| Citation: | JIAO Yun-long, DONG Lei, LIU Xiao-jun, LIU Kun. Spreading features of droplet on micro-textured surface[J]. Journal of Traffic and Transportation Engineering, 2017, 17(4): 98-105.
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There is a widespread phenomenon in engineering technology where fluids drip or splash onto solid surfaces and then spread and flow along their surfaces[1-2]In automotive internal combustion engines, the cylinder liner piston ring is an important friction pair, and the spreading behavior of lubricating oil on the cylinder liner surface has a significant impact on the distribution of oil film thickness and the wear of the contact surface. The micro geometric morphology of the friction pair surface also plays an important role in the spreading and wetting behavior of lubricating oil[2]It directly affects the film-forming speed of lubricating oil. In high-speed train drag reduction technology, by adding ball and socket non smooth surfaces on the surface of the vehicle body to control the turbulent characteristics of the fluid in the boundary layer, good drag reduction effects can be achieved[3]In addition, by designing patterns with concave groove type drag reduction structures on car tires, the drainage performance of the tires can be improved, and the safety of driving in rainy weather can be enhanced[4]Therefore, studying and controlling the spreading and wetting properties of fluids at the interface is of great significance for improving the lubrication mechanism of internal combustion engine cylinder liner piston ring, high-speed train drag reduction technology, and tire skid performance。
As early as 1805, Young first proposed the use of contact angle to characterize the wetting behavior of droplets on solid surfaces, and proposed the famous Young equation, which states that when the contact angle is less than 90 °, the solid surface is hydrophilic, and when the contact angle is greater than 90 °, the solid surface is hydrophobic[5]However, the Young equation is an equilibrium equation given under the assumption that the solid surface is isotropic, homogeneous, and flat; Considering the influence of the roughness of the actual solid surface on wetting, Wenzel introduced the roughness factor to describe the surface roughness, defined as the ratio of the true surface area of a solid to its projected area[6]However, the roughness defined in this way cannot actually reflect the characteristics of solid surface morphology, and surfaces with the same roughness but different morphologies will also have different effects on wetting; Cassie et al. further developed the Wenzel equation, imagining rough and uneven solid surfaces as composite or heterogeneous surfaces composed of various materials, and proposed the concept of composite apparent contact angle[7].
In recent years, many scholars at home and abroad have continued to explore and study in the field of contact angle models, mainly based on the Wenzel and Cassie models, and have derived various mixed contact angle models. Cheng Shuai et al. considered the influence of liquid wettability on solid-liquid contact angle and proposed an apparent contact angle model for regular rough surfaces[8]Yang Changwei et al. replaced the solid-liquid contact area fraction in the Cassie Baxter model with the local solid-liquid contact area fraction at the outermost edge of the contact line, which can better predict the apparent contact angle of droplets in a mixed state[9]Chen Xiaoling et al. used a polarizing microscope to observe the different forms of droplet infiltration into the gaps between microcolumns and non infiltration, as well as an intermediate state where condensed vapor partially infiltrates into the gaps between microcolumns. This partially infiltrated liquid exists in the form of internal three-phase contact lines, verifying the existence of the third type of state[10].
But with the deepening and development of research on surface wetting, scientists have discovered the limitations of simply using a static contact angle to describe the wetting and spreading characteristics of fluids on solid surfaces[11-16]Liquids with the same apparent contact angle exhibit different spreading characteristics due to the different microstructures of their solid surfaces. Based on the above research status, this paper combines two computer simulation software, Flow-3D and Solidworks, to study the spreading and wetting process of droplets on different micro textured surfaces. A three-phase contact line movement mechanism is proposed, which dynamically describes the spreading and wetting process of droplets on rough surfaces from three aspects: the spreading law of contact lines, the moving speed of contact lines, and the final spreading radius. The anisotropic characteristics of droplets spreading on micro textured surfaces are also analyzed.
