removed while the subject is exercising.

The diameter of all four above-mentioned layers is 25 mm and cut by a Laser Cutting Machine (3020, KETAILASER). A piece of P-SRMC is prepared according to the process shown in Figure 1, and the edge of the assembled chip is covered with paraffin wax to prevent external water molecules from affecting the test results. To make subjects more comfortable while doing exercise, the overall thickness of the microfluidic patch was limited to 0.3 mm to enable good flexibility and good compactness against the skin surface.

#### *2.2. Sweat Micro-Channel Parameters*

The ratio of the maximum volume of sweat monitored to the size of the whole chip is the most important index for a wearable device. The whole chip size is determined by the width of the wax line (*w*w) and the sweat channel (*w*c). If the wax line is too narrow, sweat will leak out across it in the filter paper and affect the measured result; thus, a sweat-leaking experiment was conducted to determine the minimum wax width. As to the sweat channel, if the channel is too narrow, the sweat travel velocity will be too slow. Thus, a sweat flow velocity experiment was also conducted to determine the minimum flow channel width. A chamfered fillet structure was applied on the inlet and outlet parts. To minimize the chip size, the shape of the microchannel was designed as a double spiral structure, as shown in Figure 2. In Cartesian coordinates, the equations of two spiral lines on external and internal sides are respectively obtained as:

$$\begin{cases} r = a + b(\theta/2\pi) \\ x = r\cos\theta \\ y = r\sin\theta \end{cases} \tag{1}$$

$$\begin{cases} R = a + w\_w + w\_c + b(\theta/2\pi) \\ \quad \text{x} = R\cos\theta \\ \quad y = R\sin\theta \end{cases} \tag{2}$$

where *r* is the radius of the spiral line on the external side, *R* is that on the internal side, and *θ* is the angle of spiral lines. The differential of *R* and *r* is (*w*<sup>w</sup> + *w*c). *θ*

**Figure 2.** Sweat channel with double spiral structure: (**a**) structure sketch and (**b**) photomicrograph of the wax channel impressed on filter paper using a mold.

#### *2.3. Chip Assembly*

A complete chip fabricated according to the above process is shown in Figure 3. All the assembly steps are conducted under a microscope (3R-MSUSB401, Anyty). Scale lines should be located parallel to and on the lateral side of the wax channel to show the displacement of collected sweat traveling through the channel. The scale spacing is 1 mm, with a range of 0–90 mm. The edge of the chip appears grey in color because all the layers are shaped by a laser cutting machine, and the edge is burned to ashes. This does not affect the chip's ability to collect sweat because the whole edge is covered by paraffin wax to prevent external water molecules from affecting the test results. The assembled chip is dried for 30 min in a vacuum drying oven to thoroughly remove water molecules.

**Figure 3.** (**a**) Photograph of a P-SRMC chip, (**b**) top view, and (**c**) bottom view of the assembled chip.

#### *2.4. Chip Calibration*

μ μ As a type of measuring device, the chip must be calibrated before being tested on the human body. Sweat, drawn from human skin using a suction tube, is added to the chip through the inlet in the scale layer using a pipettor (volume resolution of 0.1 µL). The liquid is added drop by drop with a single drop volume of 1.0 µL. Each droplet should be added after the previous droplet has thoroughly infiltrated into the wax channel by observing the inlet area under a physical microscope. The displacement caused by sweat moving forward along the helix wax channel is recorded via the scale lines after each sweat droplet is added based on the channel with sweat molecules turning from blue to red.

#### *2.5. Testing on Human Volunteers*

Two healthy, active male and female volunteers, 24 years old, participated in indoor running sweat-collecting trials. The weight and height of male candidate are 83 kg and 175 cm, respectively and that of female are 52 kg and 162 cm, respectively. The average room temperature and humidity were 28.9 ◦C and 74%, respectively. The volunteers ran on a treadmill (SH-T5170) under controlled conditions with a running speed of 8.8 kph. When considering localized areas of interest, the choice of sampling area is very important, as it has been reported that sweat rate depends significantly on the sampling location [37]. The sweat-secreting rates on the forehead, nape of the neck, and left forearm are larger than the others on human body. These positions are usually exposed to air while candidates are exercising and suitable for affixing the P-SRMCs. In this study, the chips were positioned on the forehead, nape of the neck, and left forearm, as shown in Figure 4.

A mobile phone (iPhone XR with resolution of 1080p and frame rate of 240 fps), fixed on the left forearm by a designed holder and with its camera aligned with the sensing chip, was used to record video of the sweat-collection process. The displacement in chips on the forehead and nape of the neck were recorded by photos taken every 5 min and then used to calculate sweat volume using Formula (3), as the displacement value can be read from the scale lines. Scientific research shows that it takes about 30 min for an average person to have the best sports effect. So, the testing time is set as slightly longer than 30 min. Sweat rates (υs) are expressed as g·m−<sup>2</sup> ·h −1 , for it is usually calculated in grams per square meter of body surface area per hour.

υ <sup>−</sup> <sup>−</sup>

**Figure 4.** Experimental setup involving a male volunteer running under controlled conditions with chips located on the forehead, left forearm, and nape of the neck.

#### **3. Results and Discussion**

#### *3.1. Sweat Micro-Channel Parameters*

μ A sweat leakage experiment was conducted to determine the minimum wax line width to prevent sweat leaking through the filter paper. 3D-printed molds of different sizes were designed to form wax lines with different widths on the filter paper. Sweat (2.5 µL) was added on the initial site using a pipettor, and the paper was placed on a piece of horizontally situated glass slide to observe leakage using a microscope. As shown in Figure 5, when the width (*ww*) of the wax lines was 0.5 mm and 0.6 mm, the CoCl<sup>2</sup> solution leaked across the wax lines. When the width was no less than 0.7 mm, the wax lines completely prevented leakage. Therefore, 0.7 mm was determined to be the minimum wax width. μ

**Figure 5.** Sweat leakage experiment between neighboring wax lines with different widths: (**a**) mould for wax channels; (**b**) photo of channels with sweat.

