Investigation of shear-force distribution in the hollow fiber membrane module based on FBG sensing technology

Journal Pre-proofs Investigation of shear-force distribution in the hollow fiber membrane module based on FBG sensing technology Qingwen Qin, Jie Wang, Zhiyang Cheng, Zhao Cui, Juan Li PII: DOI: Reference:

S1383-5866(19)34321-7 https://doi.org/10.1016/j.seppur.2019.116458 SEPPUR 116458

To appear in:

Separation and Purification Technology

Received Date: Revised Date: Accepted Date:

22 September 2019 3 November 2019 12 December 2019

Please cite this article as: Q. Qin, J. Wang, Z. Cheng, Z. Cui, J. Li, Investigation of shear-force distribution in the hollow fiber membrane module based on FBG sensing technology, Separation and Purification Technology (2019), doi: https://doi.org/10.1016/j.seppur.2019.116458

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Investigation of shear-force distribution in the hollow fiber membrane module based on FBG sensing technology Qingwen Qina, b, Jie Wanga, b*, Zhiyang Chenga,b, Zhao Cuia,b , Juan Lia,b, a

State Key Laboratory of Membrane filtration and Processes, Tianjin

Polytechnic University, Tianjin 300387, China b

School of Environmental Science and Engineering, Tianjin Polytechnic

University, Tianjin 300387, China

* Corresponding author: 1. Email: [email protected](Jie Wang) tel.: +86 022 8395 5668; fax: +86 022 8395 5451;

Abstract: Membrane fouling is the most critical problem associated with separations. Increasing the surface shear forces is a common physical method to slow down membrane fouling. In this study, it was described the extension of the Fiber Bragg Grating (FBG) sensing technology for the in suit real-time measurement of shear-force distribution in the hollow fiber membrane module. The result shows that the distribution of shear forces caused by crossflow, aeration and hollow fiber spacings can be achieved by rationally arranging FBG. Besides, increasing the fiber spacing enhances the transfer of shear forces between the fibers. Moreover, by separately monitoring the shear component force of the extended X-axis and Y-axis caused by aeration, the shear forces distribution at different aeration rates can be mapped. As a whole, the investigation of spatial shear-force distribution and the use of FBG sensing technology would lay the

foundation for optimizing membrane module design and structures. Key words: FBG sensing, Shear-force distribution, Hollow fiber spacing, Crossflow velocity, Aeration rate

Introduction Membrane separation processes are used to concentrate, purify or remove solute from solution. It is currently a proven technology within many important areas, such as food and dairy industries, water purification and treatment of liquid fluent streams. However, membrane fouling is still a serious problem that can’t be neglected, which limits the efficiency of membrane use and widespread use. The most common method is to reduce membrane fouling by improving surface shear forces in the membrane module[1-3]. To date, crossflow[4-6], aeration[3, 7-9] and packing density[10-12] are the most common and popular physical methods that could mitigate membrane fouling in membrane technology. All of these strategies focus on how to increase and improve shear-force distribution by changing the velocity distribution of the membrane surface. Khalili Garakani et al. [13] investigated the mechanisms that led to flux enhancement and fouling reduction by both experimental approaches and numerical simulations. They computed numerically the mean gas and liquid velocities using the k-ε turbulence closure, and suggested that the shear stresses on the membrane surface had a high correlation with the filtration resistance. P. Willems et al. [14] used Particle Imaging Velocimetry (PIV) to study liquid and liquid/gas flows through spacer filled channels in order to provide experimental support for velocity distributions obtained from CFD. Jan Günther et al. [10] analyzed the effect of packing density on the distribution of the velocity film direction and found that proper packing density can increase the filtration flux of the fiber and make the axial flux distribution of the fiber more uniform. However, there is still no simple and quick way to monitor the distribution of shear forces in membrane modules, especially in hollow fiber modules. In order to better study the influence of shear forces distribution on membrane fouling, many methods for studying shear forces have been proposed. In the past decades, the most popular method to describe shear-force is CFD that can acquire the flow rate, pressure and concentration analysis at different locations on membrane interface [15-19]. In addition, there are some in suit investigation methods, such as particle image velocimetry (PIV) [20, 21], electrochemical methods [22] and sensing methods [23]. However, these

methods have their own advantages and disadvantages, as can be seen in Table 1. Table 1 Advantages and disadvantages of these methods Methods

