1 Introduction

As an emerging technology, microfluidics are widely used in the fields of biochemical analysis (Mojica et al. 2016; Xu et al. 2015), biomedical engineering (Bourbaba et al. 2016; Pandele et al. 2017) and environmental monitoring (Das 2016). Microfluidic devices have numerous advantages including reducing the reagent consumption, improving the analysis speed, have high precision and reliability, and portability. The usefulness of a microfluidic system lies in its ability to integrate different components such as actuators, mixers, valves, pumps, etc., which eventually lead to the development of micro total analysis systems (µTAS), commonly known as lab-on-a-chip (Manz et al. 1990). Currently, traditional pumps such as syringe pumps, peristaltic pumps, and regulated source of pressure or vacuum are widely used in microfluidic systems. These pumps make a precise and reliable control of the fluid flow in microchannels, but the portability is limited due to their size (Iverson and Garimella 2008). To increase the device portability, numerous research efforts have been made by utilizing piezoelectric (Opekar et al. 2016; He et al. 2017), electrostatic (Sheikhlou et al. 2015) or magnetic effects (Barker et al. 2016) but meanwhile these pumps increase the cost.

A more practical pumping method for portable microfluidic systems that requires neither any external power nor expensive on-chip microfluidic components has been proposed by Hosokawa et al. (2004). This negative pressure-driven pumping mechanism takes advantage of the inherent porosity and air solubility of PDMS. By vacuuming air from the bulk PDMS, a pressure difference associated to atmospheric pressure is created. After a sample is loaded into closed microchannels, this pressure difference which generates negative pressure causes air inside the microchannels to diffuse into the bulk PDMS and pulls the fluids from inlets into the microfluidic chip. Thus, devices that utilize this phenomenon are capable of running without any external power. This power-free pumping has previously been demonstrated for microchip immunoassays (Garg et al. 2016), gold nanoparticle-based DNA analysis (Hasegawa et al. 2015), and cell loading (Luo et al. 2010).

However, the pumping capacity of this type of pump is relatively fixed for a given PDMS microfluidic chip, and the working time is also short as the air distribution inside and outside the PDMS reaches the equilibrium soon after the degassed PDMS microchip is placed in atmosphere. More unfavorably, this pump is only compatible with a given PDMS microfluidic chip, which greatly limits its application scope in microfluidic systems.

To address the above limitations, we have developed a positive pressure-driven PDMS pump for portable microfluidic applications. In comparison with the degas-based PDMS pump to microfluidic systems, positive pressure-driven PDMS pump offers increased system flexibility and reduced individual device fabrication complexity due to its independence and versatility. More importantly, it offers the advantages that the PDMS pump can be wrapped in transfusion bottle to meet the readily available requirements, and it also easily assembled, which only requires the user use a Teflon tube to connect a PDMS pump and a microchip. Furthermore, this PDMS pump can offer many possible configures of pumping power by adjusting the geometries of the pump or by combining different pump modules. Our design makes the PDMS pump as an independent module and solves the problem of low pumping capacity of degas-based PDMS pump, but both the degas-based PDMS pump and positive pressure-driven PDMS pump can only be used as infusion-only pump and the pump cannot be stopped after being started are still waiting for further research.

2 Theory

As shown in Fig. 1, positive pressure-driven PDMS pump is a small transfusion bottle which is filled with PDMS and have a channel in the central of it. First, the pump is placed in the gasholder and then connected to the air compressor through a Teflon tube. By opening the air compressor, high pressure will be generated inside the gasholder. The pressure difference between the gasholder and pump allows air diffusion into the PDMS pump. After a period of time, the pump can be pulled out of the gasholder and then release gas into the air due to pressure difference. Therefore, the fluid can be driven inside the Teflon tube which inserted into the central channel of the pump. This approach facilitates a straight forward positive pressure pumping system that can be used with many microfluidic systems.