The sweat channel width (*wc*) is another important parameter for sweat collection, as it determines the travel rate of the sweat. Although Darcy's law, Lucas-Washburn equation [38], Modifications to Darcy's law and LW equation [39], Richards equation [40], and flow simulation or visualization tools [41] can approximately calculate the micro-fluid flow behavior in paper material, fluid imbibition into paper is a complex process governed by a highly coupled system of length and time-scaled parameters. Therefore, the sweat channel width in filter paper is typically determined by experiment, traditionally called a

trial-and-error strategy. Besides that, capillary flow velocity inner filter paper is determined by pore radius of the porous media in the hydrophilic channel and the size of the channel according to Ref. [42]. The shape of channel bas little effect on flow velocity of sweat if the flow rate is relatively low. The experiment result in straight channel is suitable for spiral-shape ones.

To minimize the chip size, a width of 1.2 mm was chosen as the micro-channel parameter for the final sweat rate monitoring chip. A CoCl<sup>2</sup> solution with a concentration of 0.65 mol/L and total volume of 1.6 µL was deposited in the channel for result visualization. The flow distance was set at 10 mm to calculate the average flow velocity, *υ*. The process of sweat flow in the paper-based wax channel with a width of 1.2 mm is shown in Figure 6 and Video S1 in the Supplementary Material. Figure 7 shows the influence of channel width on sweat flow velocity in straight paper-based channels. The average flow velocity increased rapidly in channel widths set at 1.2 mm, 1.4 mm, and 1.6 mm. More than 70 s (average velocity of approximately 0.14 mm/s) was required for sweat to travel along the channel with a relatively narrow width of 1.0 mm. μ ̅ μ ̅

**Figure 6.** Recordings illustrating the process of sweat flow in a paper-based wax channel with a width of 1.2 mm and displacement of 10 mm.

**Figure 7.** Variation in sweat flow velocity with width of the paper-based channel.

Figure 7 shows average sweat travel velocity data. However, the flow velocity was not constant and decreased slowly because of the increasing flow resistance downstream in the micro-channel. Therefore, flow displacement in a paper-based wax channel with a width of 1.2 mm was recorded at different times, and the results are shown in Figure 8. The velocity was relatively high near the sweat inlet site then decreased until displacement was less than approximately 7 mm and finally became approximately constant. The reason the velocity decreased in the first section is that CoCl<sup>2</sup> crystal particles were scoured downstream by sweat flow, causing an enrichment that increased the flow resistance. The experiment results show that sweat with a volume of 2.5 µL filled the paper-based channel in approximately 60 s. μ μ

**Figure 8.** Record of sweat flow displacement in a paper-based wax channel with a width of 1.2 mm.

#### *3.2. Chip Calibration Results*

μ In chip calibration experiments, it is time-consuming to completely fill the wax channel with sweat drop by drop. A record of sweat traveling through a certain piece of P-SRMC chip during the calibration process is shown in Figure 9. The color of the channel through which the sweat travels changed from blue to red. The scale in red shows the displacement of sweat as it travels. As shown in Video S2 in the Supplementary Material, it takes each 1-µL sweat droplet approximately 5 min on average to infiltrate the wax channel completely. The time required by latter droplets is longer than that of former droplets because of the gradually increasing flow resistance as drops are added. μ

**Figure 9.** Calibration of a P-SRMC.

Ten samples of sweat colleting chips were tested to obtain an average result and determine their consistency. As shown in Figure 10, the displacement of sweat moving forward along the spiral wax channel was recorded using the scale lines after different volumes of sweat were added from the chip inlet. μ

2

0.29 8.97 1.88 (0 13.4)

**Figure 10.** Second-order fitting curve for the variation in displacement with added sweat volume determined using scale lines.

A second-order fitting, as is shown in Formula (3), was carried out on the variation:

$$y = -0.29\mathbf{x}^2 + 8.97\mathbf{x} + 1.88 \ (0 < \mathbf{x} < 13.4) \tag{3}$$

μ where *y* is displacement (mm) and *x* is the volume of sweat (µL). The relative variance was ~10%.

0.58 8.97 According to the experimental result, the maximum volume of sweat collected in a single chip is above 14 µL, and the sensitivity (s) can be calculated by:

$$\mathbf{s} = \frac{dy}{d\mathbf{x}} = -0.58\mathbf{x} + 8.97\tag{4}$$

The sensitivity decreases gradually with increasing volume of sweat collected. Figure 10 shows that it reaches a maximum value of 8.97 mm·µL −1 .

#### *3.3. Testing Results Using Human Volunteers*

The displacement caused by sweat moving forward was read using the scale lines on the sweat-collecting chips locating on the left forearm, forehead, and nape of the neck of the human volunteers, as shown in Table 1. The sweat secretion velocity on male candidate is faster than that on female candidate. Photographs of P-SRMC changing color on male skin surface are shown in Figure 11. The time interval for the recording was 5 min. Video of sweat traveling through the chip on the left forearm of male candidate was recorded using a mobile phone, as shown in Video S3 in the Supplementary Material. The values were consequently converted to volume of sweat collected using Formula (3). According to the shape of the above fitting function, the smaller of the two solutions for the unitary quadratic equation is the sweat volume. The conversion results for each displacement of sweat traveling through the chip are shown in Figure 12.


2

0.29 8.97 1.88 (0 13.4)

0.58 8.97

μ <sup>−</sup>

μ

**Table 1.** Record of test results for human volunteers.

μ

**Figure 11.** Photographs of P-SRMC changing color on the (**a**) left forearm, (**b**) forehead, and (**c**) nape of the neck taken every 5 min while the volunteers was running on a treadmill.

**Figure 12.** Flow rate of sweat collected from (**a**) the left forearm, (**b**) forehead, and (**c**) nape of the neck measured using the P-SRMC.

The test results showed that the relationship between volume of sweat secreted from the left forearm, forehead, and nape of the neck and running time was approximately linear. In other words, the sweat secretion velocity is approximately uniform. Considering that the diameter of the sweat-collecting inlet is 2 mm, the flow rate per area can be calculated. However, during the experiment, some sweat is converted into vapor around the chip, as the temperature of the skin surface at the measurement site is much higher than that of the ambient environment. The sweat vapor formed close to the inlet hole will seep into the sensing layer and cause the experimental result to be greater than the actual value. To minimize this effect, the correction coefficient *δ* was calculated for the collecting area and set as 2. Therefore, the collecting area (*A*<sup>c</sup> = 4π mm<sup>2</sup> ) is twice that of the inlet hole diameter.

