Measurements of slip length for flows over graphite surface with gas domains

Measurements of slip length for flows over graphite surface with gas domains Dayong Li, Yuliang Wang, Yunlu Pan, and Xuezeng ZhaoCitation: Applied Physics Letters 109, 151602 (2016); doi: 10.1063/1.4964437View online: /10.1063/1.4964437View Table of Contents: /content/aip/journal/apl/109/15?ver=pdfcov Published by the AIP PublishingArticles you may be interested inOn the scaling of the slip velocity in turbulent flows over superhydrophobic surfacesPhys. Fluids 28, 025110 (2016); 10.1063/1.4941769A slip model for rarefied gas flows above a moving surface with mass transferJ. Appl. Phys. 116, 054503 (2014); 10.1063/1.4891840Slip length for longitudinal shear flow over a dilute periodic mattress of protruding bubblesPhys. Fluids 22, 121703 (2010); 10.1063/1.3531683Geometric transition in friction for flow over a bubble mattressPhys. Fluids 21, 011701 (2009); 10.1063/1.3067833Measurement of the slip length of water flow on graphite surfaceAppl. Phys. Lett. 92, 053101 (2008); 10.1063/1.2840717Measurements of slip length for flows over graphite surface with gas domainsDayong Li,1,2,a)Yuliang Wang,1,a)Yunlu Pan,3and Xuezeng Zhao 31Robotics Institute,School of Mechanical Engineering and Automation,Beihang University,Beijing 100191,People’s Republic of China 2School of Mechanical Engineering,Heilongjiang University of Science and Technology,Harbin 150022,People’s Republic of China 3School of Mechanical and Electrical Engineering,Harbin Institute of Technology,Harbin 150001,People’s Republic of China(Received 3July 2016;accepted 25September 2016;published online 11October 2016)We present the measurements of slip lengths for the flows of purified water over graphite surface covered with surface nanobubbles or nano/micropancakes,which can be produced after using high temperature water to replace low temperature water.The slip length values measured on bare graphite surface,nano/micropancake or nanobubble covered graphite surfaces are about 8nm,27nm,and 63nm,respectively.Our results indicate that the gaseous domains formed at the solid-liquid interface,including surface nanobubbles and nano/micropancakes,could act as a lubricant and significantly increase slip length.Published by AIP Publishing.[/10.1063/1.4964437]With the development of micro/nano fluidic applica-tions,a drag reduction of liquid flows at small scales has become an important issue.1–6In order to achieve an effec-tive drag reduction for liquid flows over the solid surfaces,the gaseous domains including surface nanobubbles and micro/nanopancakes have been suggested being a lubricant at a solid-liquid interface.In the recent two decades,exten-sive studies have been developed to investigate how interfa-cial gas affects the boundary condition of fluids.However,whether interfacial gas can effectively increase slip length is still on debate.The concept of slip length is first proposed by Navier,stating that the velocity v of liquid is proportional to the velocity gradient.The slip length b is the distance below the liquid/solid interface,at which the liquid velocity linearly extrapolates to zero,which can be expressed by the expres-sion v ¼b @v =@z j z ¼0.4,7The smaller slip length means a larger drag of liquid at the wall.Some early theoretical results supported that the pres-ence of nanobubbles at liquid-water interface can lead to an increased slippage of liquids flow.7–12By using an atomic force microscope (AFM),Wang et al .12initiated a slip length measurement on hydrophobic surface covered with nanobub-bles and obtained a slip length of 44nm,where a larger slip length of 257nm is also thought to ascribe to the presence of nanobubbles on a superhydrophobic surface,although no nanobubbles were observed.12Similarly,Cottin-Bizonne and his coauthors measured a typical slip length of about 20nm (Ref.13)or 100nm (Ref.14)on octadecyltrichlorosilane (OTS)surfaces,and the nanobubbles were regarded as a pos-sible reason for leading to the slip length of about 100nm.14In contrast,based on the results of the measured surface nanobubbles,Hendy and Lund 15estimated the slip length and concluded that the nanobubbles do not effectively increase the slippage of liquids.In addition,trapped bubbleson the structured surfaces were investigated in the recent studies,1–3,16,17the protrusion angle was found to dramati-cally influence the slip length,and even a negative slip length was simulated to be produced,as the protrusion angle is larger than a critical value.16,17Noteworthily,the surface nanobubbles are very special gaseous state with extremely high inner pressure 19,20and abnormal small contact angle (gas side),20which