A unified mechanism for the stability of surface nanobubbles: Contact line pinning and supersaturationYawei Liu and Xianren ZhangCitation: The Journal of Chemical Physics 141, 134702 (2014); doi: 10.1063/1.4896937View online: /10.1063/1.4896937View Table of Contents: /content/aip/journal/jcp/141/13?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inPerspectives on surface nanobubblesBiomicrofluidics 8, 041301 (2014); 10.1063/1.4891097Contact line pinning and the relationship between nanobubbles and substratesJ. Chem. Phys. 140, 054705 (2014); 10.1063/1.4863448Experimental study on macroscopic contact line behaviors during bubble formation on submerged orifice and comparison with numerical simulationsPhys. Fluids 25, 092105 (2013); 10.1063/1.4821043Effect of presence of salt on the dynamics of water in uncharged nanochannelsJ. Chem. 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Phys. 132, 024702 (2010); 10.1063/1.3283899THE JOURNAL OF CHEMICAL PHYSICS 141,134702(2014)A unified mechanism for the stability of surface nanobubbles:Contact line pinning and supersaturationY awei Liu and Xianren Zhang a)State Key Laboratory of Organic-Inorganic Composites,Beijing University of Chemical Technology,Beijing 100029,China(Received 30June 2014;accepted 21September 2014;published online 2October 2014)In this paper,we apply the molecular dynamics simulation method to study the stability of sur-face nanobubbles in both pure fluids and gas-liquid mixtures.First,we demonstrate with molecu-lar simulations,for the first time,that surface nanobubbles can be stabilized in superheated or gas supersaturated liquid by the contact line pinning caused by the surface heterogeneity.Then,a uni-fied mechanism for nanobubble stability is put forward here that stabilizing nanobubbles require both the contact line pinning and supersaturation.In the mechanism,the supersaturation refers to superheating for pure fluids and gas supersaturation or superheating for the gas-liquid mixtures,both of which exert the same effect on nanobubble stability.As the level of supersaturation in-creases,we found a Wenzel or Cassie wetting state for undersaturated and saturated fluids,stable nanobubbles at moderate supersaturation with decreasing curvature radius and contact angle,and finally the liquid-to-vapor phase transition at high supersaturation.©2014AIP Publishing LLC .[/10.1063/1.4896937]I.INTRODUCTIONThe first report of the existence of nanobubbles ap-peared in the work by Parker et al.,1in which they sup-posed that the surface nanobubbles were responsible for the long-range hydrophobic attraction between two objects im-mersed in liquid.Since then many experiment techniques such as AFM measurement,2–11rapid cryofixation,12neutron reflectometry,13and direct optical visualization 14,15have con-firmed that these nanobubbles can exist for a substantially long period of time.Nanobubbles are of great interest as they have potential applications in many fields,such as boundary slip in fluid,16,17froth-flotation,18and protein adsorption.19,20But,nanobubbles also pose a number of challenges for under-standing their physical behaviors.21,22In particular,the mech-anism for nanobubble stability is still an open question to-day.The contamination theory 23and the dynamic equilibrium theory 24,25were proposed but both of them have not been fully proven experimentally.6,26Recently,theoretical 27,28and experimental 29,30studies indicated that the contact line pinning effect plays a crucial role for nanobubble stability.In our pervious work,27we pro-posed that the pinning effect can account for the existence of long-lived nanobubbles in supersaturated liquids.In the the-oretic study,nanobubbles are found to be thermodynamically metastable,and it is the pinning of the contact line induced by surface heterogeneity that leads to the metastability.In a sim-ilar mechanism,nanodroplets can be stabilized by the contact line pinning effect.31,32The aims of this work are as follows.(i)First,we want to confirm our model with molecular dynamics (MD)sim-ulations.MD simulation contains thermal fluctuation,whicha)Email:zhangxr@may play a role in nanobubble stability but is not included in our previous theoretical calculations.27(ii)Second,we try to find out whether the stability mechanism for nanobubbles in the gas-liquid mixtures is different from that in pure flu-ids or not.In particular,we want to illustrate the role of dis-solved gas in the nanobubble stability.In our previous work,27we have illustrated the stability mechanism for nanobubbles in pure fluids.However,many experiments indicated that there is no nanobubble found in degassed water,3,33,34and it is demonstrated experimentally that the nanobubbles in gas-liquid mixtures indeed consist of the gas molecules.35,36(iii)Third,we try to illustrate whether gas supersaturation is re-quired for