> *δ* π

> > − −

*f*

−

μ <sup>−</sup>

μ <sup>−</sup> μ <sup>−</sup>

μ <sup>−</sup> <sup>−</sup>

Among the three measured sites, the forehead had the highest average sweat secreting velocity (*V<sup>f</sup>* ), 0.33 <sup>µ</sup>L·min−<sup>1</sup> , which is the slope of the fitted straight line in Figure 12b. The flow velocity per area for the forehead position was calculated using Formula (5) and equaled 0.026 <sup>µ</sup>L·mm−<sup>2</sup> ·min−<sup>1</sup> .

$$R\_f = \frac{V\_f}{A\_c} \tag{5}$$

Sweat rate is usually calculated in grams per square meter of body surface area per hour. Therefore, the rate of sweat secretion from the forehead position was 1734 g·m−<sup>2</sup> ·h −1 if we assume that the density of sweat is 1.1 g·cm−<sup>3</sup> . The test result showed good agreement in order of magnitude with that measured using absorbent pads [43] and Macroduct [22], which are common commercial sweat collectors for determining sweating rate. As shown in Figure 12a,c, the sweat secretion velocity on the left forearm (*V*arm) and nape of the neck (*V*nape) was 0.22 <sup>µ</sup>L·min−<sup>1</sup> and 0.19 <sup>µ</sup>L·min−<sup>1</sup> , respectively. The secretion rates for the above two positions were 1156 g· <sup>m</sup>−<sup>2</sup> ·h <sup>−</sup><sup>1</sup> and 998 g·m−<sup>2</sup> ·h −1 , respectively. Therefore, the sweat rate of the left forearm was much lower than that of the forehead and greater than that of the nape of the neck for regional variations in human eccrine sweat gland density and local sweat secretion rates during the thermal loading in exercising individuals [44].

#### **4. Conclusions**

This paper describes a low-cost, disposable, paper-based microfluidic chip for realtime sweat secretion rate monitoring. The chip consists primarily of a skin adhesive layer, a sweat-proof layer, a sweat-sensing layer, and a scale layer with a disk-shape from the bottom to top. Double spiral wax lines impressed in a piece of filter paper using a mold serve as the micro-channel through which the collected sweat travels. The micro-channel is pre-filled with a chromogenic agent to show displacement of the sweat as it travels, so sweat volume can be read directly using scale lines without any electronic elements. The diameter and thickness of the whole chip are 25 mm and 0.3 mm, respectively, which allows for good flexibility and good compactness with the skin surface. Tests of sweat flow rate monitoring on the left forearm, forehead, and nape of the neck of human volunteers during running were conducted. The average sweat secretion rates of the three positions were 1156 g·m−<sup>2</sup> ·h −1 , 1710 g·m−<sup>2</sup> ·h −1 , and 998 g·m−<sup>2</sup> ·h −1 , respectively, in good agreement with values measured using existing common commercial sweat collectors. The P-SRMC chip, as a very low-cost, disposable, and easily fabricated wearable device, has a wide range of potential applications in real-time monitoring of sweat loss for body builders, athletes, firefighters, etc., or for further sweat analyses.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/mi13030414/s1, Video S1: Sweat flow process in paper-based channel with width of 1.2 mm; Video S2: Calibration of sweat rate real-time monitoring chip; Video S3: Test of sweat flow rate monitoring on left forearm of a male volunteer doing running exercise.

**Author Contributions:** H.W. conceived the idea and wrote the paper. K.X. designed the experiments, performed the experiment, and analyzed the experiment data. H.X., A.H., Y.Z., Z.W., K.L., F.W. and Z.B. performed the experiment. L.Z., L.W. and Q.W. provided scientific support and conceptual advice. Z.F. revised the paper. All authors discussed the results and commented on the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Natural Science Foundation of China (11902107), Zhejiang Provincial Natural Science Foundation of China (LY21A020009, LY21F040005), National Natural Science Foundation of China (52175460), and Fundamental Research Funds for the Provincial Universities of Zhejiang (GK219909299001-412). ZF would like to acknowledge the support from the Shenzhen Engineering Laboratory of Single-Molecule Detection and Instrument Development (XMHT20190204002) and the Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao (51929501).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available from the corresponding author, H.W, upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


#### **References**


### *Article* **Microfluidics Temperature Compensating and Monitoring Based on Liquid Metal Heat Transfer**

**Jiyu Meng <sup>1</sup> , Chengzhuang Yu 1 , Shanshan Li 1,2, \* , Chunyang Wei 1 , Shijie Dai 1, \*, Hui Li <sup>1</sup> and Junwei Li 3, \***


**Abstract:** Microfluidic devices offer excellent heat transfer, enabling the biochemical reactions to be more efficient. However, the precision of temperature sensing and control of microfluids is limited by the size effect. Here in this work, the relationship between the microfluids and the glass substrate of a typical microfluidic device is investigated. With an intelligent structure design and liquid metal, we demonstrated that a millimeter-scale industrial temperature sensor could be utilized for temperature sensing of micro-scale fluids. We proposed a heat transfer model based on this design, where the local correlations between the macro-scale temperature sensor and the micro-scale fluids were investigated. As a demonstration, a set of temperature-sensitive nucleic acid amplification tests were taken to show the precision of temperature control for micro-scale reagents. Comparations of theoretical and experimental data further verify the effectiveness of our heat transfer model. With the presented compensation approach, the slight fluorescent intensity changes caused by isothermal amplification polymerase chain reaction (PCR) temperature could be distinguished. For instance, the probability distribution plots of fluorescent intensity are significant from each other, even if the amplification temperature has a difference of 1 ◦C. Thus, this method may serve as a universal approach for micro–macro interface sensing and is helpful beyond microfluidic applications.

**Keywords:** heat transfer; microfluidics; liquid metal; measurement; temperature monitoring; PCR

#### **1. Introduction**

In recent decades, advances in microfabrication techniques have led to the development of a wide variety of microfluidic devices [1–3]. For many microfluidic applications, the knowledge of the temperature field is of high technical and scientific importance [4,5]. However, it remains challenging to obtain accurate temperature data of the microfluid limited by size effects, such as manufacturing process and sensor accuracy [6,7]. Conventional high-precision types of equipment or temperature sensors suffer from expensive costs, professional operation, and poor interference immunity. With the development of micro-electro-mechanical systems (MEMS), while numbers of research on the measurement and calibration of microfluidics temperature have been conducted [8–10], a unified and systematic theory is still ambiguous. Therefore, the study on the microfluidic heat transfer characteristics and temperature calibration is kept hot [11–13].