Fig. 1
figure 1

Schematic illustration of the operation of the positive pressure-driven PDMS pump. a The aerating of the PDMS pump. b The composition of the PDMS pump. c The formation of the closed microfluidic system after a droplet of liquid was loaded into the inlet. d The liquid was driven into the microchannel under the positive pressure which created by the PDMS pump

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The working mechanism of the positive pressure-driven PDMS pump is based on the release of air in a closed system from PDMS. First, the air diffusion into PDMS in the gasholder and then the air release from PDMS when the pump is working. The process of air diffusion into PDMS can be characterized as a solution-diffusion process (George and Thomas 2001). Air solution first occurs at the surface of the PDMS and then dissolved air molecules diffuse into the interior of the PDMS. The solution process can be described in Henry’s law (Miller and Vandome 2010), and the Henry’s law shows that the equilibrium concentration of air dissolved in PDMS is directly proportional to the partial pressure of the air around the PDMS as

$$C=S \cdot P$$
(1)

where C is the concentration of air molecules in PDMS, S is the solubility coefficient of air in PDMS, and P is the pressure of air.

When a PDMS pump is placed in a gasholder which provide a high-pressure environment, the air dissolved into PDMS owing to its high solubility and a high-pressure dissolution equilibrium is established. After it is brought back to the atmosphere, the original equilibrium is broken, and air release to the atmosphere until a new equilibrium is reached (Li et al. 2012). In terms of solubility, the amount of air transported into PDMS, Δm, can be written as

$$\Delta m=({C_0} - {C_{{\text{atm}}}}){V_{{\text{PDMS}}}}=S({P_0} - {P_{{\text{atm}}}}){V_{{\text{PDMS}}}}$$
(2)

where C0 and Catm are the equilibrium concentrations of air in PDMS at high-pressure environment and atmosphere; respectively, P0 and Patm are the air pressure around PDMS at high-pressure environment and atmosphere, respectively; and VPDMS is the volume of the PDMS inside the pump. This equation indicates that the amount of air transferred into PDMS depends on both the size of the PDMS and the high-pressure environment level.

For the steady-state flux across PDMS, the flow rate can be determined by Skelley and Voldman (2008)

$$Q=\frac{{PA({P_0} - {P_{{\text{atm}}}})}}{{\text{t}}}\frac{T}{{273}}\frac{{76}}{{{P_{{\text{atm}}}}}}$$
(3)

where Q is the volumetric flow rate, A is the diffusion area, T is the absolute temperature in kelvin and Patm is the atmospheric pressure. For this model, it is assumed that the steady-state flux will be significantly larger across the PDMS than any flux into the bulk PDMS and the pumping time can also be calculated by this.

From Eqs. (2) and (3), the Δm and Q are directly proportional to the pressure difference (ΔP = P0 − Patm). The maximum pressure difference (ΔP = Patm − P0) of negative pressure pumping method can be considered as 1 atm, since the meaning of absolute vacuum is that the gas pressure is zero in a given space, and it can never be achieved (Smetana and Carley 1966). The pressure difference of this positive pressure-driven PDMS pump in this paper can be reached 4 atm. For high-pressure air compressors, pressure difference can even become larger. Accordingly, the driving capability of positive pressure driving can be several times than the negative pressure driving.

When the PDMS pump is working, the rough estimate of the characteristic time to allow for the air across the PDMS can be obtained by examining the diffusion time t across the PDMS (Xu et al. 2014):

$$t \approx {\text{ }}{w^2}{D^{ - 1}}$$
(4)

where w is the thickness of the PDMS and D is the diffusion coefficient of air in PDMS.

The air release from the PDMS pump causes the liquid flow in the micro-channel. If we assume that the air concentration or the air density inside the channel is unchanged during the pumping process, the volumetric flow rate Q and the pumped fluid volume V inside the channel can be expressed as (Xu et al. 2014):

$$Q(t) \approx k\frac{{FS(t)}}{{{C_{{\text{ATM}}}}}}=kD\frac{{{C_{{\text{PDMS}}}} - {C_{{\text{Chamber}}}}}}{{{C_{{\text{ATM}}}}}}\frac{{S(t)}}{w} \Rightarrow V(t)=\int {Q(t){\text{d}}t}$$
(5)

where k is an empirical factor decided by viscous effect of the pumped liquid flow and S(t) is the exchange surface area that allows air release from the PDMS pump. Equation (5) points out that there are two major parameters that can affect the flow rate: the thickness of the PDMS pump (w) and the exchange surface area (S) that allows air release from the PDMS pump.

