Article pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. 2018, 57, 12543−12550
Effect of Pipe Surface Wettability on Flow Slip Property Hongyuan Qi,*,†,‡ Aiguo Liang,§ Huayi Jiang,†,‡ Xinmin Chong,∥ and Yulong Wang†,‡ College of Petroleum Engineering and ‡Shaanxi Key Laboratory of Advanced Stimulation Technology for Oil & Gas Reservoirs, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China § Karamay Hongshan Oilfield Co. Ltd., Karamay 834000, Xinjiang, China ∥ No.1 Production Plant, Xinjiang Oilfield Branch Company, Karamay 834000, Xinjiang, China
Ind. Eng. Chem. Res. 2018.57:12543-12550. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 09/23/18. For personal use only.
†
ABSTRACT: The effect of surface wettability on the slip property continues to be a controversial subject. In this regard, the contact angles and sliding angles of ethylene glycol, tap water, and #26 white oil deposited on plexiglass pipe, 304 stainless-steel pipe, polytetrafluoroethylene pipe, and polypropylene pipe surfaces were determined using a contact angle meter. The slip velocity, slip length, shear stress, and flow increment of the three liquids flowing in the four pipes were calculated using the slip boundary condition, which refers to the laminar flow resistance of a liquid in a fully developed section of a no-slip pipe under a constant pressure drop. The results show that the main characteristic of slip flow at a solid−liquid interface is that at a constant average velocity of the liquid, the wall shear stress decreases with an increase of the contact angle and a decrease of the sliding angle. This in turn, increases the slip velocity and the slip length and results in lower flow resistance of the liquid. The negative slip phenomenon exists at low-speed flow for part of the liquid, which is different from the linear slip length model. The slip length does not tend to be constant until the average velocity increases to a certain value. Some recent studies have shown that fluid slip may occur on a solid wall, which is directly related to the surface wettability. Actually, the slip occurs easily on a hydrophobic surface; thus, the boundary slip can reduce the flow resistance of the fluid.7−11 Hendy et al.12,13 studied the flow characteristics of Newtonian fluids in a microchannel by means of molecular dynamics. The results confirmed that interface wettability had some effect on wall slip. Lauga et al.14 performed an in-depth investigation of the factors that affect slippage. They discovered that improving the roughness and wettability of a solid surface could change the slip length. The rough structure of a hydrophobic surface can increase the slip length, while that of a hydrophilic surface could reduce the slip length and even result in a negative slip. Watanabe et al.15,16 determined the slip velocity at a pipe wall from measured velocity profiles by applying Navier’s hypothesis and verified that the slippage and drag reduction phenomena of tap water and glycerol−water solution occurred in the flow of hydrophobic circular pipes. Lv et al.17 compared the experimental pressure drop of water flowing in the superhydrophobic pipe with a theoretically determined value. They found that when the Reynolds number was 3000−11 000, a drag reduction of 8.3−17.8% was obtained. The slip velocity increased with a decrease of the
1. INTRODUCTION The boundary condition of fluid flow is one of the most important factors that determine the behavior of fluid dynamics. The classical no-slip boundary conditions are used in almost all fluid mechanics, which assume that the relative moving velocity of fluid molecules on the solid wall is zero. However, with the development of modern testing methods and analytical techniques, many scholars have re-examined the boundary slip condition of fluid flow more accurately. It has been determined that the no-slip assumption of a solid−liquid interface in classical fluid mechanics is partially valid in some practical cases. This implies that the boundary slippage may occur in many cases.1−3 Pit et al.4 studied the flow velocity of cetane on a hydrophobic surface using fluorescence recovery after photobleaching and observed significant slippage on the surface for the first time via experimental investigation. The molecular dynamics simulation results of Barrat et al.5 revealed that when the contact angle was sufficiently large the acquired slip length on the boundary was enough to show that the noslip assumption was inapplicable and that obvious slip behavior of fluid occurred on the hydrophobic surface. Tian et al.6 determined the flow velocity field on the surface of a superhydrophobic horizontal plate in a circulating tank using time-resolved particle image velocimetry. The results indicated that compared with the superhydrophilic surface, the wall slip flow of water can be clearly observed on the superhydrophobic surface. © 2018 American Chemical Society
Received: Revised: Accepted: Published: 12543
June 20, 2018 August 18, 2018 August 22, 2018 September 6, 2018 DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
Article
Industrial & Engineering Chemistry Research
the attraction of the solid wall to the liquid molecule is less than that between liquid molecules), the liquid will experience partial fluid slip along the solid wall. Velocity slip refers to the tangential velocity difference between the fluid and an interface when the fluid flows on a solid surface. When the tangential velocities of the fluid and the surface are equal, this is referred to as the no-slip boundary condition, which is often used in the conventional fluid mechanics. As early as 1823, the hypothesis of a linear slip boundary condition was proposed by Navier.26 In Navier’s model, the slip velocity us, is proportional to the shear rate experienced by the fluid at the wall:
pipe’s diameter and the slip length decreased with an increase of the Reynolds number. Busse et al.18 discussed the effect of air layer thickness on drag reduction and the apparent slip length for laminar flow on an idealized superhydrophobic surface. Aljallis et al.19 concluded that obvious slippage could occur on superhydrophobic surfaces with a suitable coarse microstructure, which resulted in a reduction of pressure drop and drag for liquid flow. Some scholars adopt direct or indirect measurement methods to obtain the values of the slip parameters on a hydrophobic surface and illustrate the primary characteristics of slippage and drag reduction of these surfaces.20−22 On the contrary, other researchers are of the opinion that there appears to be some slippage on nonwetting surfaces. Ji23 performed experiments to explain the mechanism of drag reduction on hydrophobic or superhydrophobic surfaces for different flows using particle image velocimetry and flow apparatus. The results indicated that the slip velocity and slip length on hydrophobic or superhydrophobic surfaces were greater than that the values for hydrophilic surfaces, and the wall shear stress was smaller. However, the results of Choi et al.24 showed that nanoscale slip also appeared on hydrophilic surfaces in an investigation involving 100 groups of measured pressure drops and flow rates in the hydrophilic and hydrophobic microchannels. In this case, the slip length in the hydrophobic microchannel was greater than that in the hydrophilic microchannel. The same conclusion that the liquid can slip even on a completely wetted solid surface was also determined by Bonaccurso.25 In conclusion, boundary slippage can change the flow resistance of a fluid, and the surface wettability is a very important factor which can affect slip. However, the effect of surface wettability on the slip property continues to be a controversial point of discussion. In this regard, the slip velocity and slip length of three liquids flowing against four different types of pipe walls are determined based on the application of the theory of fluid mechanics through the indirect measurement method, and the results are presented herein. Thus, the primary characteristic of slippage and drag reduction is further examined. This result is of important theoretical and practical significance to in the realization of new process developments for drag reduction and transportation increase in a liquid pipe, by changing its surface wettability.
us = Ls
∂ux ∂z
z=0
(1)
where Ls is the slip length. The slip length is the distance between the imaginary solid surface (the slip velocity is zero on this surface) and the actual interface. If Ls= 0, then this satisfies the no-slip boundary condition. Otherwise, it is a slip boundary condition. Ls is a material parameter with a length dimension, which can be inferred by experimental measurement. However, the slip length cannot be directly measured by experimentation. Although this value can be obtained by plotting the experimentally obtained velocity field curve, the results often have large errors. Therefore, in this report, the corresponding flow rate measured after a pressure drop at both ends of the pipe is given, and the value of the slip length is then indirectly obtained based on a theoretical relationship. For a fully developed steady flow in a pipe, the velocity equation for Newtonian fluid under a slip boundary condition can be written as16 Vz =
1 dp 2 (r − R2) + us 4μ dz
(2)
The volume flow rate is Qs = −
π R 4 dp + πR2us 8μ dz
(3)
The average velocity is vav =
2. THEORY AND MODEL When fluid flows in a pipe, energy dissipation occurs as a result of friction and the interaction between fluid molecules and the pipe wall, and the intermolecular interactions of the fluid. Regardless of laminar or turbulent flow, the maximum velocity gradient is concentrated near the pipe wall where the largest shear stress occurs. Therefore, most of the dissipated energy is concentrated near the pipe wall when the fluid flows in the pipe, and the boundary condition of the fluid on the solid wall plays an important role in the calculation of energy loss for pipeline transportation. The traditional treatment for the boundary condition of a fluid on a solid wall considers that the fluid adheres to the wall. In most cases, since the liquid typically wets the solid wall (i.e., the attraction of the solid wall to the liquid molecule is greater than that between liquid molecules), the boundary condition that the liquid adheres to the solid wall is reasonable. However, for a small number of liquids that do not wet solid walls (i.e.,
R2 Δp + us 8μ L
(4)
The shear stress is τ=μ
dVz 4μ = (vav − us) dr R
(5)
If a fixed pressure drop (Δp) is given at both ends of the pipe, then a related slip flow rate (Qs) will be generated. As a result of the slip boundary condition, the slip flow rate (Qs) on the slip surface is greater than the no-slip flow rate (Qn) on the common surface. Therefore, a slip velocity appears on the slip surface. Q s − Q n = usA
(6)
If the no-slip boundary condition is applied in a circular pipe, the flow rate in unit time Qn in the pipe is given by Qn = 12544
πR4 Δp 8μ L
(7) DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
Article
Industrial & Engineering Chemistry Research
Liquid in a tank was circulated in the pipe using a self-priming pump. The pressure drop and flow rate in the 1.8 m test section were measured using a differential pressure transducer and a turbine flow meter with digital display screens, respectively. On the basis of the experimental results, the corresponding measured flow rate in the pipeline is compared with the theoretical flow rate under the classical no-slip boundary condition for a fixed pressure drop, to indirectly determine the occurrence of boundary slippage. Then, the slippage parameters, such as shear stress, slip velocity, slip length and flow increment, are calculated according to the eqs 5 and 8−10, respectively.