Two main methods have been reported for the microfluidics temperature measurement [14–16]: direct contact and non-direct-contact temperature measurement. Generally, the temperature can be accurately recorded, but the inherent temperature of the targeted micro fluids will be affected via external macro instruments by contact measurement. There is no heat exchange via measurement tools of the non-contact method, which make it

**Citation:** Meng, J.; Yu, C.; Li, S.; Wei, C.; Dai, S.; Li, H.; Li, J. Microfluidics Temperature Compensating and Monitoring Based on Liquid Metal Heat Transfer. *Micromachines* **2022**, *13*, 792. https://doi.org/10.3390/ mi13050792

Academic Editors: Junfeng Zhang and Ruijin Wang

Received: 26 April 2022 Accepted: 17 May 2022 Published: 19 May 2022

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difficult to achieve high accuracy by utilizing the changes in the physical properties of the target object.

For contact temperature measurement, the heterojunction structure of thermocouples with micro or even nano-size can be directly applied to the thermometry of microfluid [17–19]. However, we must suffer from damage and vibration when operating such a thin and cuspate thermocouple probe, which does not meet the requirements of high reliability and ease of use. In addition, micron or sub-micron platinum film thermal resistance is also used as an essential method for microfluidic temperature measurement [20,21]. However, it must be attached to a substrate, so it is not suitable for measuring the temperature of a small volume. As active devices, their self-heating effect caused by power may influence the micro-scale temperature distribution. The emerging carbon nanotube technology measures the volume expansion of gallium in carbon nanotubes to read temperature changing [22,23], similar to a micro-nano-scale mercury thermometer. It can be applied to microfluidic temperature measurement, but the accuracy is not high.

Due to the limit of resolution, the mainstream non-contact infrared thermal imaging temperature measurement technology cannot be directly used for microfluidic temperature measurement [24]. In recent years, optical imaging technology has been a powerful means to explore the temperature distribution of microfluidics [25,26]. For example, the temperature change can be characterized by the fluorescence intensity of temperature-sensitive fluorescent dye added to the microfluid [27]. However, reference image comparison is required, and there is considerable system uncertainty, which is susceptible to the effects of cross-color in the optical path. In addition, quantum dots have become a kind of optical temperature measurement materials with development potential due to their advantages of small size, good light stability, and high plasticity [28]. However, its size and shape distribution depending on temperature will cause uneven light emission. In addition, the polymer polyacrylamide can be used as a measure of micro-scale temperature due to its structure variation with temperature [29]. The temperature sensing range can be adjusted by combining reactive polymers with fluorophores. However, polymer-based measurement is relatively slow and unsuitable for real-time temperature monitoring.

In recent years, more and more microfluidic heat transfer principles have been explored and studied to use indirect methods to invert the microfluidic temperature [30]. For example, winding copper wire around a microfluidic pipe as a temperature change resistor to measure microfluidic temperature [31], but the effect of heat transfer from the pipe material is not considered. Color-changing temperature-sensitive materials can monitor microfluidic temperature changes [32], but it is generally effective only for a specific temperature value and have a very narrow range of application. Additionally, liquid metals with low melting points have been widely studied as high thermal conductivity and easy-to-handle materials in microfluidic heat transfer [33]. Liquid metals can be used as thermal conductive media connecting the microscopic and macroscopic to achieve a coefficient of temperature conversion.

In this work, a novel indirect temperature measurement method integrating platinum resistance millimeter-scale industrial sensor and liquid metal has been demonstrated to measure and monitor microfluid temperature in a microfluidic chip channel. With this method, the close contact between the sensor and microfluid is avoided, and it is user-friendly and repeatable. First, the relationship between the chip substrate and the microfluid temperature has been studied. Numerical simulation proves that the temperature of the top surface of the glass substrate is the same as the fluid in the microchannel that contacts it. Therefore, we measure the glass surface temperature to characterize it as the targeted fluid temperature. We then punch holes at the designed position that avoid the microchannels, place temperature sensors to contact the top surface of the glass substrate, then fill liquid metal packaging. The aperture is optimized to achieve the best temperature measurement effect, and the function compensation relationship between the measurement temperature and the microfluid in the range of 30–100 ◦C is calibrated. In addition, a highly temperature-dependent isothermal amplification PCR experiment

was presented to prove the temperature measurement validity of this method. The results show that this measurement and compensation method has great potential in microfluidic temperature monitoring.

#### **2. Materials and Methods**

#### *2.1. Chip Design and Sensor Installation*

Before conducting the numerical optimization studies, the temperature depended PCR chip is performed to validate the physical structure. Here, we present an S-shaped microchannel design that incorporates two inlets introducing two streams for reagent mixing. A through-hole is arranged on the corner, as shown in Figure 1a, which provides the design details of the proposed microfluidic chip. The microchannel consists of a rectangle cross-section channel, 100 µm wide and 30 µm deep, together with an S-shape unit at the central part, which makes the reagent mix more evenly. A circular view area is on the straight microchannel before the exit and one single outlet downstream for postprocessing. μ μ

**Figure 1.** Illustration of the temperature depended on the PCR device, including a piece of PDMS replica bonded with a glass slider, a heater, and a PT100 sensor. (**a**) The full view of our device. The PDMS replica has 2 inlets, 1 outlet, and a through-hole. The PT100 was inserted into the through-hole to measure the temperate of the top surface of the glass slide. The heater was put under the glass substrate. (**b**) Illustration of the packing for PT100 (**i**) w/o and (**ii**) with liquid metal deposited in the through-hole.

Figure 1b shows the basic concept for sensor installation. First, a sensor is arranged to the hole to ensure its sensitive components contact with the top surface of the glass slide, as shown in Figure 1b(i). Moreover, to ensure that the sensor is in complete contact with the glass surface, the liquid metal is used to fill the gap around the sensor in the hole, as shown in Figure 1b(ii). A relative precise temperature value can be recorded by this method.