Advantages

Disadvantages

References

There are certain limitations Easy to get Membrane in

the

simulation

surface shear forces spatial CFD

distribution complex

conditions,

which

are

different

from

the

complicated

experimental

without

[22, 24-27]

measuring

equipment conditions. Easy to obtain the shear PIV

[14, 20, 21, 28]

Equipment complexity forces distribution Special electrolyte solution

Electrochemical

Mature technology

method

Easy to operate

[12, 29, 30]

Measurement points are limited No special requirements for Poor Sensor method

the

solution

in

implementation

the distributed measurement

of

[23, 31-33]

membrane pool

To obtain more information on the hydraulic properties of membrane interface, in addition to considering the applicability of the in-situ monitoring method itself, it is also necessary to consider whether the method will affect the flow field within the membrane module. Therefore, the fiber Bragg grating (FBG) sensing technology was imported to investigate the spatial shear-force distribution induced by crossflow velocity, aeration rate and packing density. Compared with conventional in suit investigation methods, FBG sensors are particular in many aspects, which makes them ideal for flow-induced vibration measurement. It's simple in structure, small in size (the diameter could be as small as 80 mm), light in weight and corrosion resistance. Besides, it has little influence on the measured object and can be used to monitor the change of

the physical quantity in limit spaces. Moreover, the FBG sensors have potential to be used for simultaneous multi-point measurement on a single structure by using wavelength division multiplexing (WDM) [34]. Therefore, FBG sensing technology was used to explore the factors affecting the spatial distribution of shear forces induced by crossflow velocity, aeration and packing density in the membrane module. In this study, the effect of the fiber spacing instead of the packing density on the shear force distribution was characterized. The main aim of the present study was to find out the influence of these three factors on the shear-force distribution based on FBG sensing technology. In this study, multiple FBG sensors in series closed to membrane surface were inserted on the hollow fiber module to achieve a spatially distributed measurement of stress on the membrane. The impact of crossflow velocity, aeration rate and hollow fiber spacing was discussed, and the transverse and longitudinal shear forces distribution due to aeration has also been studied. 2. FBG sensing principle The FBG wavelength 𝜆𝐵 (nm) is given by:

𝜆𝐵 = 2𝑛𝑒𝑓𝑓Λ where Λ (nm) is the period of the grating, and 𝑛𝑒𝑓𝑓 is the effective refractive index of the fiber core. When the temperature is kept constant, the FBG is subjected to external stress, and the FBG period changes with the change of the stress, and the photoelastic coefficient also causes the refractive index to change. The formula of the photoelastic coefficient is: 𝑃𝑒 =

𝑛2𝑒𝑓𝑓 2

[𝑃12 ― 𝜇(𝑃11 + 𝑃12)]

Where 𝜇 is the Poisson's ratio of the fiber material, 𝑃𝑒 is the photoelastic coefficient of fiber, 𝑃11 and 𝑃12 are the changes of longitudinal and transverse refractive index respectively, and Δε is the axial strain in the fiber. The relationship between the photoelastic coefficient 𝑃𝑒 and the period Δ𝜆𝐵 is:

Δ𝜆𝐵 = (1 ― 𝑃𝑒)𝜀𝑧𝜆𝐵 = 𝐾𝜀𝜀𝑧 Where 𝐾𝜀 is the axial strain sensitivity coefficient of FBG, which can be expressed as: 𝐾𝜀 = 1 ―

𝑛2𝑒𝑓𝑓 2

[𝑃12 ― 𝜇(𝑃11 + 𝑃12)]

When the fiber belongs to standard single mode silica, it can be considered that 𝑃𝑒 = 0.22, and therefore the relationship between Δ𝜀 and Δ𝜆𝐵 is given by the following formula: 𝜀𝑧 =

𝜆𝐵 0.78𝜆𝐵

Considering the axial stress σ and Δ𝜆𝐵, there relationship can be described by: σ = E ∙ 𝜀𝑧 =