The slip velocity on the slip surface is determined by Qs − Qn
us =
πR2
(8)
yz R ijj Q s zz jj − 1 zz 4 jk Q n (9) { Thus, given a constant pressure drop Δp, the change of flow rate in the pipe is Qs/Qn after introducing the slip boundary condition.
and using Navier’s hypothesis, the slip length is Ls =
Qs Qn
=1+ Δp
4Ls R
4. RESULTS AND DISCUSSION 4.1. Slip Velocity. The slip velocities of the three liquids flowing in the pipes are obtained by substituting the experimental data to eq 8. To further investigate the impact of pipe surface wettability on the slip characteristics in a more intuitively manner, the dependences of the slip velocities of the three liquids on the average velocity at the same contact angle, are shown in Figures 8−10, respectively. As can be seen from Figures 8−10, the slip velocities of the three liquids at the wall increase with the increase of the contact angle at a specific velocity, and the slip velocity on the hydrophobic wall was seen to be generally greater than that of hydrophilic wall. The reason for this phenomenon can be attributed to the greater contact angle and smaller sliding angle of the solid−liquid interface, which implies that there is a weaker interaction between them. Thus, this condition is more conducive to inducing slippage phenomenon on this surface, leading to a larger slip velocity and slip length, which causes a decrease in the flow resistance of the liquid in the pipe. Besides, the apparent slip may be the result of dissolved gas bubble coming out of solution near the interface thereby reducing the liquid viscosity in close proximity to the wall and giving the appearance of a failure of the no-slip condition.27 In Figure 8, we determined that although the trend of the slip velocity of tap water with contact angle is not apparent compared with that of the hydrophilic 304 steel pipe (θ = 62.2°, α = 36°) the slip velocities of tap water in the other three pipes are positive. When the average velocity of tap water is 0.115 m/s, the maximum slip velocity (0.0403 m/s) is observed in the PTFE pipe, which is 35.04% of the average velocity. On the contrary, since the slip velocity of tap water in the 304 steel pipe is smaller, the effect of the contact angle on the flow resistance is almost negligible. Similarly, as shown for ethylene glycol in Figure 9, the slip velocity in the PTFE pipe (θ = 101.87°, α = 6°) is clearly greater than that of the in other three lyophilic pipes. When the average velocity of the ethylene glycol is 1.922 m/s, the maximum slip velocity approaches 0.32 m/s. Additionally, from Figure 9, we can see that the slip velocities of ethylene glycol in the four kinds of pipes are almost positive, and the slip velocities of the four pipe walls increase with an increase of the average velocity. The main reason may be that the minimum contact angle of ethylene glycol on four pipe walls is 53.77° which implies that the molecular force on the solid−liquid interface is relatively less than that between the liquid, and it is easier to form a thin layer of liquid molecules. Therefore, it is easier to drive the wall−liquid molecule by an external force and the forming wall slip velocity is larger.28
(10)
3. EXPERIMENTAL APPARATUS AND METHOD The three test liquids were ethylene glycol, tap water, and #26 white oil, respectively. The #26 white oil was provided by Shaanxi Huntair Co., Ltd., and the ethylene glycol was provided by Chengdu Kelong chemical factory. The properties of these three liquids are given in Table 1. Four test pipes were Table 1. Properties of Three Liquids (28°C) liquid tap water ethylene glycol #26 white oil
density (g/cm3)
dynamic viscosity (mPa·s)
surface tension (mN/m)
0.995 1.124
0.91 17.45
70.13 42.56
0.885
48.48
29.45
used which included plexiglass pipe, stainless-steel pipe, polytetrafluoroethylene pipe (PTFE pipe), and polypropylene pipe (PP pipe). They all were 5 m in length and 14 mm in inner diameter. Generally, the surface wettability of a solid is characterized by the static contact angle (contact angle for short) and sliding angle. In order to compare the surface wettability of the four test pipes, the contact angles and sliding angles of the three liquids on the four surfaces were measured using the sessile drop technique with a contact angle meter (JC2000D1, Shanghai Zhongchen Digital Technic Apparatus Co. Ltd.) at room temperature (28 ± 0.5 °C). The results are shown in Figures 1−6. The frictional resistances of the three liquids in the four pipes of various materials for fully developed laminar flow were investigated. Pressure drops were measured under different flow rates through a pipeline experimental apparatus. The schematic diagram of the apparatus is shown in Figure 7.
