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Combining the Capacitively Coupled Contactless Conductivity Detection (C^{4}D) technique and the principle of cross correlation flow measurement, a new method for flow rate measurement in millimeter-scale pipes was proposed. The research work included two parts. First, a new five-electrode C^{4}D sensor was developed. Second, with two conductivity signals obtained by the developed sensor, the flow rate measurement was implemented by using the principle of cross correlation flow measurement. The experimental results showed that the proposed flow rate measurement method was effective, the developed five-electrode C^{4}D sensor was successful, and the measurement accuracy was satisfactory. In five millimeter-scale pipes with different inner diameters of 0.5, 0.8, 1.8, 3.0 and 3.9 mm respectively, the maximum relative difference of the flow rate measurement between the reference flow rate and the measured flow rate was less than 5%.

Flow rate is one of the most important process parameters in many sectors, such as the chemical, pharmaceutical, petroleum, energy, and power engineering industries,

Some commercial flowmeters may be used in millimeter-scale pipes, such as the constriction flowmeter, rotameter, turbine flowmeter, electromagnetic flowmeter, coriollis flowmeter,

Electrical conductivity is one of the basic physical parameters. Conductivity detection techniques have been adopted to implement flow rate measurements for many years and some achievements/progress have been obtained [

Capacitively Coupled Contactless Conductivity Detection (C^{4}D) is a new conductivity detection technique, which was independently proposed by Zemann ^{4}D is a contactless detection technique and the electrodes of a C^{4}D sensor are not in contact with the measured fluid. C^{4}D can avoid the electrochemical reactions on the electrode surfaces and the polarization of the electrodes. Meanwhile, C^{4}D sensors are low cost and more robust [^{4}D is still a developing technique. To date, C^{4}D has mainly been studied and applied in the research field of analytical chemistry for ion concentration/conductivity detection in capillaries (the inner diameter is usually less than 0.2 mm) [^{4}D to the flow rate measurement in millimeter-scale pipes has been reported [

The aim of this work was to propose a new method for flow rate measurement in millimeter-scale pipes, combining the C^{4}D technique and the principle of cross correlation flow measurement. The research work included two steps: first, a new five-electrode C^{4}D sensor, which was suitable for the flow rate measurement in millimeter-scale pipes, was developed. Second, with two conductivity signals obtained by the developed sensor, the flow rate measurement using the principle of cross correlation flow measurement was implemented. Meanwhile, experiments were carried out in five millimeter-scale pipes with different inner diameters of 0.5, 0.8, 1.8, 3.0 and 3.9 mm, respectively, to verify the feasibility and effectiveness of the proposed flow rate measurement method.

^{4}D technique. As shown in ^{4}D sensor includes an insulating pipe, two metal electrodes (an excitation electrode and a pick-up electrode) placed cylindrically around the outside of the insulating pipe, an AC source and a current pick-up unit. ^{4}D sensor. _{1}_{2}_{i}

For the conventional C^{4}D sensor, from _{1}_{2}^{4}D sensor [^{4}D sensor, four electrodes are placed cylindrically around the pipe. The outer two are excitation electrodes and the inner two are pick-up electrodes. A fixed AC current source is connected between the outer electrodes and a resulting differential voltage between two inner electrodes can be obtained by a high input impedance voltmeter. Thus, from the measured differential voltage, the measurement value of the fluid conductivity can be obtained. Compared with the conventional C^{4}D sensor, the way of implementing the conductivity detection is different. The conventional current measurement way has been changed to a voltage measurement way, thus the existence of coupling capacitances (_{1}_{2}^{4}D sensor has been used in a channel with dimensions of 106 μm × 170 μm [^{4}D sensor in millimeter-scale pipes.

Although more research work should be undertaken, the detection method proposed by Laugere ^{4}D sensor in millimeter-scale pipes. The construction of the new five-electrode C^{4}D sensor was illustrated in ^{4}D sensor could only obtain one conductivity signal, so an extra electrode was added. The new sensor became a five-electrode C^{4}D sensor.