#### *2.2. Chip Fabrication*

Here, the microfluidic channel with suitable patterns is fabricated using standard soft lithography methods previously reported [34,35]. Briefly, the AutoCAD 2018 is used to design the photomasks of the electrode and channel, and then the layout is printed by a commercial high-resolution inkjet printer. Next, the SU-8 photoresist or photosensitive dry film is coated onto the silicon substrate, followed by a pre-bake, exposure, development, as well as the post-bake process to fabricate the mold master. Then, the polydimethylsiloxane (PDMS sylgard 184, Dow Corning) is cast on the mold master and cured at ~80 ◦C for 1~2 h. After that, the PDMS channel containing the imprint is detached from the mold master and punched to fabricate the inlets, outlets, and through-hole.

The glass slide is soaked in acetone for 20 min, rinsed with isopropyl alcohol and DI water each for 15 s, and then dried with an air gun. PDMS block mentioned above is bonded with a glass surface after plasma treatment by a plasma machine (PDC-MG, PTL Technology Co, Ltd., Shenzhen, China). The plasma treatment and bonding procedure are in four steps: a. Put PDMS block with the channel side exposed and cleaned glass slide into the plasma bonding machine. b. Vacuum the machine to a pressure value of about 100 Kpa. c. Turn on plasma high voltage discharge and last 40 s. d. Take out the PDMS block and bond it to the glass slide in time to avoid surface contamination or denaturation.

#### *2.3. Reagent Preparation*

The kit for duck-derived gene detection (including dry powder reagent tube, R buffer, B buffer, and positive gene template) was purchased from Anpu Biotech Co., Ltd. (Changzhou, China). The best amplification temperature of this reagent is 39–41 ◦C, and the reaction time takes 20 min. Before the experiment, it is necessary to add 45 µL R buffer, 2.5 µL positive gene template, and 2.5 µL B buffer to the dry powder reagent tube in sequence. Then, mix the reagents evenly on the rotating table. It should be noted that the entire reagent preparation process needs to be carried out in a fume hood and on an icebox to prevent air pollutants and high temperatures from affecting the reaction system. After the reagents are prepared, store them at 0–4 ◦C for later use, and keep the remaining reagents in a refrigerator at −20 ◦C. μ μ μ −

#### *2.4. Temperature Calibration and Solution Delivery*

A transparent tempered glass heater (SAPPHIRE SC-6100, TY154, Merip Technology Co, Ltd., Nanjing, China) is used to provide a heat source for the microfluidic chip, so that the bottom surface of the microfluidic chip has a constant temperature, as shown in Figure 2, and the temperature error of the heater is 0.1 ◦C. The platinum resistance temperature sensor (PT 100-2mm, Sensite, Beijing, China) is encapsulated in the through-hole of the PDMS block with glue together, packaging liquid metal to measure the temperature of the upper surface of the glass slide and record the data, as shown in Figure 2. In addition, a high-precision thermocouple temperature sensor (tt-k-40-36, Omega, New York, NY, USA) is packaged inside the microchannel to measure and record the temperature data of the microfluid. Then, we make a compensation function for the temperature relationship between the two mentioned above. According to the function calculation, the glass surface temperature can be used to characterize the temperature of the microfluid, avoiding the use of precision thermocouples.

**Figure 2.** Photo of our microfluidic device mounted on a miniaturized heater. The high-precision smart thermocouple was used to measure the temperature of the fluid within the microchannel. The industrial PT100 sensor inserted into the through-hole was to detect the top surface of the glass slide. Gallium liquid metal was used to fill the gaps between PT100 and the through-hole.

In order to quantify the performance of the temperature measurement, a PCR amplification experiment that was highly dependent on the temperature is present. Here, two streams of aqueous reagent are pumped through the inlets with separate, independently controlled programmable flow pumps (PC1, Elveflow, Paris, France) to form a laminar flow at the very beginning of the chip. Then laminar fluids flow through the S-shaped channel, ensuring more effective reagent mixing [36]. When the fluid fills the channel, the heater is carefully adjusted to a specific temperature and lasts 20 min. Then observe the fluorescence effect by a microscope (Eclipse Ti-s, Nikon, Tokyo, Japan) in the view area downstream of the microchannel.

#### **3. Numerical Analyses**

#### *3.1. Control Equation and Boundary Condition Settings*

The physical field modules of the heat transfer in solids and fluids and events are used for simulation.

3.1.1. Heat Transfer in Solids and Fluids

Energy conservation equation:

It is assumed that it is all heat transfer between solid and fluid, the energy conservation equation is given by,

$$
\rho V \mathbf{C}\_p \frac{\partial T}{\partial t} + \nabla \cdot (-Vk \nabla T) = Q\_0 \tag{1}
$$

where *ρ* is the density of the applied material, *V* is the volume of the heated object, *Cp* is the capacitance measured at constant pressure, *k* is the thermal conductivity, *Q*<sup>0</sup> is the energy generation rate for the whole system.

In order to simulate the temperature control of the heater, a constant power *p*<sup>0</sup> and a status indicator StateHeater (set in Event interface) are selected as thermal energy source, the energy generation rate is set as,

$$Q\_0 = p\_0 \times \text{StateHeater} \tag{2}$$

It is assumed that the bottom of the heater is thermal insulation, the boundary condition can be set as,

$$n \cdot (-k \nabla T) = 0 \tag{3}$$

It is assumed that the outside of the system is heat dissipated by natural convection, the convective heat flux should be given by,

$$n \cdot (-k \nabla T) = h\_{\mathbb{C}}(T - T\_0) \tag{4}$$

where *h<sup>c</sup>* is the natural convection heat flux coefficient, *T*<sup>0</sup> is the ambient temperature. The radiant heat flux of the system to the ambient can be set as,

$$m \cdot (-k \nabla T) = \varepsilon \sigma \left( T^4 - T\_0^4 \right) \tag{5}$$

where *ε* is the emissivity of the material, 0 < *ε* < 1, *σ* is the Stefan–Boltzmann constant.