The spreading motion of viscous droplets on solid surfaces is usually quantitatively described using lubrication approximation methods[12, 15-16]This method assumes that the characteristic scale of droplets in the horizontal direction is much larger than their characteristic scale in the vertical direction; Droplet spreading is dominated by surface tension and is an incompressible Newtonian fluid with isothermal motion. Based on the above assumptions, establishFigure 1In the plane Cartesian coordinate system xOz, consider the Navier Stokes equations in two-dimensional conditions, momentum and continuity equations for the spreading process of viscous droplets[12]Can be written as
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In the formula:uandwThey are respectively in the horizontal directionxAnd in the vertical directionzThe velocity component on top;TFor exhibition time;ρThe density of droplets;ηViscosity of liquid droplets during motion;▽2For Laplace operator;pFor pressure;GxandGzThey are the gravitational edgesxandzAcceleration in the direction;ФFor other forces.
It should be noted that when the size of the droplet is in the nanometer scale, the effect of separation pressure and line tension will affect the spreading process of the droplet[13]Therefore, an additional addition was made to the right side of the momentum equationФItem represents the action of these forces. The above is a theoretical model for the spreading of viscous droplets on a solid surface. Many foreign scholars have derived and simplified equations (1) to (3) based on this model, and obtained the "1/4", "1/7", "1/10" power and other standard laws for the position of the three-phase contact line on a smooth surface over time[15-16, 21]Zhao Yapu et al. also conducted a systematic study on the standard law of droplet spreading, exploring and demonstrating the spreading characteristics of droplets on hydrophilic surfaces through experimental observations and molecular dynamics simulations, using a combination of multi-scale methods[17-18]However, through these research results, it can be found that the solid surfaces considered in the theoretical model are all ideal solid surfaces, and the influence of real surface roughness factors has not been taken into account; The lubrication approximation assumption ignores the effects of separation pressure and line tension, and cannot reflect the force situation of droplets spreading on real rough surfaces. Therefore, this paper uses the computational fluid dynamics software Flow-3D as a platform, combined with the modeling function of SolidWorks 3D software, to simulate the spreading process of droplets on rough micro textured surfaces, and quantitatively describes the process using the proposed contact line movement mechanism.
The spreading problem of droplets on a solid surface is a very typical problem with a free motion interface, which involves changes in fluid morphology, contact between two-phase fluids, and collisions between fluids and solids[19]The traditional theoretical model, namely the droplet spreading momentum and continuity equations given by equations (1) to (3), strictly speaking, is only applicable to thin film spreading motion due to considerations of lubrication approximation and simplified calculation of equations, and is not suitable for general droplet spreading processes. In Flow-3D, in order to better calculate physical quantities such as pressure and velocity of fluids in the unit cell, the finite difference method discretizes the Navier Stokes equations and continuity equations, taking into account the effects of all forces including surface tension, gravity, separation pressure, and external interference forces. Therefore, it is applicable to fluid spreading motion under various conditions. Another significant advantage of Flow-3D is its ability to track free interfaces using the Volume of Fluid (VOF) algorithm. This article tracks the specific positions of droplets at various times during the spreading process, and obtains the changes in physical quantities such as radius, velocity, and pressure of droplets during the spreading process. Based on this, the movement mechanism of three-phase contact lines is established, laying the foundation for better explanation and description of droplet spreading process.
Figure 2The principle of VOF algorithm for tracking free interfaces in Flow-3D is studied by studying the fluid to grid volume ratio function in grid cellsFTo determine the free interface, ifF=1. This indicates that the unit is entirely occupied by the designated phase fluid unit liquid; likeF=If 0, then the unit is a liquid without a specified phase fluid unit; If 0<;F< 1. The unit is a solid-liquid interface. Due to the fact that the VOF method tracks the fluid volume in the grid, rather than the motion of free surface fluid body points, it can handle nonlinear phenomena such as free surface overlap.