3 Experimental section

3.1 Design and fabrication of PDMS pump

The proposed PDMS pump was a small transfusion bottle (Fig. 1b) which filled with PDMS and a channel in the central of it. The Teflon tube (Hefei Haicheng Industrial Technology Co. Ltd, China) connected the PDMS pump and the microfluidic chip so that the PDMS pump could drive the liquids in the microfluidic chip. The central channel was designed to adjust the diffusion area by changing the position of the Teflon tube in the channel.

The fabrication of PDMS pump was done in the super clean room. First, the transfusion bottle (Xuzhou Ming Zheng glass products Co. Ltd, China) was cleaned using acetone and methanol, respectively, and then rinsed in deionized water before blown dry by filtered nitrogen gas. After cleaning, the cleaned transfusion bottle was placed on a hot plate at 90 °C for 20 min to make it completely dried. Then, the prepolymer of PDMS (Sylgard 184, Dow Corning) and corresponding curing agent was thoroughly mixed at a ratio of 10:1 (wt/wt). And the mixed PDMS was degassed in a vacuum chamber for 40 min to remove all the air bubbles. After that, the PDMS mixture was carefully poured into the transfusion bottle with a core module lied in the center of the bottle and then baked on a hot plate at 90 °C for 2 h. Finally, the core module was removed from PDMS.

3.2 Operation of PDMS pump

A basic operational schematic for the PDMS pump is shown in Fig. 1. To activate the PDMS pump, the pump was placed in a gasholder and then connected to the air compressor and pumped at 50 kPa for 24 h (Fig. 1a). Subsequently, the PDMS pump was taken out from the gasholder and connected directly into the inlet of a microfluidic chip with a Teflon tube (Fig. 1c). To reduce gas leakage, the sealing cover was punched which the Teflon tube goes through. After that, liquid samples were loaded onto the inlets using a conventional micropipette (Fig. 1c). Under the positive pressure created by the PDMS pump, the samples were pushed into the microchip (Fig. 1d).

3.3 Adjustment of pumping capacity

The pumping capacity can be roughly adjusted by central channel, which is designed to adjust the diffusion area by changing the position of Teflon tube in the channel. In this experiment, three kinds of adjustment mode were designed. The Teflon tubes were inserted into the center channel at 5, 10, 15 mm from the bottom (Fig. 2a–c), thus, the height of the diffusion area was 5,10,15 mm, respectively. The experimental setup for adjusting pumping capacity of positive pressure-driven PDMS pump is shown in Fig. 2d. The pumping capacity of different adjustment modes were evaluated by monitoring the working time and height of elevation of the liquid column in the tube. A vertically positioned variable diameter Teflon tube with one end connected to the central channel of PDMS pump was used for measuring the pumping capacity. The tube was 1000 µm in inner diameter and 100 cm in length. Dye solution was served as the pumping liquid for direct optical visibility. During the measurement, a positive-driven PDMS pump which was taken from the gasholder at 50 KPa for 24 h was adhered to the surface of the elevator, and then, the tube was inserted into the central channel of the pump. The variable diameter of the tube was filled with dye solution. For all experiments, the idle time was 2 min, which was defined as the PDMS pump exposed to atmospheric conditions before sample liquid blocks the inlets of the tube or the microfluidic chips equipped with the PDMS pump.

Fig. 2
figure 2

Schematic drawing of the experimental setup for adjustment pumping capacity. a The Teflon tube is inserted into the center channel at 5 mm from the bottom. b The Teflon tube is inserted into the center channel at 10 mm from the bottom. c The Teflon tube is inserted into the center channel at 15 mm from the bottom. d The measurement for adjustment pumping capacity

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3.4 Characterization of PDMS pump

The most important and basic parameters related to the positive pressure-driven PDMS pump are back pressure and flow rate; therefore, measurements of back pressure and flow rate were done in this study. To compare the positive and the negative pressure-driving capacity, back pressure and flow rate of the negative pressure-driven pump were also tested. The test environment and conditions were the same with positive pressure-driven PDMS pump, and experimental setups were also similar to the positive pressure-driven PDMS pump. The PDMS pump which the Teflon tube inserted into the center channel 15 mm from the bottom is used in this experiment.