is very different from that of artificially trapped bubbles.Studies 19have shown that the inner pres-sure of surface nanobubbles is much higher than that of mac-robubbles.However,the trapped bubbles might have the same inner pressure as that of macrobubbles.This is because the manufactured cavity under the trapped bubbles will neu-tralize the Laplace pressure that is caused by the capillary effect.The contact angle (gas side)of surface nanobubbles is much smaller than that of macro bubbles and is usually in the range of $45 .20However,the studies showed that the protrusion angle of trapped bubbles can be changed from À60 to 60 (Refs.2and 3)(the sketch of surface nanobub-bles and trapped bubbles can be seen in Figure S1in the supplementary material ).These differences between surface nanobubbles and trapped bubbles should have different effect on slip length.So far,there are still no convictive experimental results to verify the effect of surface nanobubbles on the slippage of liquids.Especially,there is still no experimental study to focus on the slippage of liquid flow at a natural surface cov-ered by nanobubbles/nanopancakes.In this paper,the natural surface (freshly cleaved highly ordered pyrolytic graphite,HOPG)was used as substrate that is atomically flat and does not require any hydrophobic treatment.Temperature differ-ence method was used to produce surface nanobubbles,21i.e.,using high temperature water (HTW,about 38 C,obtained by water bath)to replace low temperature water (LTW,about 4 C,obtained by adding ice into air equili-brated water).The gas solubility of HTW is lower than thata)Electronic addresses:wangyuliang@ and lidayong_78@0003-6951/2016/109(15)/151602/4/$30.00Published by AIP Publishing.109,151602-1APPLIED PHYSICS LETTERS 109,151602(2016)of LTW,where replacing LTW with HTW can lead to local supersaturation of gases near to the HOPG/water interface and thus lead to the formation of nanobubbles.The measured temperature of water in the liquid cell was about 30 C after the LTW-HTW replacement,and the time interval between LTW-HTW replacement and slip length measurement is about 30min (including nanobubble scanning time and operating time).Therefore,the tempera-ture of water in the liquid cell at the moment of measuring slip length can be thought to be near to the room temperature because of heat exchange.In this case,the effect of water temperature on slip length measurements can be neglected and is not considered in this paper.Then,the nanobubbles/pancakes were imaged by using the tapping mode AFM (TM-AFM),followed by the slip length measurements on bare HOPG surface,HOPG surface covered with nanobub-bles or nanopancakes.TM-AFM (NTEGRA platform,NT-MDT Company,Zelenograd,Moscow)and rectangular cantilevers (CSG30,NT-MDT Company)with spring constant of k ¼0.13–2N m À1and resonance frequency in water/air of x 0¼23kHz/65kHz were used to image surface nanobubbles.The scanning frequency was 1Hz with a typical free amplitude value of 4.060.2nm and a set-point ratio of 95%.All the experiments were carried out at a clean room ($2561 C,relative humidity (RH):45%–55%).When measuring the hydrodynamic force,the substrate was driven with a constant velocity of V d ¼65.6l m/s to approach to a borosilicate sphere (GL018B/45–33,MO-Sci Corporation),which is attached to a rectangular cantilever (ORC8,Bruker).The measured diameter of sphere is about 44.4l m,which means a large enough separation distance between the AFM cantilever and the sample;the Stokes force acting on the cantilever thus could be neglected.6The electrostatic force and van der Waals force acting on the col-loidal probe were small comparing with the hydrodynamic force and were also neglected in this paper.In this case,we only consider the hydrodynamic force exerted on the sphere while calculating slip length.For HOPG surface,on which the liquid flow is thought to be under slip boundary condition,the hydrodynamic force is therefore given at a large separation ðD )b Þ22V F hydro¼16pg R D þb ðÞ:(1)Based on Eq.