In Situ Grafting Hydrophilic Polymeric Layer for Stable Drag Reduction

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

In-situ Grafting Hydrophilic Polymeric Layer for Stable Drag Reduction Chaoguo Tian, Xingwei Wang, Ying Liu, Wufang Yang, Haibao Hu, Xiaowei Pei, and Feng Zhou Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00321 • Publication Date (Web): 14 May 2019 Downloaded from http://pubs.acs.org on May 17, 2019

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In-situ Grafting Hydrophilic Polymeric Layer for Stable Drag Reduction Chaoguo Tian†, Xingwei Wang‡, Ying Liu*,†, Wufang Yang*,†‡ , Haibao Hu*,‡‡, Xiaowei Pei‡, and Feng Zhou†‡ †School

of Mechatronics Engineering，Nanchang University，Nanchang 330031，

China ‡School

of Materials, Northwestern Polytechnical University, Xi’an 710072, People’s

Republic of China †‡

State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics,

Chinese Academy of Sciences, Tianshui Middle Rd, 730000 Lanzhou, China ‡‡

School of Marine Science and Technology, Northwestern Polytechnical University,

Xi’an 710072, People’s Republic of China

ACS Paragon Plus Environment

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ABSTRACT Developing drag reduction techniques have attracted great attention due to their desperately needs for practical applications. However, many of the proposed strategies were subject to some evitable limitations, especially for long period of adhibition. In this work, the dynamic but stable drag reduction effect of super-hydrophilic hydrogel coated iron sphere falling freely in a cylindrical water tank was investigated. The absolute instantaneous velocities and displacements of either the hydrogel encapsulated or unmodified iron sphere falling freely in water were monitored via high-speed video. It was revealed that，in the range of Reynolds number from 104 to 106 ， the optimized hydrogel coated iron sphere with uniform stability could reduce the resistance by up to 40%, which was mainly due to the boundary slip of water and the lagged boundary separation resulted from coated hydrogel. Besides, the deliberate experiments and analysis further indicated that super-hydrophilic hydrogel layer accompanied by the emergence of the drag crisis has largely effected the distribution of flow field at the boundary around the sphere. More importantly, the drag reduction behavior based on the proposed method was thermodynamically stable and resistant to external stimulus, including fluidic oscillator and hydrodynamic pressure. The effective long-term drag reduction performance of hydrophilic substrate can be expected, correspondingly, and also provides a novel preliminary protocol and avenues for the development of durable drag reduction technologies.


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INTRODUCTION The development of drag reduction technologies has been a hot topic in contemporary world since they have made great contributions to energy conservation. Besides, its economic benefits induced by decreased fluid resistance are obvious to sustainable development as well. At the moment, many researchers are still interested in designing and developing of various drag reduction technologies. One of the hottest technologies is to introduce gas layer with ultra-low viscosity into solid-liquid surface, reducing the friction resistance induced by solid-liquid interactions. The physical drag reduction mechanism of gas layer is that the non-slip or viscous boundary conditions at the solid-liquid interface are replaced by the totally slippery boundary conditions at the gas-liquid-solid interface.1-4 As a consequence, different strategies have been proposed to construct gas-liquid-solid three phase interface.3 Among that, the surface with super-hydrophobicity is one of the typical examples, which can naturally form a thin air cushion closed to the solid-liquid interface and is usually called as the plastron.5-8 Based on this, different techniques have been developed for the preparation of superhydrophobic substrates.9-11 In addition, there are other strategies to improve and maintain the formation of air layer on the solid surface, such as cavity encapsulation,12 bubbles or gas injection near the surface,13 etc. However, the long-term application of these surfaces is hindered by their thermodynamic instabilities, especially under fluid flow.14 In recent years, the study of drag reduction in turbulent flow has made great progress as well. The results showed that the fluid resistance for the superhydrophobic