𝐸 Δ𝜆 0.78𝜆𝐵 𝐵

where 𝐸 (Gpa) is the elastic modulus of the fiber, it's determined by the inherent nature of the material as a fixed value. Since 𝜆𝐵 is constant, a constant parameter K = 𝐸 0.78𝜆𝐵, is introduced establish a theoretical model to establish an explicit linear relationship between the axial stress and the Δ𝜆𝐵. Therefore, the relationship between FBG stress and wavelength change can be obtained: σ = KΔ𝜆𝐵

3. Methods and materials 3.1 Experiment instruments A laboratory-scale hollow fiber membrane setup with FBG sensing system which could be used to measure shear-force distribution is shown in Fig. 1. The pristine polyvinylidene fluoride (PVDF) hollow fiber membrane was provided by Tianjin Motimo Membrane Technology Co., Ltd. The dimensions of these membranes were provided as follows: pore size, 0.22 µm; the outer/inner diameter, 1200/600 µm. The peristaltic pump (BT100-2J, Baoding Longer, China) purchased from Baoding Lange constant flow pump Co., Ltd. Aeration pump (ACO-003) purchased from Sensen Group

Co., Ltd. Optical sensing demodulator and matched software (SM130, Micron Optics, USA) were used to measure the wavelength change of the FBGs at different positions, which corresponded to the Fig. 2. The details of FBG sensors are shown in Table 2. Table 2 Central wavelength and position of FBGs FBGs

Central wavelength

Corresponding positions

FBG1

1540

A, (3,10), (3, 45), (3, 80)

FBG2

1545

B, (15,10), (15, 45), (15, 80)

FBG3

1550

C, (27,10), (27, 45), (27, 80)

FBG4

1555

D

FBG5

1560

E

Fig. 1 Experimental setup.

Fig. 2 The membrane module.

The experimental setup is shown in Fig. 1. Peristaltic pump was used for water supply and aeration pump was used to provide aeration. The fiber demodulator collects the grating signal and feeds it back to the computer to obtain the change signal of the shear forces. The membrane module is shown in Fig. 2. The water is fed from the lower port, the upper port is effluent, and the membranes are placed in the middle of the device. During the experiment, the water temperature was controlled at 25 ± 2 ℃. The grating arrangement is evenly arranged in the membrane module, wherein the red area indicates the position of the grating. The dimension of each channel was 90 mm long, 30 mm wide and 4 mm deep, and the inlet diameter was designed by 4 mm. Fig. 3 showed that 8 fibers were arranged in two rows from the top view and front view, and the spacing is calculated from the center position of the hollow fibers, which are 1.2, 2.2, 3.2 mm, respectively. The shear forces distribution was monitored by FBG sensors. When monitoring the longitudinal shear forces of different position, five FBG sensors (Comay Instruments, China) connected in series by single-mode fiber were placed in close contact with the membrane. When monitoring the transverse shear forces, the three FBG sensors are arranged side by side with a spacing of 12 mm, and then the transverse shear forces of the upper, middle and lower positions are respectively monitored. The details of FBGs sensors, which were black, as shown in Fig. S4. A two-dimensional coordinate system is established with the plane of the FBG sensors, the direction of the fibers is Y, and the direction perpendicular to the fiber is X. When arranged horizontally, the FBG sensors were arranged at positions 10 mm, 30mm, 45 mm, 60mm and 80 mm from the water inlet, and the code is A, B, C, D, E in order; when arranged vertically, they were 3 mm, 15 mm, and 27 mm from left to right, and the code of each position is the corresponding coordinate. The FBGs were placed in parallel to prevent interference between the various sensors. By changing the hydraulic conditions and monitoring the shear forces at various locations, the shear forces monitoring in the entire device was achieved. Data acquisition frequency was set to collect 1000 data per second and select the data within 1s of the represent.

Fig. 3 The top and front view of hollow fiber and FBG sensors (a) 1.2mm, (b) 2.2mm, (c) 3.2mm.

3.2 Method Wavelength division multiplexing (WDM), WDM method was used based on FBG sensing technology to investigate the shear-force distribution of membrane interface[34]. FBG sensors can be used for simultaneous measurement of multiple points on a single structure, and there is no limit to the number of measurement points. There is a linear relationship between the stress experienced by the FBG sensor and the amount of wavelength change. Therefore, by changing the resultant force at a certain point into forces extending in the X-axis and Y-axis directions, the changes in wavelengths Δλ1 and Δλ2 caused by the component forces F1 and F2 in the longitudinal and lateral directions, respectively, can be monitored. The direction θ of the force at the fixed point can be obtained by calculation, as shown in Fig. 5.