The new five-electrode C^{4}D sensor consists of an insulating pipe, five cylindrical metal electrodes (one excitation electrode, one ground electrode and three pick-up electrodes), an AC source and a data acquisition unit. _{x1}∼C_{x5}_{x1}∼R_{x4}_{x1}_{x1}∼R_{x4}_{x5}_{in}_{in}

The differential voltage _{x1}_{x2}_{x1}_{x2}

Thus, two conductivity signals can be obtained by measuring the differential voltages _{x1}_{x2}

Comparing ^{4}D sensor and the new five-electrode C^{4}D sensor is the way conductivity detection is implemented. The new five-electrode C^{4}D sensor is based on the detection method proposed by Laugere ^{4}D sensor, the unfavorable influence of the coupling capacitances on conductivity detection can be avoided and its linearity, accuracy, and sensitivity of the measurement can be improved [_{x2}_{x3}

The data acquisition unit can be roughly divided into two parts: the signal processing circuit and the data processing computer system. The function of the signal processing circuit is to demodulate and to amplify the conductivity signals obtained from the AC path. The function of the data processing computer system is to acquire the data and display the detection results (in this work, the data processing computer system was based on the data acquisition module of National Instruments (NI cDAQ-9172) and a microcomputer).

As shown in _{1}_{2}_{3}_{1-2}_{2-3}_{1}_{2}

The new five-electrode C^{4}D sensor can obtain two independent conductivity signals (the differential voltages _{1}_{2}_{U1}_{U2}(

The cross-correlation coefficient _{U1}_{U2}(

Then the average flow velocity ^{4}D sensor, the combination of electrode 2 and electrode 3 and the combination of electrode 3 and electrode 4 can be regarded as two independent sensors of conductivity detection, the up-stream sensor and the down-stream sensor).

Thus, the flow rate _{0}

The experiments included two parts: first, the conductivity measurement experiments of the new five-electrode C^{4}D sensor in millimeter-scale pipes were carried out to test the conductivity measurement performance of the new five-electrode C^{4}D sensor. Second, the flow rate measurement experiments were carried out to verify the effectiveness of the proposed flow rate measurement method in millimeter-scale pipes.

The conductivity measurement experiments of the new five-electrode C^{4}D sensor were carried out in five millimeter-scale pipes with different inner diameters of 0.5, 0.8, 1.8, 3.0 and 3.9 mm, respectively. The comparison conductivity measurement experiments between the new five-electrode C^{4}D sensor and the conventional C^{4}D sensor were also carried out. A commercial contact conductivity meter (FE30, Mettler Toledo Inc., 0.00 μS/cm∼199.9 mS/cm, ±0.5%F.S.) was used to obtain the reference conductivity data. The AC source was a function generator (CA1640-02, RIGOL Technologies Inc.). The signal frequency of the input voltage (AC source) was 10 kHz for the new five-electrode C^{4}D sensors with the inner diameter of 0.5 and 0.8 mm, 60 kHz for the new five-electrode C^{4}D sensors with the inner diameter of 1.8 and 3.0 mm and 120 kHz for the new five-electrode C^{4}D sensors with the inner diameter of 3.9 mm. The experimental material was KCl solution. The conductivity range of KCl solution was 0.1865 mS/cm∼13.21 mS/cm. The temperature was around 26 °C. The electrodes were made by painting five rings of silver paint over the glass pipes. The length of the electrodes and the distance between two adjacent electrodes were all 10 mm. The output of the new five-electrode C^{4}D sensors was volt signal and the noise was millivolt signal. The signal‐to‐noise‐ratio could meet the requirement of the measurement. The output signals (the differential voltages U_{1} and U_{2}) reflected the conductivity of KCl solutions, which could be seen from the _{1}, U_{2}, were pre-determined respectively by experiments. Then the measurement values of conductivity were determined.

Relative difference between the reference data obtained by the commercial contact conductivity meter and the measurement value obtained by the new five-electrode C^{4}D sensor was used to analyze the conductivity measurement results of the new five-electrode C^{4}D sensor. The relative difference _{c}_{r}_{m}^{4}D sensor.