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sphere could decrease by 50% to 80% in the high Reynolds number.15 The representative example of drag reduction under high Reynolds number is the use of Leidenfrost effect,16-18 where the solid sphere was heated to a certain temperature which was generally higher than the boiling point of surrounding liquid so that a continuous vapor layer can be maintained. It has been proved that this unique effect is an effective method to decrease the fluid resistance of solid object by more than 85% through triggering the early drag crisis transition.19-22 Here, the so-called drag crisis is caused by the turbulent state transition of the viscous boundary layer, where the resistance will drop suddenly and the velocity will exceed the critical value when the blunt body moves in the fluid. And the hydrodynamic resistance for a smooth solid sphere with diameter D and moving at velocity U in a fluid with a density ρ can be





described by the drag coefficient C D  8 FD / D 2 U 2 , where FD is the resistance to the solid sphere. The CD for a solid sphere varies with the Reynolds number

Re  DU /  , where µ is fluid shear viscosity, and is well known. Especially, the drag reduction effect for the ice hockey surface, which is caused by the boundary layer torsion because of the phase transition and mass transfer on the ice hockey surface，is most notable.23 While different from the previous gas layer drag reduction mechanism, ice hockey drag reduction is a novel drag reduction mechanism with thermodynamic stability and high cost-effect, therefore, drag reduction strategy based on this new type of drag reduction mechanism but occupied with enough thermodynamic stability is worthy of research and development.


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In this present work, we studied the free fall behavior of an iron sphere encased in a super-hydrophilic hydrogel in a finite cylindrical basin. The drag reduction effect of the super-hydrophilic interface was explored when the sphere was affected by water. And their intrinsic drag reduction mechanism was proposed as well. Compared with the existing hockey drag reduction technology, the drag reduction performance based on super-hydrophilic hydrogel might support a more practical technique and is expected to reveal a deeper cognition about hockey drag reduction. EXPERIMENTAL SECTION Iron sphere modification The spheres used were fresh polished iron spheres, the density and diameters of applied iron spheres are 7.8 g·cm-3, 25 mm and 30mm, respectively. Moreover, in order to secure a single variable, hollow iron spheres with a varying diameter and an average density of 7.07 g/cm3 were used to study the effect of hydrogel thickness on drag-reduction performance. The average surface roughness given by the manufacturer was Ra < 0.06 μm. A cotton cord with a diameter about 0.3 mm was tethered to the iron sphere surface via commercially available glue to facilitate handling of the sphere without touching the sphere surface. All of the iron spheres, including the control sample, were used after washing thoroughly with dehydrated alcohol. While, iron sphere with super-hydrophilic hydrogel layer was fabricated through surface self-catalyst polymerization reaction by soaking the fresh iron sphere into pre-polymerization solution for certain time. In this case, the pre-polymerization solution was composed of acrylic and acrylamide monomers, initiator potassium


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persulfate, and cross-linker MBA. The typical experimental process for the preparation of hydrogel is as follows, acrylic acid (1.68 g), acrylamide (8.52 g), 3-sulfopropylester potassium methacrylic acid salt (SPMA, 0.85 g), potassium persulfate (0.02 g) and MBA (0.04 g) were added into 80 mL deionized water. The pre-polymerization solution was obtained after degassing for 10 minutes using N2. Then, the cleaned iron sphere was immerged into the as-prepared solution for certain time. The surface self-catalyzed polymerization was happened and hydrogel layer with controllable thickness can be achieved by tailoring the reaction time. Finally, the hydrogel encapsulated iron sphere was obtained by soaking the sample into deionized water for 3 minutes to remove residual pre-polymerization solution. For comparison, two types of samples were used with diameters 25 mm and 30 mm, respectively, including the smooth polished iron spheres and the iron spheres modified by super-hydrophilic hydrogel with variety of layer thickness and toughness (Fig. 1).

Fig. 1 (a) picture shows a modified iron sphere with 30 mm diameter through a super-hydrophilic hydrogel after immersed in water shortly. The surface of an iron sphere appears to be covered with obvious water film due to the hydration effect of the hydrogel component. (b) Picture shows the same iron ball soaked in water for five hours, with obvious cracks appearing on its surface and the thickness of hydrogel layer increased greatly because of swelling effect. Accordingly, the sphere free fall experiments were conducted after the hydrogel coated iron spheres were emerged into water for a few minutes.