Fig. 5 Resultant force determination principle diagram

3. Results and discussion 3.1 Crossflow velocity Fig. 6 shows the results obtained at different crossflow velocities, corresponding to A-E of the module, at 1.2mm hollow fiber spacing. As the crossflow velocity increased, the shear forces experienced at the five positions increased. But as shown in Fig. 6, the shear forces did not increase all the time, and reached a maximum at the crossflow velocity of 0.15m/s, especially in the position of B, D and E. Moreover, the increase in the three positions of the B, D, E was significantly greater than that of A and C, which seemed to be contrary to the inlet position should have a larger shear force. The reasons may be due to the influence of the spacing of the fibers. In order to further study this phenomenon, the spacing of the fiber was further increased. The hollow fiber spacings of 2.2 mm and 3.2mm were added in analyzing, and monitoring the effect of shear forces on the crossflow velocity under the same conditions.

Fig. 6 Longitudinal shear forces in the crossflow velocity of 0, 0.02, 0.08, 0.15, 0.20, 0.30m/s

under 1.2mm hollow fiber spacing.

3.2 The hollow fiber spacings The result of Fig. 7(a) shows that the fiber spacing was increased to 2.2 mm. And as the crossflow velocity increased, the shear forces continued to increase after reaching 0.15m/s, and finally kept stable at 0.20m/s. Fig. 7(b) shows the shear forces distribution when the fiber spacing was increased to 3.2 mm. It can be seen that the variation trend was similar to that when the fiber spacing is 2.2 mm. After 0.15 m/s, the shear forces at position B and C continued to increase. However, while obtaining the spatial distribution of the shear forces, it also can be found that the change in the fibers spacing had a large influence on the shear forces at each position. On this basis, the changes of each position were compared under different fiber spacings.

Fig. 7 Longitudinal shear forces in the crossflow velocity of 0, 0.02, 0.08, 0.15, 0.20, 0.30m/s under (a) 2.2mm, (b) 3.2mm hollow fiber spacing.

The fiber spacing has a significant effect on shear forces at local positions in the membrane module. Fig. 8 shows the relationship between the shear-force change in local position and the fiber spacing. At positions A, B and C, as the fiber spacing increased, the shear forces increased, and the maximum shear forces occurred at 3.2mm. When position D was at the fiber spacing of 2.2 mm, a large shear forces occurred at a crossflow velocity of 0.02 m/s, compared to the other two fiber spacings, and as the crossflow velocity increased, a higher shear force was also exhibited. Position E showed a change in shear forces opposite to positions A, B and C. As the fiber spacing increased, the shear forces decreased. The reasons may be the FBG sensing area was located between the fibers, and the crossflow velocity between the fibers is affected by the fibers, resulting in a decrease in the flow velocity between the fibers, which in turn affects the shear forces.

Fig. 8 The shear forces variations of the position A-E under different fiber spacings.

Besides, the fibers also have a guiding effect on the flow field to a certain extent. This guiding effect is reflected in the diversion of the liquid. Increasing the fiber spacing facilitates the shear forces between the fibers near the inlet. However, in some places far from the inlet, the shear forces are weakened due to a decrease in the flow rate of the liquid. At the same time, due to the splitting of the liquid caused by the fibers, the flow rate of the liquid outside the fibers is reduced, which further causes the shear forces to be weakened. Moreover, the diversion effect has a significant relationship with the fiber spacing. By comparing the shear force distribution of 1.2mm, 2.2mm and 3.2mm fiber spacing, respectively, as can be seen in Fig. 6 and Fig. 7, the difference between the maximum and minimum Δ𝜆𝐵 at 1.2mm is 0.00761nm, 0.00482nm at 2.2mm and 0.00646 nm at 3.2 mm. The result shows that an appropriate increase in the fibers spacing promotes a uniform distribution of shear forces, and when the fiber spacing is 2.2 mm, the shear forces can be distributed more evenly.