There is contact heat loss between the heating block and the glass slide, which mainly includes contact and gap thermal resistance, which can be expressed as

$$n \cdot (-k \nabla T) = h \left( T\_{down} - T\_{up} \right) + rQ\_0 / A\_l \tag{6}$$

where *r* is the heat partition coefficient.

$$h = h\_{\text{contact}} + h\_{\text{gap}} \tag{7}$$

The heat transfer coefficient of thermal contact resistance is closely related to the surface roughness, microhardness, and contact pressure of the material. It should be expressed as [37],

$$h\_{\text{contact}} = 1.25 k\_{\text{contact}} \frac{m\_{\text{asp}}}{\sigma\_{\text{asp}}} \left(\frac{P}{H\_{\text{c}}}\right)^{0.95} \tag{8}$$

where *kcontact* is the thermal conductivity of materials in contact, *masp* and *σasp* are the asperities average slope and height surface roughness, respectively. *P* is contact pressure between the heater and glass slide. *Hc* is the microhardness of the glass.

The gap thermal resistance is related to the gas type and contact pressure between two contacting objects. Still, there is no specific expression function yet, and the value range can be checked.

#### 3.1.2. Events

The Event interface is used to control the temperature of the heater to simulate closedloop PID control. First, the steady-state error is defined as *Terror* = 0.1 K. First, the discrete state of the Event is defined as StateHeater = 1, and the given power *Q*<sup>0</sup> = *p*<sup>0</sup> × State-Heater, then heating starts. When heating to the upper limit of the target temperature, *T* > *Terror* + *Ttarget*, at this time StateHeater = 0, stop heating. When the temperature drops to *<sup>T</sup><sup>t</sup>* <sup>&</sup>lt; *<sup>T</sup>targe* <sup>−</sup> *<sup>T</sup>error*, the heater starts working again, StateHeater = 1. The state function can be set as, x ൏ −

௧௧ ௦ ௦

$$\text{StateHeater} = \begin{cases} \begin{array}{c} \begin{array}{c} T \leq T\_{\text{target}} + T\_{\text{error}} \\ \downarrow \end{array} \\ \begin{array}{c} T > T\_{\text{error}} + T\_{\text{target}} \\ \downarrow \end{array} & \begin{array}{c} \begin{array}{c} \begin{array}{c} \begin{array}{c} T \end{array} \end{array} \end{array} \end{array} \end{cases} \end{(1)}$$

After state (1) reaches its peak, states (2) and (3) act cyclically to stabilize the temperature. Feedback temperature is taken from the integral temperature of the circular sensor on the heater, as shown in Figure 3a. The simulation domain and boundary condition settings are shown in Figure 3a.

**Figure 3.** (**a**) Boundary condition settings of the microfluidic heating system. (**b**) The temperature field of the microfluidic heating system. Here the target temperature is 60 ◦C and d1/d<sup>2</sup> = 2. (**c**) The real-time temperature of the heater, glass, and microfluid with different hole sizes. Here the heating power is 30 W. (**d**) The experimental steady-state temperature as a function of d1/d<sup>2</sup> .

#### *3.2. Parameter Settings in the Simulation*

Since the structure of the 3D model is relatively regular and has similar vertical sections, here we did not propose an actual 3D model to calculate the heat transfer process. For simplicity, we presented a longitudinal cross profile 2D numerical model herein. The heat transfer model is conducted using commercial finite element software COMSOL Multiphysics 5.4. The model discretization and grid independence, as well as convergence

solving methods, are shown in the Supplementary Material, including a discrete grid for the simulation model (Figure S1), numbers of the domain and boundary elements in different element sizes (Table S1) and grid independence verification (Figure S2). The physical and geometry parameters in our study are set as the same as those in experiments, as listed in Table S2 in Supplementary Materials.

#### **4. Results and Discussion**

#### *4.1. Effects of Aperture on Temperature Measurement*

The temperature signal measurement by platinum (Pt) resistance sensor is contact conduction via energy. The heat transfer capacity for ambient materials placed adjacent to the sensor has a significant influence on receiving feedback signals. First, we put the Pt sensor directly into the hole, get as close as possible to contact the top surface of the glass slide, then seal it with gel. For instance, making the aperture of the hole equal to twice that of the sensor, and setting the target temperature is 60 ◦C. The numerical result shows the temperature distribution of the 2D microfluidic chip heat transfer system in Figure 3b. It can be seen that the temperature gradient on the heater is not visible to the naked eyes due to the excellent performance for heat transfer of aluminum products. The temperature distribution on the vertical profile of the glass slide presents a slight bottom-up temperature gradient and a lower overall temperature than the heater. Two reasons cause the loss of energy: convection heat dissipation between the top surface of the glass slide and the ambient soft-temperature air; contact heat resistance between the bottom surface and the heater. Further, the microfluidic temperature, on which visual appearance, is almost the same as that of the top surface of the glass slide. However, the temperature traversing the vertical profile of the PDMS block decrease clearly and gradually from bottom to top due to the character of low thermal conductivity of PDMS and great convective heat flux presented on the top layer. The temperature appears to be the weakest at the corners caused by concurrent heat flux on both the top and side surfaces. In addition, the temperature measured by the Pt sensor on the top surface of the glass slide is almost uniform and slightly lower than that covered by the PDMS block. The intrinsic heat conduction of the Pt sensor, air, and sealing gel results in a decrement in temperature.

The heat transfer time-dependant process can be decomposed as follows. First, the temperature of the heater rises to the steady-state status within 1 min heating by 30 W power with ±0.1 ◦C error, as shown by the black solid curve in Figure 3c, which is consistent with the control method utilized in the experiment. The temperature of the top surface of the glass slide rises to the stable target later than that of the heater due to the thermodynamic hysteresis effect, as shown by the solid red curve in Figure 3c. It almost simultaneously reaches a stable status compared to microfluidic temperature with the top surface temperature of the glass, and the difference in the steady value is negligible, as shown by the blue star marks in Figure 3c. Therefore, the microfluidic temperature can be an equivalented substitute to that of the top surface of the glass slide. The Pt resistance sensor is used to sense the temperature of the top surface of the glass slide by packaging it in a cylindrical hole through the PDMS block. Actually, the feedback temperature via the Pt resistance sensor is later and lower than that of the top surface of the glass slide. The stable temperature changes regularly with the aperture, as shown by dotted curves in Figure 3c. When the aperture (d1) is equal to the diameter of the Pt resistance sensor (d2), that is d1/d<sup>2</sup> = 1, the pieces of the PDMS block in contact with the Pt resistance sensor carry away the heat making the temperature measured by the sensor much less than that of the top surface of the glass slide. The feedback temperature of the Pt resistance sensor gradually increases as the aperture duo to the contact between the sensor and PDMS has been blocked by air with relatively high thermal conductivity blocks. The feedback temperature is not monotonically increasing with the continued expanding aperture but will eventually stabilize at a certain value, as shown in Figure 3d. This phenomenon is caused by the balance of heat transfer and dissipation around the sensor. Since the error value is ±0.1 ◦C, the measured temperature of the sensor will reach a stable value when

d1/d<sup>2</sup> = 2.5. The average steady-state temperature is calculated as 58.08 ◦C. In order to facilitate the hole processing and sensor packaging in the experiment, take d1/d<sup>2</sup> = 3 for experimental research.