Figure 3Numerical simulation process for droplet spreading process. Firstly, use the 3D drawing software SolidWorks to create a solid surface geometry with dimensions of 10mm × 10mm × 0.5mm and a microstructure area of 10mm × 10mm. Four types of microtextures, including square pits, square protrusions, rectangular pits, and rectangular protrusions, were selected, along with the original smooth surface. A total of five solid surfaces were named S in sequence1~S5, sequentially representing surfaces without texture, square pits, square protrusions, rectangular pits, and rectangular protrusions. according toTable 1Using three-dimensional software, draw five solid surface geometries based on the given dimensions of individual microtextures and the spacing between adjacent microtextures. It should be noted that,Table 1The spacing and size of micro textures are empirical parameters determined based on the actual volume and spreading radius of droplets. In contact angle measurement experiments, the volume of droplets is usually controlled between 1.5~2.5 μ L, with a radius of 0.71~1.3mm. Therefore,Table 1The given microstructure size meets the simulation requirements.
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The density of the grid in Flow-3D determines whether geometric entities and fluids can be clearly expressed, which is related to the convergence and stability of the solving process. Based on the research content of this topic, it has been determined that图 4The solution area and grid density. In addition, considering the actual process of droplet spreading, according to the set coordinate system direction, the droplet spreads vertically downwards, with the boundary condition set as no slip on the solid wall surface, and default boundary conditions selected for the other five directions. Select water at room temperature and pressure as the liquid type, with the following parameters: density of 1g · cm-3The viscosity is 0.001Pa · s and the liquid gas surface tension is 0.073 N · mm-1The gravitational acceleration is 9.8m · s-2The final step in the preparation work is to choose a suitable physical model. During the spreading process, droplets are subjected to forces such as surface tension, gravity, separation pressure, and linear tension. Therefore, the simulation process selects gravity, surface tension, turbulence, and viscosity models, and sets appropriate parameters. Finally, based on empirical parameters, provide the convergence time of the droplet spreading process, select the output term, and complete the simulation preparation phase。
In order to investigate the influence of microtexture on the spreading process of droplets, the volume of the droplets was kept constant (all at 1.5 μ L) during the simulation process, and the solid substrate material was the same, All T values are 0.01s and have reached a stable equilibrium state.Figure 5~7Droplets in S1~S3The surface spreading process can be observed by observing the simulation results, and it can be found that the equilibrium contact angle of the droplet on three surfaces isθ1~θ3satisfyθ1> θ2> θ3The relationship; Micro texture promotes the spreading motion of droplets on solid substrates, improving the spreading characteristics of droplets. Moreover, the stronger the dominance of micro protrusions compared to micro pits, the more favorable it is for droplet spreading.
Wenzel et al. defined the influence of surface structure characteristics as roughness factor r and proposed a modified equilibrium contact angle θ[6-7]do
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In the formula:rThe ratio of the actual contact area between solid and liquid to the apparent contact area.
be directed againstTable 1The micro texture type designed (S2、 S3）, roughness factorrCan be expressed as
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In the formula:dThe side length of a square pit or protrusion;LThe spacing between adjacent microtextures.
obviously,rGreater than 1,θShrinking and improving the spreading characteristics of droplets on rough surfaces。
Although the contact angle model proposed by Wenzel et al. can explain the influence of surface microstructure characteristics on droplet spreading process, S can be calculated by equation (5)2And S3On the surface, the roughness factor r is the same, but droplets exhibit different spreading characteristics on two different surfaces.Figure 8Spread radius for dropletsRAlong with the exhibition timeTThe relationship curve shows that the droplet is in S3The final spreading radius on the surfaceR1.62mm, with the best spreading characteristics; S2Surface second, final spreading radiusR1.30mm; S1The surface spreading characteristics are the worst, and the final spreading radiusRIt is 1.05mm.
The dominant promoting effect of micro protrusions compared to micro pits is related to the continuity of the three-phase contact line during the droplet spreading process.Figure 9For S2The continuity of the surface three-phase contact wire can be observed as follows:TAs the size of the droplet increases, the solid-liquid contact area gradually increases. Due to the effect of micro pits, the droplet spreading process obtains additional driving force, and the droplet spreading radius increasesRIt also increases accordingly; However, as the spreading time increases, the liquid molecules flowing into the micro pits on the surface become discontinuous with each other, resulting in the three-phase contact wire ultimately being pinned inside the micro pitsFigure 9 (c).