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Free falling sphere experiments The water tank required for the free fall sphere experiments was custom made by TianChang Organic Glass (ShangHai), China. The tank is 2.0 m high and has diameter 20 cm. The column wall of the tank is transparent reinforced organic glass that provides the possibility to monitor the whole process of spheres falling through tank via high-speed video (Fastec Imaging IL3-100SM4). As a consequence, the instantaneous velocity and displacement of falling sphere can be obtained by digital video post-process (see video-1 and video-2 in the Supplemental Information). For the characterization process, the tank was fixed on an aluminum alloy test frame and equipped with a highlighted LED light at the rear of tank. All experiments were conducted in water medium at room temperature about 20 ℃.The spheres were carefully dipped below the surface of water and suspended by a metal rod. When it was not oscillated any more, the cotton cord was instantaneously blown to allow the sphere falling freely. Besides, to ensure the accuracy of test process, the outside wall of tank was marked with a scale line, and all the sphere samples fell at the same position which was remarked as zero point. The typical process of spheres falling in the tank was recorded by a high-speed video camera with a filming rate of 500 fps. The sphere trajectory coordinates vs. time and the corresponding instantaneous velocity were determined by processing the videos (see video-2 and Fig. S1 in the Supplemental Information) with the camera software (Fastec-FasMotion). Each experiment for the hydrogel modified spheres was conducted under the same conditions exactly and was repeated for at least three different runs.


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Determination of the drag coefficient There are many strategies to describe the movement of a sphere moving in a fluid. Considering the motion velocity of the sphere occupied large range, the classical Basset-Boussinesq-Oseen (BBO) equation24-26 was used in this paper. The drag coefficient could be approximately expressed as, CD 

4D   S   g   S  0.5  dU  2  3U  dt 

(1)

where D = 2R, ρS is the density of the sphere, ρ is the density of the fluid, and U is the instantaneous velocity of the sphere corresponding to a certain time t, g is the acceleration due to gravity. Using the BBO equation, the evolution of the sphere velocity over time could be predicted when the relationship between resistance coefficient and velocity is known for the entire range of the sphere falling.24 For a sphere falling with steady free fall velocity at terminal velocity UT, derived from the balance between buoyancy, gravity and drag forces, this equation converges to the expression as follow, CD 

4D  S   g 2 3U T

(2)

For all of the spheres studied in this experiment, the dependence of experimental velocity vs. time can be well fitted by exponential form,



U  U T 1  e t /



(3)

This equation has been used previously to predict the terminal velocity of the sphere for the case where the sphere is still accelerating at the bottom of the tank and the terminal speed UT has not yet been reached.27 However, here, equation (3) was limited


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to use as a smoothing function for the experimentally observed dependence of U and t during the fall of the sphere in the 2.0 m tank. (Fig. S4 and Fig. 2 and Fig. 3) Among them, the fitting process of the velocity-time curve was shown in Fig. S3 and was fitted in the same way. RESULTS AND DISCUSSIONS The hydrogel layer crosslinker dependence In the process of hydrogel layer preparation, it was found that pre-polymerization solutions with variable cross-linker contents would produce hydrogel layers with different toughness, and the corresponding falling peculiarity of the hydrogel layer coated iron sphere would change significantly. Therefore, the dependence of drag reduction behavior on the interface toughness was investigated firstly. Taking the 30 mm diameter spheres with different interface toughness (crosslinking degree) but same hydrogel layer thickness (0.33 mm) as an example ， the fitted velocity-time curves for different samples could be derived from post-processing of the recorded video file. For example, by measuring the momentary displacement of iron sphere at the same time interval (video-2 and Fig. S1 in the Supplemental Information), both the displacement-time curves (Fig. S2) and the corresponding velocity-time curves (Fig. 2) could be derived. Meanwhile, the terminal velocities of the different samples also could be speculated according to the changed trend of their velocity curves. Here, four different samples with different cross-linker contents were prepared (the contents of cross-linker were 0.04 g, 0.24 g, 0.32 g and 0.4 g ， respectively), and it was obvious to find that the terminal velocity of hydrogel layer coated iron sphere with