(1),slip length b can be described as the linear extrapolation of V /F hydro (where V is the approaching velocity and F hydro is the hydrodynamic force applied to the sphere),which intercepts the D axis at a distance b ¼D from the origin.14This method avoids introducing the parameters,such as the dynamic viscosity of liquid g and the measured value of sphere radius R ,and reduces the experimental error;thus,the experimental accuracy is ensured.22Fig.1(a)shows the surface nanobubbles that were pro-duced through temperature difference method on freshly cleaved HOPG surface.21These nanobubbles are generally spherical-cap shaped,and their height and diameter are in the order of $25nm and $500nm,respectively.A typical nanobubble labeled as b 1in Fig.1(a)is with a diameter about 350nm and a height about 20nm,which can be seen from the section analysis in Fig.1(c).After scanning the surface nanobubbles,slip length measurements were carried out immediately on the same HOPG substrate.The ratio of V/F hydro as a function of separation distance D is shown in Fig.2,and the interception for the liner fitting line of V/F hydro at the axis of separation distance is about 63nm,which corresponds to a slip length b of 63nm.The nanopancakes were also produced through tempera-ture difference method in our experiments.As shown in Fig.3,these nanopancakes are with irregular shape and their height and diameter are in the order of $3nm and $1l m,respec-tively.As can be seen from the section analysis in Fig.3(c ),a typical nanopancake labeled as P 1in Fig.3(a)is with a diame-ter about 350nm and a height about 3nm,which is comparable to that of nanopancakes in Ref.21.The slip length measured on the corresponding HOPG surface is about 27nm.This is can be seen from Fig.4(a).Furthermore,we measured the slip length on bare HOPG surface (without nanobubblesandimage (a)and corresponding phase image (b)show the nanobubbles pro-duced on HOPG surface by using tem-perature difference method;image (c)shows a cross-sectional profile of bub-ble b 1in image(a).FIG.2.Slip length measurements on HOPG surface covered by nanobubbles using contact mode (CM)AFM.V/F hydro (driven velocity V d ¼65.6l m =s)as a function of the separation distance,the inset is the 3D image of nano-bubbles formed on corresponding HOPG surface produced through tempera-ture difference method.nanopancakes)in air equilibrated water,and the 3D image of bare HOPG surface can be seen in the inset of Fig.4(b),on which the slip length obtained is about 8nm.This is in good agreement with the result of Maali et al .23From the experi-mental results above,the measured slip length values on bared HOPG surface,nanopancake mattress and nanobubble mattress are 8nm,27nm,and 63nm,respectively.It is obvious that the slip length of liquid flow is affected by the accumulated gas domains on the surface.In view of any dust of size of slip length b attached to the sphere will give a hydrodynamic force behavior in the form of Equation (1),it is necessary to prove that the measurements of slip length are not artifacts.We have presented a zoom of data for small distance and fit them with the exact expression of Cottin-Bizonne 14to distinguish the dust and the real slip (shown in Figure S2in supplementary material ),which indicates that the measured slip length on HOPG surface covered by nanobubbles/nanopancakes is not an artifact but a real one produced by the nanobubbles or nanopancakes.The surface coverage of nanobubbles and nanopancakes obtained at five different locations are about 29%and about 30%,respectively.The obtained average heights of nanobub-bles and nanopancakes in this study are about 11nm and 2.5nm,respectively.By using these bubble parameters,the effective slip length b can be evaluated based on the theoreti-cal model of Wang et al .12who considered nanobubbles as a continuous gas layer at solid-liquid interface,and the effective slip length can be expressed by surface coverage of nanobub-bles /and the average bubble height as b ¼ðg l =g g À1ÞH b /,where g l ¼851.5l Pa s and g g ¼18.6l Pa s at a temperature of 300K are the viscosity of water and the density of gas,respectively.12The calculated value of slip length on the basis of nanopancake parameters is 33nm,which is close to the experimental value of 27nm.Noteworthily,the calculated value of slip length on the basis of nanobubble parameters is about 143nm,which is much larger than the experimentalvalue of 63nm.This could be because the effect of morphol-ogy of nanobubble is neglected in this model.Simulation studies 2,3and numerical studies 11,16have predicted that the protrusion angle (quantifying the morphology of liquid-vapor menisci)of bubbles trapped on structured surface can lead to a transition from slippage to friction.16–18This indicates that the morphology of nanobubbles should also be an important factor affecting the slip length.To conclude,we have presented the measurements of slip length on bare HOPG surface,HOPG surface covered by surface nanobubbles or nanopancakes.The nanobubbles and nanopancakes were produced by temperature difference method,which eliminates the effect of alcohol (the common method to produce nanobubbles/nanopancakes on HOPG sur-face is to replace alcohol with water)on the measured slip length.In addition,the freshly cleaved HOPG surface is atomi-cally flat and difficult to