Figure 10For S3The continuity of the surface three-phase contact wire also varies over timeTAs the size increases, the solid-liquid contact area gradually increases, and the droplet spreading radius increasesRIt also increases accordingly; Droplets in S3The surface spreading process can be divided into two parts. The liquid molecules located at the front are the first to be attracted by the solid molecules and rapidly spread forward, while the liquid molecules located in the body region are attracted by the precursor membrane molecules[17]The foundation moves forward; S3The micro protrusions on the surface can form microchannels, and the liquid molecules are continuous with each other. During the droplet spreading process, the three-phase contact lines always maintain continuity characteristics. Therefore, compared with S2On the surface, S3The equilibrium contact angle on the surface is the smallest, and the spreading characteristics of droplets on it are the best.
Section 3.1 provides a detailed analysis of the influence of surface microtexture on the droplet spreading process, and based on the Flow-3D simulation results, provides the droplet spreading radiusRAnd timeTCurve. followFigure 8It can be seen that in S2And S3Surface spreading radiusRover timeTThe increase in S1On the surface, there is a pattern of first increasing and then decreasing, and the difference in this pattern is related to the Laplace pressure difference generated by the curved liquid surface. When a droplet spreads on a smooth surface, due to the lack of surface microtexture promotion, the liquid molecules located on the solid-liquid contact surface first spread forward and spread at a faster speed, while the liquid molecules far away from the contact surface still remain spherical under the action of surface tension, due to the existence of Laplace pressure difference at the curved liquid surface[20]When the pressure difference reaches a certain level, the spreading speed of the droplet along the z-direction suddenly increases, causing the central position of the droplet to collapse, and the liquid molecules on both sides will experience a "collapse effect"[21]Under the influence of, continue to expand and form the maximum expansion radius. Subsequently, due to the inherent wetting characteristics of the solid surface, the droplet cannot balance at the maximum spreading radius, and the three-phase surface tension at the three-phase contact line is unbalanced, which does not satisfy the Young's equation equilibrium condition. As a result, the contact line moves towards the center of the droplet and contracts, leading to a decrease in spreading radius. However, the spreading process of droplets on micro textured surfaces is not entirely the same. Due to the additional driving force provided by protrusions or pits, the spreading process of droplets is fast and does not occurFigure 5The 'collapse effect', therefore the spreading radiusRover timeTThe increase continues to increase.
图 11The spreading radius of droplets in logarithmic coordinate systemRAnd timeTCurve, it can be observed that the droplet spreading radiusRAnd timeTSatisfy a certain linear relationshipR-T1/nAmong them, 1/nAs a proportional coefficient. Droplets on microstructured surfaces and smooth surfaces respectively satisfyR-T1/4andR-T1/7The spreading law, as the proportionality coefficient increases, indicates that microtextures have a promoting effect on the spreading process of droplets, and the spreading characteristics of the liquid become better. There are currently multiple conclusions regarding the calibration law of droplet spreading radius over time, Based on the lubrication approximation assumption, Tanner theoretically derived the properties of silicone oil on smooth wallsR-T1/10Standard law[16]Kim et al. studied the spreading process of droplets on hydrophilic columnar arrays and obtained that the spreading radius and time satisfyR-T1/4Standard law[22]Yuan et al. also studied the spreading behavior of water droplets on hydrophilic columnar arrays and obtainedR-T1/3Standard law[17-18]。
Based on the standard law verified in this article, a common conclusion can be drawn: the spreading process of droplets on rough surfaces is faster, and the presence of surface microtextures increases the actual contact area between solid and liquid during droplet spreading, providing additional driving force for droplet spreading; Final spreading radius of dropletsRA reasonable micro textured surface can improve the spreading process of droplets on a solid surface, which is determined by both the surface roughness and inherent wetting characteristics of the solid.
Figure 12、13Droplets in S4、 S5On the surface of the spreading process, it can be clearly seen that the droplet spreads quickly along the x direction, while there is almost no spreading along the y direction, and the three-phase contact wire is nailed in place without moving.