3.3 Effect of aeration and hollow fiber spacings When considering the shear forces change caused by crossflow, the shear forces perpendicular to the fibers’ direction was not considered. Since the magnitude of the shear forces in the direction of the fibers is much larger than the direction perpendicular to the fibers, the shear forces perpendicular to the direction of the fibers can be ignored. However, unlike merely increasing the crossflow velocity, aeration causes a stronger turbulence in the membrane module. Therefore, when investigating the shear forces distribution caused by aeration, the distribution of shear forces from both the longitudinal and transverse directions would be considered.

3.3.1 Distribution of longitudinal shear forces Fig. S9 shows the change in shear forces at 1.2, 2.2 and 3.2mm hollow fiber spacings at aeration rates of 0.3ml/s, 1ml/s, 1.8ml/s, 2.5ml/s, 3.5ml/s. The increase of aeration rate changes the distribution of shear forces. The reason may be that the distribution and shape of the bubble change due to the increase of the hollow fiber spacing. By longitudinal comparison, when the hollow fiber spacing was 1.2mm, increasing the aeration rate had little effect on the shearing force signal, probably because the bubbles failed to enter the fibers, and the shear forces caused by the bubbles was not located in the sensing area. On the outside, the change in shear forces was not fully felt by the FBG sensors. When the hollow fiber spacing was 2.2mm, as the aeration rate increased, the shear forces signal gradually increased and the fluctuation became larger, indicating that a small amount of bubbles can enter the hollow fiber spacing of the membrane at this time, causing a change in the shear forces in the membrane. When the hollow fiber spacing was increased to 3.2mm, the change of shear forces was more obvious, indicating that the bubbles can enter the hollow fiber spacing, and the shear forces among the fibers increases. The reason is that the fiber spacing affects the distribution of shear forces by interfering with the bubble running path during aeration. When the hollow fiber spacing was 1.2 mm, the bubble only shifted sideways. When it reached 2.2 mm, the bubbles would be cut by the fibers on one hand, and the size would be reduced. On the other hand, the bubbles still moved sideways, and the shear forces would be weakened. For position C, regardless of the hollow fiber spacing, the shear forces was the smallest when the hollow fiber spacing was 2.2 mm, and the shear forces was the largest at 3.2 mm. This is because the bubble does not rise straight. As the bubble moved laterally at the water inlet, the bubble at the position C deviated from the FBG sensing area, causing the signal to weaken. For position E, the shear forces value was small regardless of the fiber spacing, but the shear forces fluctuated as the aeration rate increased. The reason may be that the aeration rate is increased and the space occupied by the bubbles is increased, which causes the FBG sensors to be located in the bubble for more time, and the change in the shear forces is

not obvious. The average of the shear forces can be obtained by averaging the values of the shear forces at five locations A, B, C, D and E monitored in one minute. By comparison, as shown in Fig. 10(a), when the fiber spacing was 1.2 mm, the shear forces was mainly distributed in the water inlet A. When the fiber spacing was 2.2 mm, the shear forces was mainly distributed in the water inlet A, as shown in Fig. 10(b). As the aeration rate increased, the shear forces of the positions B and D gradually increased, but the shear forces at the C and E positions were small. When the fiber spacing was continued to increase to 3.2mm, the shear forces at the C position suddenly increased sharply, and the value of the shear forces exceeded the A position, as shown in Fig. 10(c). The reason for these phenomena is that the distribution of bubbles between the fibers and the outside of the membrane has changed due to the spacing of the fibers, which in turn causes an uneven distribution of shear forces. By observing the overall trend of shear forces, increasing the fiber spacing can increase the shear forces value, and cause a change in local shear forces. When the fiber spacing is 1.2 mm, the distribution of shear forces is relatively uniform. When the fiber spacing is increased to 2.2 mm, the shear forces at positions A and B gradually increase, and are significantly higher than the shear forces at other positions. When the fiber spacing is increased to 3.2 mm, the shear forces values at positions A and C are significantly higher than other positions. This shows that by adjusting the fiber spacing and aeration rate, it is beneficial to control the level of local shear forces, which has achieved the purpose of controlling membrane fouling. In this study, the optimum range is 1.8-3.5ml/s at a spacing of 3.2mm. Considering the energy consumption, the optimal aeration rate is 1.8ml/s.