#### *4.2. Liquid Metal Filled and Experimental Temperature Calibration*

It is hard to make a Pt resistance sensor repeatedly be placed closely in a giant hole, which should affect the accuracy of the feedback signal. In order to ensure that the sensitive elements of the sensor are entirely in contact with the top surface of the glass slide, meanwhile, away from the PDMS block, liquid metal with high thermal conductivity and flexibility is used to fill the gap between the cylindrical hole and the Pt resistance sensor. In this way, the measurement accuracy of the sensor gets significant improvement. As shown in the double *y*-axis plot in Figure 4a, when the hole is, the temperature distribution of the sensor has become uniform with liquid metal filled in the gap, and the steady-state temperature is higher than that of air that exists. When the steady-state temperature is reached, the average measured temperature difference between the filled liquid metal and air medium is about 0.5 ◦C, which is five times the allowable error.

**Figure 4.** (**a**) The temperature (left *y*-axis) and temperature difference (right *y*-axis) as a function of time, with the condition of with and without liquid metal filled in the gap. Here d1/d<sup>2</sup> = 3. The theoretical, simulated, and experimental temperature of glass surface (**b**) and microfluid (**c**) with the set temperature in a range of 30–100 ◦C. (**d**) The comparison of experimental temperature between the glass surface and microfluid. Here the average temperature error is 1.74%.

There were three times experimental measures were performed to record the steadystate temperature value of the top surface of the glass slide in five different locations within the range of 30–100 ◦C. The average temperature and variance are shown in Table 1.


**Table 1.** The steady-state temperature value of the top surface of the glass slide.

The difference value between the top surface of the glass slide measured by Pt sensors and the set temperature gradually increases from 30 ◦C to 100 ◦C, as shown by the green column in Figure 4b. The measured temperature has a linear relationship with the set temperature of the heater (R<sup>2</sup> = 0.99995), within the range of 30–100 ◦C. The linear fitting relationship can be expressed as

$$T\_{\rm act} = 0.94 T\_{\rm set} + 1.35\tag{10}$$

where *Tact* is the measurement temperature of the top surface of the glass slide, *Tset* is the set temperature.

At the unperforated position, the temperature of the top surface of the glass slide changes with the set temperature in simulation, as shown by the cyan column in Figure 4b. The simulated results are almost the same as the theoretical values but greater than the measured by the experiment, as shown in Figure 4b. It means that under the same set temperature, the temperature of the top surface of a glass slide that is unperforated is higher than that of the sensor location. It is consistent with the law of steady-state temperature difference calculated by the simulation mentioned above when the target temperature is 60 ◦C. In order to further determine the relationship between the temperature of the glass surface at the perforation and that of the microfluid, the temperature of the microfluid was measured by placing a precision thermocouple in the microchannel. The average temperature value and variance of the three measurements are shown in Table 2.

The results are highly consistent with the simulated top glass surface temperature where unperforated, as shown in Figure 4c, which further illustrates the accuracy of the measurement and the rationality of the glass surface temperature characterizing the microfluidic temperature. In addition, according to the theoretical steady-state heat transfer of the multilayer medium, the heat transfer rate can be expressed as [38]

$$q = \frac{T\_{\text{set}} - T\_0}{\left[1/\left(h\_1 A\_1\right) + L\_i/\left(k\_i A\_i\right) + R\_{\text{cont}} + 1/\left(h\_{i+1} A\_{i+1}\right)\right]}\tag{11}$$

where *h*<sup>1</sup> and *hi*+<sup>1</sup> are the convective heat-transfer coefficient of the bottom and top, respectively. *A* is the surface area of the object with heat flux. *L<sup>i</sup>* and *k<sup>i</sup>* are the thickness and thermal conductivity of each layer (*I* = 2, 3, . . . ), respectively. *Rcont* is the contact resistance between heater and glass slide, *<sup>R</sup>cont* = 0.3–0.6 <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>m</sup><sup>2</sup> ·K/W.


**Table 2.** The steady-state temperature value of the microfluid.

Assuming that each layer constructed in the microfluidic system could transfer heat uniformly in the vertical profile, and take the bottom of the heater as the zero point, the temperature of the upper layers can be expressed as:

$$T(y) = T\_{\text{set}} - q \frac{y}{k\_i A\_i} \tag{12}$$

where *y* is the distance from the bottom surface of the heater.

According to Equation (12), the relationship between the temperature of the top surface of the glass slide and the set temperature can be calculated as shown by the pink column in Figure 4b. The theoretical analyses are extremely consistent with the simulation and experimental results. Therefore, we can analyze the relative temperature relationship between the top surface of the glass slide measured by the Pt 100 resistance sensor at the hole punching and the microfluid. As shown by the blue curve in Figure 4d, the difference between the microfluidic and measured temperature at each temperature is mostly concentrated between 1% and 2%. Excluding the more significant error at 30 ◦C, the average error is 1.74%. Therefore, the temperature function between the microfluid and the heater can be expressed as

$$T\_{\rm micro} = T\_{\rm act} \times (1 + 1.74\%) = 0.96 T\_{\rm s\varepsilon t} + 1.37 \tag{13}$$

The microfluidic temperature value can be derived from the temperature setpoint without precision sensor measurements in this system. Even though it would be desirable to place a temperature sensor as close as possible to the location of the microfluidic, practical limits usually prevent this, such as limited space and tight bonding requirements. The emergence of precision instruments can break through the limitations of assembly space but still suffer from damage and expensive cost. On the other hand, customized MEMS sensors integrated on a microfluidic chip may lead to unexpected contaminations into liquid samples. Here, a millimeter-scale industrial grade temperature sensor is introduced for microfluidic temperature sensing, and the compensation relationship between the microfluids and the glass substrate is investigated. As a more reliable and low-cost sensor, Pt100 is also capable of providing industrial-grade precisions. It also establishes a link between micro and macro scale, which enriches the selectivity of external control devices. Although calculations are required, the optimized relational equation can be embedded inside the temperature control system to achieve a one-step operation in the future. When the substrate material is changed, the microfluidic temperature value can still be calculated from the upper surface temperature value of the substrate.