Figure 14Furthermore, the spreading radius of the droplet in two directions parallel and perpendicular to the rectangular depression is providedRover timeTThe change clearly shows that the spreading characteristics of droplets parallel to the texture direction are good, with a final spreading radiusRThe spreading characteristics of droplets perpendicular to the texture direction are poor, with a final spreading radius of 1.13mmRIt is 0.94mm.
The anisotropic spreading process of droplets caused by microstructural geometric anisotropy is related to the continuity of the moving contact line. When the droplet spreads along a direction parallel to the texture, the three-phase contact line is continuous inside the texture, and the spreading process experiences less resistance and faster spreading speed; The moving contact line perpendicular to the texture direction is blocked by a discrete texture, which does not have continuity. Droplets crossing adjacent textures require more energy transformation[23-25]It experiences significant viscous resistance and spreads slowly.
(1) For hydrophilic solid surfaces, surface microtextures increase the true contact area between solid and liquid during droplet spreading, providing additional driving force for droplet spreading, resulting in better spreading characteristics of the liquid compared to non textured solid surfaces; The spreading radius of droplets on microstructured surfaces approximately satisfiesR-T1/4According to the standard law, compared to non textured surfaces, the spreading speed of fluids is faster and the final spreading diameter is larger. Among them, the square convex surface has a maximum spreading diameter of 1.62mm.
(2) The stronger the dominance of micro protrusions compared to micro pits, the more favorable it is for the spreading of droplets, which is related to the continuity of the three-phase contact line during the spreading process. The microchannels formed between micro protrusions ensure the continuity of the solid liquid gas three-phase contact line; On the other hand, on the surface of micro pits, although micro pits increase the contact area between solid and liquid, providing additional driving force, the liquid molecules flowing into the pits are discontinuous with each other, causing the three-phase contact lines to be nailed inside the micro pits. As the spreading speed gradually decreases, the droplets eventually reach a stable equilibrium position。
(3) The flat wall spreading process of droplets exhibits anisotropy, with strong continuity of three-phase contact lines parallel to the texture direction. The spreading process is subjected to relatively small resistance forces, resulting in a final spreading radius of 1.13mm and good spreading characteristics; Droplets perpendicular to the texture direction are blocked by discrete textures, and the three-phase contact lines do not have continuity, resulting in a final spreading radius of 0.94 mm and poor spreading characteristics.
| [1] |
PAWLAK Z, URBANIAK W, OLOYEDE A. The relationship between friction and wettability in aqueous environment[J]. Wear, 2011, 270 (9/10): 1745-1749.
|
| [2] |
YANG Shu-yan, GUO Feng, MA Chong, et al. Influences of the liquid/solid wettability on thin hydrodynamic lubrication films[J]. Tribology, 2010, 30 (2): 203-208. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-MCXX201002019.htm
|
| [3] |
ZHU Hai-yan, ZHANG Yi, ZHAO Huai-rui, et al. Drag reduction technology of high-speed train based on boundary layer control[J]. Journal of Traffic and Transportation Engineering, 2017, 17 (2): 64-72. (in Chinese). doi: 10.3969/j.issn.1671-1637.2017.02.007
|
| [4] |
ZHOU Hai-chao, LIANG Chen, YANG Jian, et al. Bionic method for improving tire anti-hydroplaning performance[J]. Journal of Mechanical Engineering, 2015, 51 (8): 125-130. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201508018.htm
|
| [5] |
YOUNG T. An essay on the cohesion of fluids[J]. Philosophical Transactions of the Royal Society of London, 1805, 95: 65-87. doi: 10.1098/rstl.1805.0005