In this experiment, there are three factors to the back pressure (P): static fluid pressure (Ps), capillary pressure (Pc), and dynamic pressure (Pd); and P = Ps + Pc + Pd. Ps is the pressure contributed by the potential energy of the fluid in the tube, i.e., Ps = ρgh, where g is the acceleration of gravity, and h is the height of the liquid column in the tube. Pc is the pressure contributed by capillary force, which is about 70 Pa according to the calculation of Li et al. (2012). Pc is affected by the dynamic contact angle which is about 110° between pure water and Teflon (Goswami et al. 2008). The contact angle will be decreased when the theoretical capillary pressure is reduced. As a result, the Pc of Teflon tube is negligible. Pd is the pressure contributed by the kinetic energy of the fluid in the tube which is affected by the flow rate of the fluid. A typical flow rate is less than 0.1 mm/s, which related to Pd is far less than Ps. Thus, the contribution of Pd is negligible in the calculation of P, and the pumping pressure (P) is simply calculated by the static fluid pressure (Ps).

The experimental setup for the back pressure measurement of positive pressure-driven PDMS pump is shown in Fig. 3a. The way of this experiment is similar to that of adjustment pumping capacity. The back pressure was evaluated by monitoring the elevation of the liquid column in the tube. A vertically positioned variable diameter Teflon tube with one end connected to the central channel of PDMS pump was used for measuring the back pressure. For all experiments, the PDMS pump was taken from the gasholder at 50 KPa for 24 h and the idle time was 2 min. Once the variable diameter part of the tube was filled with dye solution and inserted into the pump, the images were captured at an interval of 1 min using the CCD camera until the movement of the liquid stopped.

Fig. 3
figure 3

Schematic drawing of the experimental setup for measuring the back pressure. a The measurement for positive pressure-driven PDMS pump. b The measurement for negative pressure-driven PDMS pump

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As shown in Fig. 3b, the measurement of back pressure for negative pressure-driven PDMS pump are similar to that for a positive one. And the back pressure was also calculated by monitoring the elevation of the liquid column in the tube. The negative pressure-driven PDMS pump was placed in a vacuum desiccator and degassed at 0 kPa for 24 h. Subsequently, the degassed PDMS pump was taken out from the vacuum chamber and tested the back pressure. Compare to the positive one, the Teflon tube’s one end was inserted to the dish which was filled with dye solution and the other end was inserted into the negative-driven PDMS pump which was adhered to the wall.

The experimental setup for the flow rate measurements is shown in Fig. 4, which are similar to the measurement of back pressure. Figure 4a, b are respectively the measurements for the positive pressure-driven PDMS pump and the negative pressure-driven PDMS pump. The PDMS pump was assembled with a horizontally variable diameter tube and equipped with a CCD camera. When the measurement was begun, the images were captured at an interval of 30 s using the CCD camera until the movement of the liquid stopped. The flow rate was evaluated by monitoring the movement of the liquid column in the tube.

Fig. 4
figure 4

Schematic drawing of the experimental setup for measuring the flow rate. a The measurement for positive pressure-driven PDMS pump. b The measurement for negative pressure-driven PDMS pump

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3.5 Sealing effect of PDMS pump

As shown in Fig. 1, the PDMS pump was sealed in a transfusion bottle, so several experiments on the sealing effect have been made. The sealing effect was measured by the test of the back pressure. A total of three groups of experiments were conducted immediately after being taken out of gasholder, 3 days later, and 5 days later. When the PDMS pumps were taken from the gasholder, screw the sealing cover at once and put it in the same environment as the PDMS pump which tested immediately. During the measurement, the positive-driven PDMS pumps which were taken from the gasholder at 50 KPa for 24 h, and then, one of the PDMS pumps was immediately tested and the rest was sealed for subsequent experiments. For all experiments, the idle time was 2 min and the Teflon tube was inserted into the center channel 15 mm from the bottom.