#### *4.3. Temperature-Dependent PCR Experiment*

A temperature-dependent PCR experiment is conducted to test the accuracy of the temperature measurement method described above. The reaction reagents are pumped into the microfluidic chip and then placed the chip on the heater to stay for 20 min. At a suitable temperature, the DNA template, primers, and enzymes in the reaction reagents interact to complete the unwinding and replication of the double-stranded strands. Concurrently, the fluorophores are activated so that the reacted sample exhibits a fluorescent effect. According to the fluorescence intensity, the content of the target DNA in the original sample can be calculated. The sample kit indicates that the best temperature for reagent amplification is between 39–41 ◦C. In order to explore the effect of temperature on the amplification effect, we set low and high temperatures relative to the optimal value for isothermal amplification of sample reagents. After the reaction is completed, the fluorescence of the reagent is observed through a microscope. The blue light is selected as the excitation light, and the fluorescence diagram of the view area is shown in Figure 5a. A 300 µm square centrally inside the view area (d = 500 µm) is cut out as the analysis area for fluorescence intensity to avoid the error caused by the edge of the microchannel. As shown in the top part of Figure 5b, the results show the fluorescence graphs of the isothermal amplification PCR with a microfluid temperature of 37–43 ◦C. The temperature measured by the sensor is 36.4 ◦C, 37.4 ◦C, 38.3 ◦C, 39.3 ◦C, 40.3 ◦C, 41.3 ◦C, and 42.3 ◦C. In order to obtain a consuming contrast, grey-level images are processed with pseudo-color, as shown in the bottom part of Figure 5b. The results show that the fluorescence intensity at 39–41 ◦C is higher than that at 37 ◦C, 38 ◦C, 42 ◦C, and 43 ◦C, which is consistent with the informed. The accuracy and practicability of the method mentioned above for temperature measurement are explained. The reason for the varying fluorescence intensity in the graphs is mainly due to the inevitable precipitation in the reactants, which makes the fluorescence intensity of some areas increase locally. Another reason is speculated as to the thickness error in the chip manufacturing process. Hence, we can analyze the difference in fluorescence intensity of each group through the overall surface average fluorescence data. μ μ

μ **Figure 5.** (**a**) The microfluidic chip for PCR tests with the microscopic image of a microchamber. (**b**) Top: fluorescent images of control and positive reagents at 37–43 ◦C. Bottom: blue pseudo-color images of the top. The scale bar is 50 µm.

The average surface grey level of each picture is calculated, which is used to represent the fluorescence intensity. Each picture contains 20,736 pixels. The distribution of surface grey levels (0–255) at different temperatures is shown in Figure 6a. It can be seen that the grey level of the control group is the smallest and most concentrated. The rest of the distribution is also obviously discriminative at each temperature, and it shows a trend of first increasing and then decreasing. In order to further quantify the raw data, the weighted average of each grey band is calculated, as shown in the black curve of Figure 6b. The grey level reaches the maximum at 40 ◦C, and it has a slight distinction at 39–40 ◦C. Three experiments were performed to verify the reliability of this measurement method. The percentage increase in the average fluorescence intensity of the fluorescence group relative to the control was calculated as shown in the blue curve in Figure 6b.

**Figure 6.** (**a**) Probability distribution of grey scales from 0 to 255. (**b**) Weighted average grey level of each image and increment percentage to control group against the different temperatures of microfluid.

The percent of fluorescence intensity increasing at different temperatures is shown in Table 3. These results show that this measurement method has a good ability to distinguish temperature variation. In previous studies, temperature sensors were placed outside the microfluidic area similar to our method, such as, next to the microfluidic device [39], together with the heater [40], in the reference position [41]. However, the issue in these cases is the precise inside temperature cannot be guaranteed. Therefore, the compensation relationship between the microfluids and the substrate is investigated in this work. In other research, one approach to reducing temperature errors is modifying the control method [42]. Unfortunately, the complex circuit systems and electrode fabricated increase uncertainty. The nanophotonic sensor [43] embedded in a microfluidic chip reaches high precision but is customized. As a more reliable and low-cost sensor, industrial-grade temperature sensors used in our model are capable of providing industrial-grade precisions suitable for various devices to reuse.


**Table 3.** The percent of fluorescence intensity increased.

#### **5. Conclusions**

Here in this work, a heat transfer model was presented to investigate the relationship between the microfluids and the glass substrate of a typical microfluidic device. With an intelligent structure design and liquid metal, the millimeter-scale industrial temperature sensor could be utilized for temperature sensing of micro-scale fluids. The method overcomes the limitations of temperature sensing for microfluids. The dynamic linear range of measured temperature is demonstrated from 30 ◦C to 100 ◦C, and the uncertainty error is below 0.5 ◦C. Further, temperature-sensitive nucleic acid amplification experiments have been conducted to clarify the temperature resolution of this method. Therefore, it can be surmised that this method shows high potential for micro–macro interface sensing and is helpful beyond microfluidic applications.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/mi13050792/s1, Table S1: Numbers of the domain and boundary elements in different element sizes. Table S2: Parameter settings in the fluid-structure interacted simulation model. Figure S1: Discrete grid for the simulation model. Figure S2: Grid independence verification.

**Author Contributions:** Conceptualization, S.L.; experimental investigation, J.M.; experimental assistant C.Y., C.W. and H.L.; writing—original preparation, numerical simulation, J.M., J.L. and S.L.; writing—review and editing, J.L. and S.D.; supervision, S.L. and S.D.; funding acquisition, S.L. and J.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 51728502; Fund for Distinguish Young Scholars in Tianjin 2018 3rd Round, grant number 180191; Hebei Science and Technology Foundation, grant number 19271707D; Hebei Natural Science Foundation, grant number E2020202101, E2022202127 and F2021202001; Department of Human Resources and Social Security of Hebei Province, grant number C20200314 and C20210337; and Jiangsu Key Laboratory of Advanced Manufacturing Equipment and Technology, grant number FMZ202016.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author, upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