be degraded during the measurement,which is in contrast with that of coated surfaces.The measured slip length on bared HOPG surface,nanopancake mattress and nanobubble mattress are 8nm,27nm,and 63nm,respectively.This indicates that the accumulated gas domains on the surface can effectively increase the slip length.See supplementary material for the sketch of surface nanobubbles and trapped bubbles;figures of a zoom of data are measured on a bare HOPG surface,HOPG surface cov-ered by nanopancakes or nanobubbles.The authors acknowledge the financial support of Heilongjiang Province Natural Science Foundation of China (No.E2016059)and the National Natural Science Foundation of China (Nos.51475118,51505108,and 51305019).1C.Cottin-Bizonne,J.L.Barrat,L.Bocquet,and E.Charlaix,“Low-friction flows of liquid at nanopatterned interfaces,”Nat.Mater.2,237–240(2003).2A.Steinberger,C.Cottin-Bizonne,P.Kleimann,and E.Charlaix,“High friction on a bubble mattress,”Nat.Mater.6,665–668(2007).image (a)and corresponding phase image (b)show nanopancakes pro-duced on HOPG surface by using tem-perature difference method;image (c)shows the cross-sectional profile of nanopancake p 1in image(a).FIG.4.Slip length measurements on HOPG surface covered by nanopan-cakes and on bare HOPG surface using CM-AFM.Image (a)typical slip mea-surement on HOPG surface covered by nanopancakes,the inset is the 3D image of nanopancakes formed on cor-responding HOPG surface,V/F hydro (driven velocity V d ¼65.6l m =s)as a function of separation distance;image (b)typical slip measurement on bare HOPG surface,the inset is the 3D image of bare HOPG surface,V/F hydro (driven velocity V d ¼65.6l m =s)as a function of separation distance.3E.Karatay,A.S.Haase,C.W.Visser,C.Sun,D.Lohse,A.Tsai,and R.mmertink,“Control of slippage with tunable bubble mattresses,”Proc.Natl.Acad.Sci.U.S.A.110,8422–8426(2013).4Y.Pan and B.Bhushan,“Role of surface charge on boundary slip influid flow,”J.Colloid Interface Sci.392,117–121(2013).5Y.Pan,B.Bhushan,and X.Zhao,“The study of surface wetting,nanobub-bles and boundary slip with an applied voltage:A review,”Beilstein J. Nanotechnol.5,1042–1065(2014).6D.Jing and B.Bhushan,“Boundary slip of superoleophilic,oleophobic, and superoleophobic surfaces immersed in deionized water,hexadecane, and ethylene glycol,”Langmuir29,14691–14700(2013).7O.I.Vinogradova,“Drainage of a thin liquidfilm confined between hydro-phobic surfaces,”Langmuir11,2213–2220(1995).uga and M.P.Brenner,“Dynamic mechanisms for apparent slip on hydrophobic surfaces,”Phys.Rev.E70,026311(2004).9P.G.de Gennes,“Onfluid/wall slippage,”Langmuir18,3413–3414(2002). 10L.Bocquet and uga,“A smooth future?,”Nat.Mater.10,334–337 (2011).11M.Sbragaglia and A.Prosperetti,“Effective velocity boundary condition at a mixed slip surface,”J.Fluid Mech.578,435(2007).12Y.Wang,B.Bhushan,and A.Maali,“Atomic force microscopy measure-ment of boundary slip on hydrophilic,hydrophobic,and superhydrophobic surfaces,”J.Vac.Sci.Technol.,A27,754–760(2009).13C.Cottin-Bizonne,S.Jurine,J.Baudry,J.Crassous,F.Restagno,and E. Charlaix,“Nanorheology:An investigation of the boundary condition at hydrophobic and hydrophilic interfaces,”Eur.Phys.J.E:Soft Matter Biol. Phys.9,47–53(2002).14C.Cottin-Bizonne,B.Cross,A.Steinberger,and E.Charlaix,“Boundary slip on smooth hydrophobic surfaces:Intrinsic effects and possible artifacts,”Phys.Rev.Lett.94,056102(2005).15S.C.Hendy and N.J.Lund,“Effective slip lengths forflows over surfaces with nanobubbles:The effects offinite slip,”J.Phys.:Condens.Matter21, 144202(2009).16A.M.J.Davis and uga,“Geometric transition in friction forflow over a bubble mattress,”Phys.Fluids21,011701(2009).17C.O.Ng and C.Y.Wang,“Effective slip for Stokesflow over a surface patterned with two-or three-dimensional protrusions,”Fluid Dyn.Res.43, 065504(2011).18J.Hyv€a luoma and J.Harting,“Slipflow over structured surfaces with entrapped microbubbles,”Phys.Rev.Lett.100,246001(2008).19D.Li,D.Jing,Y.Pan,Z.Zhao,and W.Wang,“Coalescence and stability analysis of surface nanobubbles on the polystyrene/water interface,”Langmuir30,6079–6088(2014).20D.Li and X.Zhao,“Micro and nano bubbles on polystyrenefilm/water interface,”Colloids Surf.,A459,128–135(2014).21M.Guan,W.Guo,Y.Tang,J.Hu,and Y.Dong,“Investigation on the temperature difference method for producing nanobubbles and their physi-cal properties,”ChemPhysChem13,2115–2118(2012).22C.Cottin-Bizonne,A.Steinberger,B.Cross,O.Raccurt,and E.Charlaix,“Nanohydrodynamics:The intrinsicflow boundary condition on smooth surfaces,”Langmuir24,1165–1172(2008).23A.Maali,T.Cohen-Bouhacina,and H.Kellay,“Measurement of the slip length of waterflow on graphite surface,”Appl.Phys.Lett.92,053101 (2008).。