Fig. 10 The average of longitudinal shear forces in one minute of different position under the aeration rate of 0.3ml/s, 1ml/s, 1.8ml/s, 2.5ml/s, 3.5ml/s and hollow fiber spacing of 1.2mm, 2.2mm, 3.2mm.

3.3.2 The distribution of transverse shear forces According to above results, the effect of aeration on the longitudinal shear-force distribution has been investigated. In order to further explore the influence of changes in hydraulic conditions on the shear forces distribution, the distribution of transverse shear forces was explored. Fig. 11 is a shear forces distribution diagram for nine positions. It can be seen that the maximum shear force was at the water inlet (15,10), followed by the position (27,45) and (3,45) at the intermediate position. At position (15,10), the shear forces decreased slightly with the increase of aeration rate. This may be due to the increase of aeration rate, which causes the bubble volume to increase. When the FBG is inside the bubble, it is not subjected to any force. The shear forces values exhibited are reduced. The same trend has occurred at the position (27,45) and (3,45).

From the distribution of the overall shear forces, the magnitude of the shear forces was small at the water outlets positions (3,80), (15,80), and (27,80), which was caused by the increase in volume during the ascent of the bubble, and the position (27,45) and (3,45) phases at the intermediate position. It was larger than position (15,45) because the bubbles can’t enter between the fibers, and thus the shear forces between the fibers can’t be increased, which is also a cause of heavy contamination between the fibers. Positions (3,10) and (27,10) were subjected to turbulence caused by the water inlet, and were subjected to a large shearing force.

Fig. 11 The average magnitude of transverse shear forces for nine positions under the aeration rates of (a)0.3ml/s, (b)1ml/s, (c)1.8ml/s, (d)2.5ml/s, (e)3.5r/min

Because of the large turbulence caused by aeration, it is of great significance to understand the dominant shear forces at each position. After analyzing the transverse shear forces and longitudinal shear forces at each position, it can be found that the transverse shear force is mainly distributed near the inlet and the middle zone. The longitudinal shear force is mainly distributed in the water inlet due to the influence of the fiber spacing, but the middle of the two areas is smaller. This is consistent with the

path of motion of the bubbles observed during the study. During the aeration process, the air bubbles were disturbed by the fibers, and then offset, resulting in an increase in the transverse shear forces near the water inlet. Then the bubble was blocked by the wall and moved in the opposite direction, which caused the lateral shear forces at the intermediate position to increase. In the process of the bubble shifting to the wall surface, the longitudinal shear forces caused was small, and the difference of the dominant shear forces in different regions occurred.

3.4 The spatial distribution of shear forces According to the monitoring of the transverse and longitudinal shear forces, the direction of the shear forces at each position can be obtained. As shown in Fig. 13, the red arrow indicates the direction of shear-force distribution at different aeration rates and fiber spacings. When the fiber spacing was 1.2 mm, as the aeration rate increased, the direction of the shear forces caused by the aeration was more likely to extend the fibers. However, since the distance between the fibers at this time is narrow, it is difficult for the bubbles to enter the fibers, so the direction of the shear forces does not completely extend the fibers. In this case, the bubbles moved to the side, causing an increase in the transverse shear forces. As the fiber spacing increased to 2.2 mm, this phenomenon was improved, and the direction of the shear forces tended to be in the direction of the fibers, indicating that the bubbles entered the fibers and had a positive effect on the distribution of shear forces. When the fiber spacing was further increased to 3.2 mm, the shear forces was further inclined to the direction of the fibers, compared with the fiber spacing of 2.2 mm. It is further explained that the shearing force caused by the movement of the bubble between the fibers is more stable. As a whole, increasing the aeration rate and the fiber spacing favors the direction of the shear forces toward the direction of the fibers. wherein the fiber spacing has a much greater influence on the direction of the shear forces than the aeration, which is more conducive to the distribution of the shear forces between the fibers.

Fig. 12 The direction of shear-force distribution under the aeration rate of 0.3ml/s, 1ml/s, 1.8ml/s, 2.5ml/s, 3.5ml/s and hollow fiber spacing of 1.2mm, 2.2mm, 3.2mm.