Figure 1. Contact angles of tap water on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE. 12545
DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
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Figure 2. Sliding angles of tap water on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE.
increasing the average velocity of the liquid, and the viscous layer further becomes thinner and the slip length gradually becomes positive. For ethylene glycol, as shown in Figure 12, since the contact angles on the four kinds of pipe walls are generally larger than those of the white oil, the slip lengths on the four pipe walls are almost positive regardless of the average velocity, which increase gradually with the increase of the average velocity. However, the impact of a smaller slip length on the fluid dynamic behavior is almost completely ignored. When the average velocity increases to a certain extent, the slip length on the pipe wall no longer increases but gradually becomes constant. The main reason may be that the liquid stress caused by the driving force effect is much greater than the interaction force between the solid and liquid at that instant. When the viscous layer formed by the pipe wall and liquid is pushed by external forces, this layer no longer exists. In other words, when the pressure of the liquid flowing in the pipe is relatively large, the wall slip length exhibits a weak relation with the average velocity. According to the linear slip length model, the slip length is constant and is not related to the shear rate. However, the calculation results indicated that the slip lengths do not tend to be constant until the average velocities increase to a certain extent. In addition, as shown in Figure 11, when the water flows in the PTFE pipe, the average of the wall slip lengths approaches 0.65 mm. Thus, it can be seen that the larger the contact angle of the solid−liquid interface the larger the slip length on the wall and the smaller the flow resistance of liquid flowing in pipe. 4.3. Shear Stress. This study is an investigation into the shear stresses of three liquids flowing in different pipes. The shear stresses of each liquid under different contact angles are compared at the same average velocity, and the results are shown in Figures 14, 15, and 16, respectively. From Figures 14−16, we can see that the wall shear stress has a linear relationship with the average velocity of each liquid and that the wall shear stress increases with the increase of the average velocity. This also indirectly confirms the relationship between these parameters in the calculation of the wall shear stress. For the three kinds of liquids, the shear stress on the wall decreases with an increase of the contact angle and a decrease of the sliding angle at the same average velocity, in all cases. Additionally, as shown in Figures 15 and 16, when the average velocity is small, the differences in the wall shear
Figure 3. Contact angles of ethylene glycol on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE.
In the case of the white oil shown in Figure 10, a positive slip velocity does not appear until the contact angle or the average velocity increases to a certain extent, because of the smaller contact angles of the white oil on the four pipe walls compared to the tap water and ethylene glycol. This phenomenon may be due to the fact that when the average velocity of the white oil flowing in the lyophilic pipe at the same pressure drop is smaller; this implies that the shear stress of the liquid near the wall is smaller. However, the surface wettability of the white oil for the pipe wall is stronger. Thus, a viscous layer similar to that observed at the macro level appears, which results in a negative slip velocity of white oil on the lyophilic pipe wall and a greater flow resistance. The experimental results also verify that the slip velocity is proportional to the shear stress in the slip length model. 4.2. Slip Length. According to the experimental data on flow resistance characteristics, the slip lengths of the three kinds of liquids in the different pipes are calculated for different average velocities. The results are shown in Figures 11, 12, and 13, respectively. As depicted in Figure 13, when the average velocity of the white oil is relatively small, the slip length associated with the four pipe walls is negative, resulting in negative slip. As the average velocity increases, the slip length gradually becomes positive. The reason for this phenomenon is that the contact angles of white oil on the pipe walls are small, since the white oil is strongly attracted by the molecular attraction potential of the pipe wall and the white oil molecules near the pipe wall are adsorbed when it flows through the lyophilic wall. Then, a viscous layer which cannot flow at a certain pressure gradient is formed. At this instant, the liquid molecules are stratified and orderly distributed with a property of similar to that of a solid. It is equivalent to narrowing the flowing pipe and reducing the effective pipe diameter. The shear stress increases with
Figure 4. Sliding angles of ethylene glycol on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE. 12546
DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
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Industrial & Engineering Chemistry Research
Figure 5. Contact angles of #26 white oil on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE.