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variable moduli heavily depended on the cross-linker mass content and increased with the decrease of the content of cross-linking agent. As shown in the Fig. 2, the terminal velocity for the undecorated iron sphere was 2.28 m/s, while the terminal velocity of sphere modified with highly crosslinked hydrogel layer would be significantly smaller and far lower than the terminal velocity of the control. For example, the corresponding terminal velocity was 2.0 m/s for the hydrogel-0.4 sample in the Fig. 2, in which 0.4 indicated the mass content of MBA. While, reducing the mass content of cross-linker, the measured terminal velocity would not only gradually increase but even be higher than the terminal velocity of the unmodified sphere. For example, the terminal velocity for the hydrogel-0.04 sample was high up to 2.7 m/s, which indicated an obvious drag reduction performance of the hydrogel coated sphere. In this case, since the polymer network was produced with lower crosslinking degree, the observed drag reduction property might be attributed to the unique interface properties of hydrogel layer with relative weak toughness. Combining the terminal velocities depicted in the Fig. 2, the drag coefficient of the spheres can be calculated via equation (2). At the same time, due to the intervention of the hydrogel, the velocity gradient of the sphere falling in the water was affected, and the velocity gradient of the hydrogel-modified sphere was smaller than that of the unmodified sphere because the hydrogel layer reduces the frictional resistance of solid-liquid interface. The time taken for the hydrogel layer modified sphere to reach the terminal speed in Fig. 2 was longer than that of the unmodified sphere. Two different results were observed compared with the drag coefficient CD=0.46 of the unmodified sphere


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at terminal velocity. When the content of the cross-linking agent was large, the drag coefficient of the sphere was CD=0.62 (for the hydrogel 0.4 g sample), and the drag coefficient was CD=0.38 when the content of the cross-linking agent was small (for the hydrogel 0.04 g sample). These experimental results showed that the drag reduction effect was not found in the case of large cross-linking agent content, but was more obvious in the case of small cross-linking agent content, and the corresponding drag reduction efficiency could reach up to 17%. In order to further explain the influence of degree of crosslinking on the drag reduction performance of hydrophilic hydrogel layer, the physicochemical properties of hydrogel layer (including rheological properties, equilibrium water content, mechanical loss, etc.) were studied. The Fig. 3 (a) stated the rheological properties of the hydrogel layer with different crosslinking degrees. It can be found that both storage modulus (G’) and loss modulus (G’’) of the hydrogel layer decreased with the decrease of mass content of crosslinking agent. Meanwhile, the change trend of equilibrium water contents and corresponding mechanical loss (It was expressed as G’’

the tangent of the loss angle tanδ = G’ ) of hydrogel layer alone with mass content of cross-linker were presented in the Fig. 3 (b). It was not difficult to find that the mechanical loss and the equilibrium water content of the hydrogel layer decreased continuously alone with increase of mass content of crosslinker. As a consequence, the water content of the hydrogel layer was increased, and the water in the outer hydrogel layer had a certain fluidity, which caused the velocity gradient at the interface to decrease, resulting in a drag reduction effect. These measured results


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stated that the interface properties of hydrogel coating, including the water content and viscosity modulus changed with the crosslinking agent, might have a great influence on the solid-liquid interaction, and drag reduction phenomenon for iron sphere falling freely in water. Therefore, the drag reduction performance can be maintained

by

tailoring

hydrophilic

component

with

specified

interface

physicochemical parameters.

Fig. 2 The velocity-time curves of the spherical samples falling freely in water, in which the samples were prepared with different cross-linker contents. The open black block represents the control iron sphere without hydrogel modification; however, the red circle, the blue triangle and the green triangle indicate the velocity-time curves of hydrogel encapsulated iron spheres with variable cross linker content as depicted in the picture, respectively. The hydrogel thickness for all the applied samples was constant at 0.33 mm.