nanobubble stability.Some experimental results demonstrate that dissolved gases affect strongly to the for-mation of nanobubbles 11,33,34and thus supersaturation may be an essential ingredient.But Seddon et al.37suggested that supersaturation of dissolved gases is not a requirement for nucleation of bubbles.We want to clarify this point in the work.To answer these questions,in this work we applied the molecular dynamics (MD)simulation to explore the stabil-ity of surface nanobubbles in both pure fluids and gas-liquid mixtures.We confirmed the existence of stable nanobub-bles in both cases.Then we proposed a unified mechanism for nanobubble stability,namely,stabilizing nanobubbles re-quires both the contact line pinning and supersaturation.Here supersaturation refers to superheating in pure fluids and gas supersaturation or superheating for gas-liquid mixtures.We also found that nanobubbles exist at moderate supersatura-tion and both the curvature radius and contact angle of sta-ble nanobubbles decrease with the increase of the level of superheating/gas supersaturation.At high level of superheat-ing/gas supersaturation,however,nanobubble becomes unsta-ble again,and the liquid-to-vapor transition occurs instead.0021-9606/2014/141(13)/134702/7/$30.00©2014AIP Publishing LLC141,134702-1II.SIMULATION SYSTEMIn this work,MD simulations were performed by using LAMMPS.38We employed a quasi-two dimensional simu-lation box with a size of 22.4×6.6×H nm 3as shown in Fig.1(a),with H the height of the simulation box that fluc-tuates at a given pressure.Periodic boundary conditions were used in the x and y directions,while in the z direction two restraining substrates were used at the top and bottom of the box.The substrates were made up of frozen solid molecules on a FCC lattice with lattice parameter of 5.606Å,and the (100)surface was exposed to the fluid.The bottom substrate was fixed during the simulations,and a square pore with a width of 10.6nm and a depth of 5.6nm was introduced on the substrate to pin the contact line of nanobubbles.We used the pore to provide the pinning effect based on two facts:first,the pore can provide a strong pinning force to stabilize the nanobubbles,especially when the substrate is not highly hydrophobic;39second,the substrates with regular pores are potential to induce nanobubbles having uniform spatial and size distributions.403.4 nmx=0xzHw /2=5.3 nmp extLx=22.4 nm Ly=6.6 nmSo u rce region to control the gas concentration3.4 nm(a)-6-4-202462468101214X (nm)Z (n m )0.0017.034.0ρ (mol/L)R=6.1 nm θ=89 deg(b )FIG.1.(a)A typical representation of the simulation box.The green parti-cles represent the liquid molecules,the blue ones represent the gas molecules,the red ones represent the solid particles of the top substrate,and the black particles represent the solid particles of the bottom substrate.The shaded area shows the gas source to control the gas concentration in the mixture.(b)A typical two-dimensional density distributions of the liquid molecules in the system with a small droplet on a smooth substrate at T =101.2K.TABLE I.The parameters for the Lennard-Jones interaction between differ-ent molecules.Moleculesσ(Å)ε(meV)Liquid-liquid (LL) 3.4110.30Liquid-gas (LG)3.41 6.87Liquid-solid at top (LS top ) 3.41 5.15Liquid-solid at bottom (LS bot ) 3.41 5.66Gas-gas (GG)3.41 3.43Gas-solid at top (LS top ) 3.41 1.72Gas-solid at bottom (LS bot ) 3.41 1.89Solid-solid (SS)The system was simulated in the isothermal,isostress (NP zz T )ensemble,with a fixed number of molecules N =39216(including both liquid and gas molecules).An external force along z direction was exerted on the smooth top substrate,and thus it fluctuates during our simulations to maintain the given pressure.This kind of method to control the pressure was successfully used in the study of the bubble nucleation,41and our extra simulation runs also confirm that this method produces nearly the same density-temperature re-lation for the bulk liquid as the Nosé-Hoover method.The velocity Verlet algorithm with a time step of 5fs was used for the integration of equations of motion,and the Nosé-Hoover thermostat with a time constant of 0.5ps was used to control the fluid temperature.For the simulations in gas-liquid mixtures,a reservoir of gas molecules [see the shaded region in Fig.1(a)]was intro-duced to give the target gas concentration far from nanobub-bles.In practice,the identity exchange of liquid and gas molecules in the reservoir was performed every 0.1ns to maintain the target gas concentration.For all intermolecular interactions,the truncated Lennard-Jones (LJ)12-6potential was employed (see Table I for LJ parameters)and the cutoff distance was set to 1.1nm.The interaction between liquid molecule and solid molecule composing of the bottom substrate was chosen to represent a substrate with neutral