4. Conclusion The spatial distribution of shear forces of hollow fiber membrane modules was monitored in situ based on FBG sensing technology. Exploring the effects of crossflow velocity and aeration rate on shear forces distribution. Based on this study, a number of key conclusions could be provided as following: 

As an in-situ non-intrusive monitoring method, FBG sensing technology can monitor the flow field and shear forces in the membrane module through

reasonable arrangement. By monitoring the longitudinal and transverse shear forces, the shear forces at any point within the membrane module can be obtained. 

Significant correlation was observed between the shear forces and hollow fiber spacing. Considering crossflow, reasonable fiber spacing has a positive effect on the uniform distribution of shear forces. By comparing the difference between the maximum and minimum Δ𝜆𝐵, ie 0.00761nm at 1.2mm, 0.00482nm at 2.2mm and 0.00646 nm at 3.2 mm, the result shows that when the fiber spacing is 2.2 mm, the shear forces can be distributed more evenly in this study.



It contributes to the increase of shear forces to some extent by increasing the crossflow velocity and the aeration rate, but there are differences between the two methods for the contribution to the shear forces. Under the same operating conditions, ie using the same peristaltic pump operating parameters, the shear forces caused by aeration is significantly higher than the crossflow. When considering the crossflow, the Δ𝜆𝐵 at 1.2mm is 0.00178-0.0077nm, 0.001540.00782nm at 2.2mm and 0.00178-0.01026 nm at 3.2 mm; When considering the aeration, the Δ𝜆𝐵 at 1.2mm is 0.00103-0.1178 nm, 0.00008-0.1846nm at 2.2mm and 0.0008-0.0253 nm at 3.2 mm. The Δ𝜆𝐵 of aeration is significantly larger than the Δ𝜆𝐵 caused by crossflow.



By monitoring the shear forces at various locations inside the membrane module, the distribution of shear forces can be mapped. Fiber spacing and aeration rate have a significant effect on the shear forces distribution. Increasing the aeration rate and the fiber spacing favors the direction of the shear forces toward the direction of the fibers. The reasons may be that the fiber spacing further enhanced the distribution of longitudinal shear forces by interfering with the bubble path during aeration. This approach appears to be a powerful tool for the understanding and control of

the process. These results will also be used to develop models taking into account the non-homogeneities of the shear forces. By changing the local shear forces, the shear forces distribution can be made more uniform, ultimately inhibiting membrane fouling and prolonging membrane life. Therefore, how to optimize the design of the membrane module and the arrangement of the membrane fibers so that the shear forces is evenly

distributed, which will greatly improve the efficiency and life of the membrane, still needs to do further research.

Acknowledgements This study is financially supported by the National Natural Science Foundation of China (No. 51978464, 51638011), Science and Technology Planning Project of Tianjin, China (16PTGCCX00070), and Program for Innovative Research Team in University of the Ministry of Education of China (Grant no. IRT-17R80).

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Highlights: 

The FBG sensing technology was applied to monitor shear forces



Reasonable fiber spacing promoted the uniform distribution of shear forces



By affecting the bubbles path, fiber spacing can enhance the shear forces



The study mapped the distribution of shear forces induced by aeration

Table 1 Advantages and disadvantages of these methods Methods

Advantages

Disadvantages

References

There are certain limitations Easy to get Membrane in

the

simulation

surface shear forces spatial CFD

distribution complex

conditions,

which

are

different

from

the

complicated

experimental

without

[22, 24-27]

measuring

equipment conditions. Easy to obtain the shear PIV

[14, 20, 21, 28]

Equipment complexity forces distribution Special electrolyte solution

Electrochemical

Mature technology

method

Easy to operate

[12, 29, 30]

Measurement points are limited No special requirements for Poor Sensor method

the

solution

in

implementation

the distributed measurement

of

[23, 31-33]

membrane pool

Table 2 Central wavelength and position of FBGs FBGs

Central wavelength

Corresponding positions

FBG1

1540

A, (3,10), (3, 45), (3, 80)

FBG2

1545

B, (15,10), (15, 45), (15, 80)

FBG3

1550

C, (27,10), (27, 45), (27, 80)

FBG4

1555

D

FBG5

1560

E

Conflict of Interest Statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in the manuscript entitled “Investigation of shear-force distribution in the hollow fiber membrane module based on FBG sensing technology”.