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Fig. 3 (a) The rheological properties of the hydrogel layer. The black, the red, the green and the blue lines indicate the change trend of G' and G'' when the contents of hydrogel crosslinking agent were 0.04 g, 0.2 g ,0.24 g and 0.4g, respectively. (b) The variation trend of water contents and mechanical loss of hydrogel layer with different crosslinker contents, where the red triangle represents water content and the blue triangle represents mechanical loss, tan.

The hydrogel layer thickness dependence According to equation (2), it was necessary to investigate the influence of the hydrogel thickness on the velocity curve and further clarify the relationship between the thickness of hydrogel layer and drag coefficient. Since the diameter D of the sphere was also one of the factors affecting the drag coefficient CD, in order to make sure that the thickness of the hydrogel layer was the only variable, the gravity-buoyancy for all of the employed samples were kept constant by injecting the lead powder into the iron with different original diameters. The variable hydrogel thickness was prepared by controlling the polymerization time, and the corresponding thickness of the modified hydrogel layer on the spheres was determined by measuring the diameter of rapidly frozen sample. Fig. 4 showed the velocity curves of hydrogel layer coated iron spheres with different thicknesses, and 30 mm apparent diameter of hydrogel coated iron spheres were used to complete the experiment. The experimental


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results showed that the thinner the hydrogel layer thickness, the higher the terminal velocity of the sphere falling in water. Besides, the results also showed that, the terminal velocity of the sphere would lower than the unmodified iron sphere with further increasing the hydrogel layer thickness, there was even no drag reduction effect was observed. For example, the calculation results showed that the terminal velocity of the sphere modified by the thin hydrogel layer could reach up to 2.45 m/s and significantly increased compared with the terminal velocity of the unmodified sphere (1.98m/s). The probable drag reduction mechanism in terms of the evolution of boundary layer was depicted in the Fig. 5, for the pristine iron sphere, the particles of fluid were accelerated and started moving forward by the suitable pressure in the front of sphere although affected by the skin-friction resistance (Fig. 5a). Then the particles of fluid moved into the transition zone and the velocity started to decrease when the pressure becomes lower than the skin-friction. Finally, the velocity gradually approached to zero, which was mainly induced by the combined interaction between the decreased suitable pressure and frictional resistance. As a consequence, boundary separation occurred and vortex generated to exhaust the energy for the back flow ahead caused by counter pressure. However, for the case of sphere coated by thin hydrogel layer (Fig. 5b), the skin friction interaction between hydrogel and water decreased greatly since the hydrogel can be regarded as the water with prodigious viscosity but possess relatively limited liquidity, the fluid particles therefore could accelerate to higher speeds by the suitable pressure which possessed higher inertial force to overcome the counter pressure, and the separation point was delayed and


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close to the back of the sphere consequently. However, for the situation of the iron sphere with thick hydrogel layer (Fig. 5c), the deformation of hydrogel layer was more prominent. Especially, the larger hydrodynamic pressure caused the larger deformation alone the downstream direction but smaller deformation along vertical direction of fluids flow, which resulted in the sphere became into an ellipsoid with rotation axis parallel to the flow direction. Under this circumstance, the gradient of counter pressure was more intense and particles of fluid could not overcome the counter pressure despite of the lower frictional resistance of hydrogel layer, therefore, the corresponding drag reduction effect decreased even disappeared. As a conclusion, the thickness of the hydrogel layer should be controlled within a certain range to endow the sphere falling in water with a drag reducing character.

Fig. 4 The velocity versus time curves of falling velocities of spherical samples with different hydrogel thicknesses. The black curve is the velocity curve of the unmodified iron sphere with 30 mm diameter. The red, blue and green curves are the velocity curves of hydrogel coated sphere with different thickness as depicted in the picture, respectively.


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Fig. 5 Schematic diagram of boundary separation of a sphere moving in water. (a) shows the separation of the spherical boundary layer without modification. (b) shows the separation status of spherical boundary layer modified by thinner hydrogel layer, with obvious boundary layer separation delay. (c) shows the boundary separation of the sphere modified by a thicker hydrogel layer, and the boundary layer separation delay is insignificant.