wettability,corresponding to a macro-scopic contact angle of ∼89◦[Fig.1(b)].Although reduced units were used in our simulations,all variables were reported here in their actual physical units.To convert reduced units to their real units,both mass m and LJ parameters were chosen as those of argon atom,e.g.,m =40amu,σ=3.41Å,andε=10.30meV .42Therefore,we approximately have 1nm ≈2.9σ,1ns ≈462 mσ2/ε,and 1K ≈0.008ε/k B with k Bthe Boltzmann constant.III.RESULTS AND DISCUSSIONA.Determination of the liquid boiling pointAt first,we determined the vapor-liquid coexistence for the pure fluid with a series of NVT-MD simulations.We placed a liquid slab of ∼2000liquid molecules in the mid-dle of a simulation box of 3.7×3.7×18.4nm 3,and pe-riodic boundary conditions were applied in all three direc-tions.We equilibrated the system sequentially at differentp (a t m )T (K)FIG.2.The phase diagram for the pure fluid in the pressure-temperature plane.The boiling point is 101.2K at 5atm.The empty square symbols indi-cate the saturated pressure at different temperature from the simulation.The diamond symbols indicate the stability limit of the metastable liquid.Other symbols represent the states simulated to investigate the nanobubble stability in the pure fluid.The triangle symbols indicate the Wenzel state,the star sym-bol indicates the Cassie state,the empty circle symbols indicate the presence of stable nanobubbles,and the solid circle symbols indicate the occurrence of liquid-to-vapor phase transition.See Fig.3for typical snapshots.temperatures varying from 70to 130K,and for each tem-perature a 20ns simulation was performed for data collection and average.By obtaining the saturation pressure as a func-tion of the temperature,we determined the phase diagram for vapor-liquid coexistence (Fig.2).In our simulations on the formation of nanobubbles,the external pressure exerted on the top substrate was set to p ext =5atm,for which the corresponding boiling temperature is T b =101.2K (Fig.2).Hereafter,at the given pressure of 5atm,we use T =T -T b to describe the level of supersat-uration,namely,the driving force for the nucleation of new (vapor)phases.The pure liquid is superheated at T >0but undersaturated at T <0.B.Nanobubble stability in the pure fluidsThen,we explored the nanobubble stability in the pure fluids.We performed the simulations as follow:at first,39216liquid molecules were randomly placed between the bottom and top substrates except the pore;then,a 20ns MD simula-tion run was performed at T =0to equilibrate the system.The obtained configuration [see Fig.3(b)]was then heated or cooled to the given temperature with the heating/cooling rate of 1K/ns.After reaching the desired temperature,a 50ns isother-mal MD simulation was carried out.Figure 3(a)shows typ-ical time evolutions of the height of simulation box at dif-ferent temperatures.At T <0K (e.g., T =−4K),the height shows a sudden decrease,indicating that the pore is completely filled by the liquid [see the inset of Fig.3(a)].Thus,the system is in a Wenzel state and there is no stable nanobubble at this temperature.At a temperature equal to or higher than the boiling point,in contrast,the height fluctu-ates around a certain value for T in the range of (0K,14K)but increases rapidly at T =15K.The typical snapshotsΔT= -4 K ΔT= 0 K ΔT= 8 K ΔT= 12 K ΔT= 14 K ΔT= 15 K01020304050202326293235H (n m )t (ns)ΔTΔT=-4 K(a)FIG.3.(a)Time evolution of the simulation box height at different tem-peratures.The inset figure shows the snapshot of final configuration at T =−4K that corresponds to a Wenzel state.(b)Final configurations corre-sponding to different temperatures from T =0K (Cassie state),8K (stable nanobubble),12K (stable nanobubble)to 14K (stable nanobubble).(c)Sev-eral typical snapshots during the liquid-to-vapor phase transition process at T =15K.for different temperatures within the range of T =0–15K are given in Figs.3(b)and 3(c).At T =0,a Cassie state was found,and the planar vapor-liquid interface on the pore can be interpreted from the fact that at this temperature the system is in the state of vapor-liquid equilibrium.At T =8,12,and 14K,stable surface nanobubbles were observed [Fig.3(b)],as expected from our theoretical work 27based on lattice gas model.43At T =15K,however,the liquid-to-vapor phase transition occurs,leading to the rapid expansion of the simu-lation box [Fig.3(c)].The figure shows that the nanobubble grows slowly at first and the contact line depins at about 3ns,followed by a rapid expansion of the simulation box.The time averaged density distributions of liquid molecules at different temperatures in the range of T =0∼14K are shown in Fig.4.The vapor-liquid interface for stable nanobubbles was determined through finding the loca-tions at which the fluid density is equal to half of the bulk liquid density.As showed in Fig.4,the vapor-liquid