|
| [6] |
WENZEL R N. Resistance of solid surfaces to wetting by water[J]. Industrial and Engineering Chemistry, 1936, 28 (8): 988-994. doi: 10.1021/ie50320a024
|
| [7] |
CASSIE A B D, BAXTER S. Large contact angles of plant and animal surfaces[J]. Nature, 1945, 155 (3923): 21-22. doi: 10.1038/155021a0
|
| [8] |
CHENG Shuai, DONG Yun-kai, ZHANG Xiang-jun. Study of the influence of apparent contactangle on regular rough surface considering liquid wetting properties[J]. Mechanical Science and Technology for Aerospace Engineering, 2007, 26 (7): 822-827. (in Chinese). doi: 10.3321/j.issn:1003-8728.2007.07.002
|
| [9] |
YANG Chang-wei, HE Feng, HAO Peng-fei. The apparent contact angle on the micro-structured hydrophobic surface[J]. Scientia Sinica: Chimica, 2010, 40 (10): 1545-1549. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JBXK201010010.htm
|
| [10] |
CHEN Xiao-ling, LU Tian. Study of apparent shape of the droplet on rough surface[J]. Scientia Sinica: Physics, Mechanica and Astronomica, 2009, 39 (1): 58-62. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK200901009.htm
|
| [11] |
BLAKE T D. The physics of moving wetting line[J]. Journal of Colloid and Interface Science, 2006, 299 (1): 1-13. doi: 10.1016/j.jcis.2006.03.051
|
| [12] |
ORAN A, DAVIS S H, BANKOFF S G. Long-scale evolution of thin liquid films[J]. Reviews of Modern Physics, 1997, 69 (3): 931-980. doi: 10.1103/RevModPhys.69.931
|
| [13] |
DE GENNES P G. Wetting: statics and dynamics[J]. Reviews of Modern Physics, 1985, 57 (3): 827-863. doi: 10.1103/RevModPhys.57.827
|
| [14] |
LEGENDRE D, MAGLIO M. Comparison between numerical models for the simulation of moving contact lines[J]. Computer and Fluids, 2015, 113: 2-13. doi: 10.1016/j.compfluid.2014.09.018
|
| [15] |
BARENBLATT G I, BERETTA E, BERTSCH M. The problem of the spreading of a liquid film along a solid surface: a new mathematical formulation[J]. Proceedings of the National Academy of Sciences of the United States of America, 1997, 94 (19): 10024-10030. doi: 10.1073/pnas.94.19.10024
|
| [16] |
TANNER L. The spreading of silicone oil drops on horizontal surfaces[J]. Journal of Physics D: Applied Physics, 1979, 83 (9): 1473-1484.
|
| [17] |
YUAN Quan-zi, ZHAO Ya-pu. Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface[J]. Journal of Fluid Mechanics, 2013, 716 (2): 171-188.
|
| [18] |
YUAN Quan-zi, ZHAO Ya-pu. Wetting on flexible hydrophilic pillar-arrays[J]. Scientific Reports, 2013, 3 (6), DOI: 10.1038/srep01944.
|
| [19] |
BONN D, EGGERS J, INDEKEU J, et al. Wetting and spreading[J]. Reviews of Modern Physics, 2009, 81 (2): 739-805.
|
| [20] |
PUJADO P R, HUH C, SCRIVEN L E. On the attribution of an equation of capillarity to Young and Laplace[J]. Journal of Colloid and Interface Science, 1972, 38 (3): 662-663.
|
| [21] |
JIAO Yun-long, LIU Xiao-jun, PANG Ming-hua, et al. Analyses of droplet spreading and the movement of wetting line on a solid surface[J]. Acta Physica Sinica, 2016, 65 (1): 016801-1-8. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201601040.htm
|
| [22] |
KIM S J, MOON M W, LEE K R, et al. Liquid spreading on superhy drophilic micropil lararrays[J]. Journal of Fluid Mechanics, 2011, 680: 477-487.
|
| [23] |
SHANAHAN M E R. Simple theory of"stick-slip"wetting hysteresis[J]. Langmuir, 1995, 11 (3): 1041-1043.
|
| [24] |
JIAO Yun-long, LIU Xiao-jun, LIU Kun. Mechanical analysis of a droplet spreading on the discrete textured surfaces[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48 (2): 353-360. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201602011.htm
|
| [25] |
JIAO Yun-long, LIU Xiao-jun, PANG Ming-hua, et al. Study of contact angle hysteresis at moving contact lines based on CFD simulation and mechanical analysis[J]. Applied Mathematics and Mechanics, 2016, 37 (1): 14-26. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201601003.htm
|
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