4 Results and discussion

4.1 Results of adjusting pumping capacity

As shown in Fig. 2, the pumping capacity of different adjustment modes are evaluated by monitoring the working time and height of elevation of the liquid column in the tube. Table 1 shows the experimental measurement results. Type (a) means the Teflon tube is inserted into the center channel at 5 mm from the bottom. Type (b) means the Teflon tube is inserted into the center channel at 10 mm from the bottom. And type (c) means the Teflon tube is inserted into the center channel at 15 mm from the bottom. The pumping capacity of type (c) which tested immediately kept increasing for about 120 min. It can be seen from Table 1 that the rising height of liquid can reach 83 cm. However, the maximum rising height of liquid of type (a) is about 37 cm and there was no more increase after 37 min.

Table 1 Summary of pumping capacity for different kinds of adjustment modes
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For the same PDMS pump, the time the liquid can be driven increases with the increase of the time of the PDMS pump aerated by the air compressor. Our group is studying the relationship between them. The PDMS pump aerated by the air compressor of experiments involved in this paper are 6 h, 12 h, 18 h and 24 h. The time the liquid can be driven by the PDMS pump are 47 min, 83 min, 109 min and 120 min.

4.2 Results of back pressure

As shown in Fig. 3, the back pressure was measured by monitoring the liquid level change in a Teflon tube when the PDMS pump is placed onto the elevator connected with the tube. Figure 5 shows the experimental measurement results of the back pressure after these positive pressure-driven PDMS pumps were taken out of gasholder. As a comparison, the negative-driven PDMS pumps were also tested immediately after being taken out of vacuum desiccator. In order to prove the reliability of the experimental results, these two kinds of PDMS pumps were tested three times respectively.

Fig. 5
figure 5

Measurement results on the pumping pressure for positive/negative pumping

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The back pressure of the positive pressure-driven PDMS pump which tested immediately kept increasing for about 120 min. It can be seen from Fig. 5 that the back pressure can reach about 8300 Pa. However, the maximum back pressure of negative pressure-driven PDMS pump is about 2300 Pa and there was not any more pressure increase after 70 min. Compared to the negative pumping, the back pressure of positive pressure-driven PDMS pump is about four times than it. The upper deviation and the lower deviation of the error bars in Fig. 5 respectively represent the maximum and minimum of experimental results. The points in the figure are the average values of the experiments. At 120 min, the back pressure of positive pumping can reach the maximum 8450 Pa and the minimum is 8000 Pa. The back pressure of negative pumping can reach the maximum 2600 Pa and the minimum at 70 min is 2000 Pa. Table 2 summaries the driving capacity for these two types of PDMS pump, which shows positive-driven PDMS pump has a strong driving capacity than the negative one.

Table 2 Summary of driven capacity for different types of PDMS pump
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4.3 Results of flow rate

Figure 6 shows the experimental measurement results of the flow rate which PDMS pumps are tested immediately after being taken out of gasholder or vacuum desiccator. To prove the reliability of the experimental results, these two kinds of PDMS pumps were tested three times, respectively. It can be seen in Fig. 6, the initial flow rate started with about 32.18 µL/min for positive pumping, and even 30 min later, there is still a relative high flow for the devices. While for the negative pumping, the initial flow rate started with about 16.48 µL/min and decreased to 0 in 30 min. The upper deviation and the lower deviation of the error bars in Fig. 6, respectively represent the maximum and minimum of experimental results. The points in the figure are the average values of the experiments. The initial flow rate of positive pumping can reach the maximum 33.98 µL/min and the minimum is 30.56 µL/min. The initial flow rate of negative pumping can reach the maximum 17.92 µL/min and the minimum is 15.27 µL/min.

Fig. 6
figure 6

Measurement results on the flow rate for positive/negative pumping

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4.4 Results of sealing effect

Figure 7 shows the experimental measurement results of the sealing effect which PDMS pumps are tested immediately after being taken out of gasholder, 3 days later, and 5 days later. To prove the reliability of the experimental results, these three kinds of experiments were tested three times, respectively.