Figure 6. Sliding angles of #26 white oil on four pipe surfaces: (a) stainless steel, (b) plexiglass, (c) PP, and (d) PTFE.
Figure 7. Schematic diagram of the pipeline experimental apparatus.
Figure 8. Dependence of the slip velocity of tap water on average velocity.
Figure 9. Dependence of the slip velocity of ethylene glycol on average velocity.
stresses for the same liquid in different pipes are smaller. The gap gradually widens with the increase of the average velocity. It therefore seems that the larger the contact angle of the solid−liquid interface the smaller the sliding angle and the smaller the wall shear stress. As a result, flow resistance of the same liquid in different pipes is reduced.
4.4. Flow Increment. Under the same pressure drop, the ratios of the slip flow rates of each liquid in different pipes and the no-slip flow rates are calculated. The results are shown in Figures 17, 18, and 19, respectively. According to the definition of the flow change after introducing the slip boundary condition at the same pressure 12547
DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
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Industrial & Engineering Chemistry Research
Figure 10. Dependence of the slip velocity of white oil on average velocity.
Figure 13. Dependence of the slip length of white oil on average velocity.
Figure 11. Dependence of the slip length of tap water on average velocity.
Figure 14. Dependence of the shear stress of tap water on average velocity.
Figure 12. Dependence of the slip length of ethylene glycol on average velocity.
Figure 15. Dependence of the shear stress of ethylene glycol on average velocity.
drop, the flow change in the pipe is proportional to the slip length and the greater the slip length on the wall, the greater the flow rate of liquid in the pipe. When the calculated slip length and the characteristic length of the pipe are of the same order of magnitude, a significant drag reduction can be
achieved. When the slip length is much smaller than the characteristic length of the pipe, then the slip length can be almost ignored. At this time, the ratio of the slip flow for the slip boundary condition to the no-slip flow condition is one, and it is considered that no slip occurs in the flow. From Figures 17−19, this is confirmed from the curves of the 12548
DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
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Industrial & Engineering Chemistry Research
Figure 19. Dependence of the flow increment of white oil on pressure drop.
Figure 16. Dependence of the shear stress of white oil on average velocity.
degrees of slip phenomenon on the pipe wall appear, which results in an increase in the flow of the fluid. When the contact angles between the three kinds of liquids and the pipe walls are less than the corresponding values respectively, the slip flow rates of the liquids are consistent with the variations of the pressure drops. It shows that at a certain pressure drop the larger the contact angle of the same liquid in different pipes the easier the ratio of the slip flow to the no-slip flow exceeds one. Thus, it can be seen that whether slip flow of the same liquid in different pipes occurs is closely related to the wettability of the solid−liquid interface and the pressure drop.
5. CONCLUSIONS In this investigation, the correlations between flow velocity and slip parameters of fluid in a pipe were derived by applying the basic theory of fluid mechanics. The slip parameters of ethylene glycol, water, and #26 white oil flowing in different pipes were calculated using the slip boundary condition. The influence of surface wettability on the flow slip characteristics and the mechanism of drag reduction were discussed. The main results are as follows: (1) The reduction of liquid flow resistance is mainly attributed to the increase of the contact angle and the decrease of the sliding angle. Thus, this leads to a decrease of the shear stress on the pipe wall, which results in the increase of the slip velocity and the slip length. (2) The negative slip phenomenon exists at low-speed flow for part of the liquid, which is different from the linear slip length model. The slip length does not tend to be constant until the average velocity increases to a certain value. It is shown that the increase of the average velocity can reduce the negative effect of wettability on the flow to a certain extent. When the flow velocity is sufficiently large, the wall slip length is basically independent of the wettability of the solid−liquid interface.
Figure 17. Dependence of the flow increment of tap water on pressure drop.
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Figure 18. Dependence of the flow increment of ethylene glycol on pressure drop.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
pressure drop and flow increment of the three liquids flowing in the different pipes. Without considering the change of pressure drop in the pipe, when the contact angles of the tap water, ethylene glycol and white oil on the pipe walls are greater than 62.2, 53.77, and 60.81° respectively, different
ORCID
Hongyuan Qi: 0000-0003-2578-6065 Notes
The authors declare no competing financial interest. 12549
DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
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DOI: 10.1021/acs.iecr.8b02759 Ind. Eng. Chem. Res. 2018, 57, 12543−12550