Reynolds number dependence For a deeper understanding of the drag reduction behavior based on hydrophilic hydrogel layer, the dependence of the drag coefficient on Reynolds number (ranging from 104 to 106 , water at 20℃, =1.00 kg m-3, μ=1.005 mPa s) was investigated as well. Based on the previous data analysis about Fig. 2 and Fig. 4, the influence trend of Reynolds number on the drag coefficient of the sphere was calculated using equation (1). It was easy to find from the Fig. 6 that the drag coefficient decreased abruptly when the drag crisis occurred, in which the falling velocity of sphere has reached a certain point. For example, the boundary layer became turbulent and the flow separation point moved downstream to the rear of the sphere at the critical value of Re≈3×105 for the Leidenfrost surface. Meanwhile, the corresponding sphere drag


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coefficient dropped sharply from CD≈0.44-0.5 to CD≈0.1-0.2.23,28,29 For the different types of surface investigated in this study, the drag coefficient went down as reducing the content of crosslinking agent under the same Reynolds number condition (Fig. 6a). Firstly, for the case of sample with higher mass content of cross-linking agent (0.4g), the hydrogel-modified iron sphere even showed higher drag coefficients than the unmodified sphere and was less affected by the Reynolds number, which indicated that there was no drag reduction effect endowed by the hydrogel layer with higher cross-linking degree. After that, an obviously change of drag coefficient alone with Re has been observed as long as the content of crosslinking agent was controlled within a certain range. Taking the sample with 0.04g mass content of crosslinking agent as an example, its corresponding drag coefficient decreased as the Reynolds number increased until the sphere reached the terminal velocity. The corresponding drag coefficient of the sphere declined from CD=0.54~0.50 to CD=0.42~0.38 at Re≈4×105. Such change was attributed to the transformation of boundary layer separation since the hydrogel layer impacted the boundary condition which contained solid-liquid contact conditions as well as surface physicochemical conditions, parameters, etc. and moved the separation point to the reverse pressure gradient on the downstream side of the sphere.30 On the other hand, the effect of hydrogel thickness on the drag reduction performance was investigated in terms of the relationship between the drag coefficient CD with Reynolds number Re. As shown in the Fig. 6b, the content of cross-linker was kept constant but the thicknesses of the hydrogel layer were changed for all the


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prepared samples. It was clear to find that the falling process of the hydrogel layer coated iron spheres changed with the Reynolds number and the changed trends were largely different from each either. Absolutely, it’s remarkable that the interface can be endowed with robust drag reduction ability when the crosslinking degree and the thickness of coated hydrogel layer were controlled within a certain range.

Fig. 6 The effect of the Reynolds number on the drag coefficient of hydrogel layer coated sphere falling in water. (a) the dependence of drag coefficient on the Reynolds number for hydrogel modified iron sphere with diverse crosslinking agent amount, open blue squares are for the unprocessed iron sphere, and the open red nabla, round, and diamond are for the hydrogel layer coated iron sphere in which the contents of crosslinking agent were 0.04, 0.2 and 0.4 g respectively. (b) the dependence of drag coefficient on the Reynolds number for hydrogel modified iron sphere with diverse hydrogel layer thickness, open blue squares represent the unprocessed iron spheres, open red nabla, round and diamond are for hydrogel coated iron sphere in which the thicknesses of the hydrogel layer were 0.225, 0.33, and 0.67 mm, respectively.

In the range of Reynolds number studied, the calculated results showed that the drag coefficient of the hydrogel-modified sphere changed from CD=0.678~0.664 to CD=0.558~0.402 with the variation of the hydrogel layer thickness (from 0.67 mm to 0.225 mm). Compared with the drag coefficients of the unmodified sphere (CD=0.678~0.664), the drag reduction efficiency of the hydrogel-modified sphere can be calculated and varied from -0.2% to 40.17% with decreasing the thickness of hydrogel, which indicated that the drag reduction efficiency of hydrogel coated sphere