Fig. 7
figure 7

Measurement results of sealing effect

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It can be seen in Fig. 7, the back pressure of the positive pressure-driven PDMS pump which was tested 3 days later kept increasing for about 60 min and the back pressure can reach 2650 Pa. Even after 6 days, it can still be reached 1120 Pa and kept working for 25 min. The upper deviation and the lower deviation of the error bars in Fig. 7, respectively, represent the maximum and minimum of experimental results. The points in the figure are the average values of the experiments. The measurement results of sealing effect which tested immediately can reach the maximum 8450 Pa and the minimum is 8000 Pa. The measurement results of sealing effect which tested after 3 days can reach the maximum 2870 Pa and the minimum is 2400 Pa. The measurement results of sealing effect which tested after 6 days can reach the maximum 1280 Pa and the minimum is 1050 Pa.

Possible causes of errors for back pressure (Fig. 5), flow rate (Fig. 6) and sealing effect (Fig. 7) are: (1) insertion position of the Teflon tube into the central channel position. Though the PDMS pump which the Teflon tube inserted into the center channel 15 mm from the bottom is used in this experiment, manual operation can still cause errors. (2) Idle time. In this experiment, the idle time was 2 min but the time difference between each step of preparation experiment within this 2 min will lead to errors. (3) Measurement of experimental results. The measurement of experimental results obtained by ruler, which will lead to measurement errors.

5 Application

5.1 Design and fabrication

To use easily, the aerated PDMS pump can be stored in a transfusion bottle (Fig. 8). In practical applications, a user only required to open the sealing cover, then use a Teflon tube to connect a PDMS pump and a microfluidic chip. This aerated PDMS pump not only provides convenience for user but also expands the application range. As shown in Fig. 8, we demonstrated the utility of this pumping method by applying it to a PDMS-based viscometer microfluidic device (30 mm × 15 mm × 5 mm).

Fig. 8
figure 8

A PDMS-based viscometer with positive pressure-driven PDMS pump

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As shown in Fig. 9, the PDMS viscometer microfluidic chip consisted of two liquid chambers (LC) (r = 2000 µm, h = 100 µm), two liquid inlets, an air inlet (AI), an air storage chamber (ASC) (r = 1000 µm, h = 100 µm), and two outlets. Here r and h are the radius and height of the chambers, respectively.

Fig. 9
figure 9

Schematic overview of the PDMS-based viscometer microfluidic chip

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Microchannels between liquid chambers and air storage chamber are air channels (AC): (L = 3000 µm, h = 100 µm, w = 100 µm). Here, L, h and w are the length, height and width of the channels, respectively. Microchannels between liquid chambers and outlets are sample channel (SC) and reference channel (RC) (L = 12 cm, h = 100 µm, w = 100 µm).

The PDMS-based viscometer microfluidic chip was fabricated using standard soft lithography replica-molding techniques (Xia and Whitesides 1998). A mold was created using a negative photoresist, SU8-2050 (Micro-Chem Corp, Newton, MA, USA), which was spun onto a glass substrate using a spin coater (SC-1B, Beijing Jinshengweina Technology Co. Ltd, China). The resist was spread onto the glass substrate at 500 r/min for 10 s and then 1500 r/min for 20 s.

The glass substrate was soft baked at 65 °C for 15 min and 95 °C for 120 min and then UV exposed for 6 min using a mask aligner (BGT-3B, Beijing Chuangweina Technology Co. Ltd, China). The glass substrate was then post baked for 15 min at 65 °C and 120 min at 95 °C, allowed to cool to room temperature, after developing and finally blown dry with nitrogen.

PDMS (Sylgard 184, Dow Corning) was prepared according to the instructions of the manufacturer, degassed in a vacuum chamber for 30 min, then poured onto the SU8 mold, and cured at hot plate for at 95 °C for 30 min. After that, PDMS was peeled off from the mold, five small holes with a diameter of about 0.6 mm were drilled on five chambers of the PDMS viscometer. Followed by oxygen plasma treatment for irreversible bonding between PDMS and glass slide at the top surface. Lastly, the chip was baked over a hot plate for 2 h at 95 °C to improve the bonding strength and stabilize the surface property of the devices.