^{4}D sensors in millimeter-scale pipes with different diameters. ^{4}D sensor (the inner diameter of the pipe was 0.5 mm) and the conventional C^{4}D sensor (the inner diameter of the pipe was also 0.5 mm). The sensitivity can be defined as Δ^{4}D sensor was successful. The measurement accuracy of the new five-electrode C^{4}D sensor was satisfactory. Compared with the commercial contact conductivity meter, the maximum relative differences _{c}^{4}D sensors (either obtained by the up-stream sensor or obtained by the down-stream sensor) were all less than 5%. The conductivity measurement experiments verified the new five-electrode C^{4}D sensor was suitable for the cross correlation flow rate measurements in millimeter-scale pipes. Meanwhile, the experimental results also showed that the detection method proposed by Laugere

^{4}D sensor. If the fluid flow rate was less than 3.6 L/h (60 mL/min), tap water was driven by syringe pump 1. The reference flow rate was obtained by syringe pump 1 (flow rate range: 0∼60 mL/min, accuracy: 0.35%). If the fluid flow rate ranged from 3.6 L/h to 25 L/h, tap water was driven by the high-pressure nitrogen tank. The reference flow rate was obtained by rotameter 1 (flow rate range: 2.5∼25 L/h, accuracy: 2.5%). If the fluid flow rate ranged from 25 L/h to 100 L/h, tap water was also driven by the high-pressure nitrogen tank. The reference flow rate was obtained by rotameter 2 (flow rate range: 25∼250 L/h, accuracy: 2.5%). The flow rate of milk tracer ranged from 0.006 L/h to 0.18 L/h.

The relative difference _{f}^{4}D sensor, can be calculated by the following equation:
_{r}_{m}^{4}D sensor.

According to the experimental results, the calibration coefficient ^{4}D sensor with the inner diameter of 0.8 mm and was 1.0 for the five-electrode C^{4}D sensor with the other four inner diameters, respectively. ^{4}D sensor. _{m}_{r} = 25.12 L/h. Comparing _{m}_{r}, it could be found that the relative difference _{f}

_{f}^{4}D technique and the principle of cross correlation flow measurement, was effective. The new five-electrode C^{4}D sensor was successful and was suitable for the flow rate measurement in millimeter-scale pipes.

Compared with the commercial flowmeters (such as the constriction flowmeter, rotameter, turbine flowmeter, electromagnetic flowmeter and coriollis flowmeter,

In this research, a new method, which combined the C^{4}D technique and the principle of cross correlation flow measurement, was proposed for flow rate measurement in millimeter-scale pipes. A new five-electrode C^{4}D sensor was developed. Meanwhile, experiments were carried out in five millimeter-scale pipes with different inner diameters. The research results showed that the flow rate measurement of this method had a relative difference lower than 5%, which was considered accurate and satisfactory for the flow rate measurement application in millimeter-scale pipes. As a preliminary study, this research work verified the feasibility of the application of C^{4}D technique to the flow rate measurement in millimeter-scale pipes. However, more research works (improving the measurement accuracy, extending the application scope, ^{4}D sensor and then to implement the flow rate measurement without the help of the tracer is also a challenge in future.

This work was supported by National Natural Science Foundation of China (No. 51076141, No. 61074173 and No.11132008).

Principle of C^{4}D technique. (^{4}D sensor. (^{4}D sensor.

The new five-electrode C^{4}D sensor. (^{4}D sensor; (

The signal processing circuit.

Experimental results by using the new five-electrode C^{4}D sensor in five pipes. (_{r} is the reference data obtained by the commercial contact conductivity meter. _{c}^{4}D sensor. The upper and lower lines are defined as _{c}

A typical sensitivity plot of the experiments in 0.5 mm i.d. pipe.

Experimental setup.

An example of the flow rate measurement. (

The experimental results in five millimeter-scale pipes. (_{r}_{f}^{4}D sensor. The upper and lower lines are defined as _{f}