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changed from small to large as the thickness of the hydrogel layer decreased. These experimental results were mainly attributed to the delayed separation of the boundary layer from laminar flow state to turbulent flow state and the continuous increase of the velocity of fluid particles on the boundary layer. In detail, for the boundary fluid particles of the undecorated sphere, the emergence of the drag crisis was not very easy because of the larger surface friction resistance. However, the surface friction overcame by fluid particles reduced because of the intervention of hydrogel layer, and the boundary layer drag crisis was more likely to occur. What is more, compared with the thicker hydrogel layer modified sphere, the thinner hydrogel layer boundary was more likely to have a drag crisis in advance (Fig. 6 (b)) and even an obvious increase of falling velocity (Fig. 5). These experimental result and analysis process above showed that the early occurrence of the drag crisis would result in a large reduction of the drag coefficient, appearing a drag reduction effect.


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Fig. 7 The distribution of the flow field around the sphere during falling process. (a) shows the unstable flow field distribution around the unmodified sphere as it falls in the water and a slight boundary layer back movement; (b) shows that the flow field around the sphere covered by the thinner hydrogel layer gradually stabilizes and the surface boundary layer has a large backlash; (c) shows the longitudinal deformation of a sphere covered by a thicker hydrogel layer and the unstable flow field around it and the inconspicuous boundary layer back-slope phenomenon.

Finally, the change of flow distribution of the boundary layer around the sphere from solid sphere boundary to hydrogel layer boundary was shown in Fig. 7. For the thinner hydrogel layer with less crosslinker content, the flow field around the sphere would develop to a more stable state with smaller eddy current and decreased hydrodynamic resistance to the sphere when compared with the solid sphere boundary (Fig. 7 (a)), its drag crisis therefore occurred at a smaller Reynolds number. Besides, the boundary separation point had a larger offset toward the downstream of the sphere, and the drag reduction effect was more pronounced (Fig. 7 (b)). This result confirmed that the sphere modified by thin hydrogel layer with less crosslinking agent has better drag reduction effect, and its surrounding flow field tended to be more stable. However, in terms of the boundary layer belonging to a thicker hydrogel layer, it was more likely to undergo a larger deformation which might not bring a steady


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flow field under the condition of hydrodynamic pressure. The corresponding effect of the flow field was that the offset from the boundary layer separation point to the downstream of the sphere was relatively small (Fig. 7 (c)). As shown in Fig. 4 and Fig. 5, even a drag increase phenomenon was obtained when the sphere was modified by the thicker hydrogel layer. CONCLUSIONS In this study, the effect of the hydrophilic coating on the drag reduction performance of iron sphere falling freely in water was investigated, and was mainly reflected in the fact that the hydrogel-modified iron sphere had a higher instantaneous velocity at the same displacement than the unmodified sphere. More importantly, it was found that the optimal drag reduction effect could reach up to about 40% when the content of cross-linker and the thickness of hydrogel were controlled within a certain range, which exceeded the limit of drag reduction efficiency based on polymer additives.30 The essential drag reduction mechanism of the hydrophilic polymer was different from either the lubricant-impregnated surfaces drag reduction effect31 or drag reduction effect of polymer which acted as additives in multiphase flow,32,33 but was mainly attributed to the decreased surface frictional resistance of the fluid particles near the boundary layer and the developed more stable flow field around the sphere because of the intervention of hydrogel layer. Besides, the drag reduction capability also can be proved by the delayed boundary layer separation and the advanced occurrence of drag crisis. These results will provide a preliminary research foundation for the development of a more practical prototype of the drag technology


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with thermodynamic stability and strengthen the theoretical investigation concerning drag reduction exploration. Supporting Information Quasi-static displacement of steel sphere during falling freely in water, the displacement-time curve of hydrogel modified spheres falling freely in water with variety of crosslinking degrees and thicknesses, velocity-time curves of hydrogel coated steel sphere and blank steel sphere. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author *E-mail: [email protected]

Tel: 0086-791-83968875l.

[email protected]

Tel: 0086-931-4968045

[email protected] Tel: 0086-029-88491571 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This research was finally supported by NSFC (21773274, 21434009 and 51573198).

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In Situ Grafting Hydrophilic Polymeric Layer for Stable Drag Reduction

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