5.2 Experimental

The PDMS-based viscometer was placed under a microscope (6XD-3, Shanghai Optical instrument, China) equipped with a CCD camera (Panasonic Super Dynamic II WV-CP460). A sample inlet was used to introduce the solution which need to measure its viscosity, and reference inlet was used to deionize water as a reference. A PDMS pump connected to the viscometer by a Teflon tube was used to drive the liquid flow in the viscometer. During the measurement, the CCD camera captured the images at an interval of 1 s for 50 s. The CCD images were analyzed by MATLAB to measure the distances of the running front of each stream from the inlets. The CCD images were opened with MATLAB, and the three-dimensional coordinate system was established based on PDMS-based viscometer dimensions. The starting and ending points were selected from the imdistline toolbox in MATLAB, and the length of each line could be calculated. The ratio of the viscosity of the solution to the viscosity of the reference fluid was determined from data analysis. In this experiment, absolute ethyl alcohol, isopropyl alcohol, and acetone were used to measure their viscosities. The experimental process of absolute ethyl alcohol as an example is shown in Fig. 10.

Fig. 10
figure 10

Photos of a test run for absolute ethyl alcohol on the PDMS-based viscometer

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5.3 Analysis and results

From our previous analysis of the PDMS viscometer, we have (Han et al. 2007):

$$\frac{{L_{{{\text{reference}}}}^{2}({t_2}) - L_{{{\text{reference}}}}^{2}({t_1})}}{{{t_2} - {t_1}}}=\frac{{{\eta _{{\text{sample}}}}}}{{{\eta _{{\text{reference}}}}}}\frac{{L_{{{\text{sample}}}}^{2}({t_2}) - L_{{{\text{sample}}}}^{2}({t_1})}}{{{t_2} - {t_1}}}+2d_{h}^{2}\frac{{{P_{{\text{c}} \cdot {\text{reference}}}} - {P_{{\text{c}} \cdot {\text{sample}}}}}}{{S{\eta _{{\text{reference}}}}}}$$
(6)

where L(t) is the length of the fluid column inside the channel at time t with the subscripts reference and sample indicating the reference and sample fluids; η is the viscosity of the fluid; S is a constant related to channel geometry, and for a rectangular cross-section S is 32 (Perry and Green 2008); Pc is the pressure caused by capillary force; dh is the hydraulic diameter of the channel.

Assume that Pc is constant for both sample and reference fluids. Thus, ηsample/ηreference was obtained by the slope value of the curve of \(\left[ {L_{{{\text{reference}}}}^{2}({t_2}) - L_{{{\text{reference}}}}^{2}({t_1})} \right]/({t_2} - {t_1})\) and \(\left[ {L_{{{\text{sample}}}}^{2}({t_2}) - L_{{{\text{sample}}}}^{2}({t_1})} \right]/({t_2} - {t_1})\) (Fig. 11). Each sample fluid was measured viscosity three times. And the coordinate in the Fig. 11 was the average value of experimental results. Then, the points were fitted into a straight line. The results after data analysis according to Eq. (6) is shown in Table 3. And compared to the normal viscosity, the viscosities of various fluids measured by PDMS viscometer obtained a good test accuracy for which the relative error range is about 5%.

Fig. 11
figure 11

The plot of sample versus reference of three liquids which measured by PDMS viscometer

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Table 3 Viscosities of various fluids measured by PDMS viscometer at 20 °C
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This study only shows a case of positive pressure-driven PDMS pump in viscosity measurement. There are three general areas to be further investigated for positive pressure-driven PDMS pump: (1) mixing, (2) blood separation, and (3) droplet generation.

6 Conclusion

A positive pressure-driving technique-based PDMS pump has been developed. This paper presents a PDMS pump that utilizes the air release from the aerated PDMS to create a positive pressure for in microfluidic devices. Different from pumps in several existing microfluidic systems, the aerated PDMS pump can be easily removed and replaced, which increased system flexibility and reduced individual chip fabrication complexity due to its independence and versatility, meanwhile reducing the complexity and cost of microfluidic chips. In addition, the performance of the aerated PDMS pump were also investigated. These parameters include the adjustment of pumping capacity, sealing effect, pumping pressure and flow rate. The experimental results demonstrate that it is possible to flexibly build microfluidic system combination with an above-mentioned PDMS pump for achieving the desired function.