interface can be well described with a circle equation,from which the curvature radius R and the contact angle θ(measured from the liquid phase)of nanobubbles can be obtained.The fig-ure clearly indicates that θis always larger than the macro-scopic contact angle of the liquid,and both R and θdecrease with the increase of temperature.These observations are691215(a)ΔT=0 K R=∞Z (n m )(b )ΔT=8 KR=16.4 nm θ=164.5 deg-6-3036691215(c)ΔT=12 KR=8.1 nm θ=138.4 degX (nm)Z (n m )-6-3036ρ (mol/L)(d)ΔT=14 KR=6.2 nm θ=112.2 degX (nm)0.0017.034.0FIG.4.The two-dimensional density distributions for the liquid molecules at different temperatures.The black regions represent the bottom substrate.The red solid lines represent the site at where the fluid density is equal to half of the bulk liquid density.The black solid lines indicate the liquid-solid interface.The blue lines represent the vapor-liquid interface fitted from a circle approximation.accordance with the conclusions in our pervious work:27for stable nanobubbles,R ,θ,and the pinning radius r (r =w /2here)must meet the size relationship of sin θ=r /R (θ>90◦)and R equals to the radius of critical nucleus for ho-mogeneous nucleation that decreases with increasing level of superheating.44–47As a result,R and θdecrease as the temper-ature increases.Besides,the absence of stable nanobubbles at T =15K implies that R <r at this temperature.39Moreover,for the stable nanobubbles at T =8,12,and 14K,their contact lines are always pinned at the border of the pore,as shown in Figs.3(b)and 4.To reconfirm the crucial role of the contact line pinning effect on the nanobubble sta-bility,we carried out a simulation at T =14K,but used a smooth bottom substrate in order to remove the contact line pinning effect.Figure 5(a)shows that in the absence of the pinning effect,the nanobubble shrinks rapidly and disappears within 1ns.This observation stresses that the contact line pin-ning effect plays a crucial role for the nanobubble stability.The effect of pore depth on nanobubble stability was also considered here.We simulated the stability of nanobubbles at T =14K on three substrates with different pore depths (h=5.6,1.7,and 1.1nm).Figure 6(a)shows that for the systems of h =5.6and 1.7nm,stable nanobubbles are found and featured with the same curvature radius [see Fig.6(b)].For the system of h =1.1nm,however,the roughness cannot pin the contact line,and as a result the nanobubble disappears [Fig.6(a)].Therefore,the pore depth determines the substrate ability to pin the contact line and thus affects the nanobubble stability.However,for stable nanobubbles,their morphologies are independent of pore depth.39Above we show that at a given pressure,as the system temperature gradually increases from an undersaturated state,stable nanobubble is observed in superheated liquid until a phase transition takes place.Here we also considered another pathway to achieve superheating,namely gradually decreas-ing the system pressure while fixing the system temperature at 101.2K.The pressure values considered and the presence of stable nanobubbles are shown in Fig.2.Again,our results01234523.023.524.024.525.0H (n m )t (ns)(a)01234520.721.021.321.6H (n m )t (ns)(b )FIG.5.Time evolution of the simulation box height and the typical snap-shots for the system with a pre-existing nanobubble on a smooth substrate:(a)the pure liquid system at T =14K,and (b)gas-liquid mixture at x gas =0.104and T =−20K.confirm that a stable nanobubble is observed as the liquid be-comes superheated until the phase transition takes place at a high supersaturation.In general,with molecular simulation we demonstrated,for the first time,the existence of stable surface nanobub-bles.In the pure fluids,stable nanobubbles can be found only when the contact line is pinned and the liquid is superheated (i.e., T >0).Furthermore,the curvature radius and con-tact angle of nanobubbles decrease with the increase of tem-perature.The observation that no stable nanobubble is in the undersaturated pure fluids (i.e., T <0)is consistent with the experiment results that there is no stable nanobubble af-ter degassed process at the temperature below the boiling point.3,33,34These results also imply that the dissolved gas is necessary if T <0.C.Determination of the equilibrium gas concentrationNext,we explored the nanobubble stability in gas-liquid mixtures.Here the temperature was set to T =−20K,much lower than the boiling point of the solvent,and hence no stable nanobubbles presents in the pure liquid.Note that here the T is still the difference obtained by subtracting the boiling temperature of the pure liquid from T ,namely, T =T –T b .To consider the role of dissolved gas on the1020304050242628303234H (n m )t (ns)h=5.6 nmh=1.7 nmh=1.1 nm(a)-6-4-2024646810121416ρ (mol/L)R=6.2 nm θ=112.2 degX (nm)Z (n m )0.0017.034.0(a) h=5.6 nm (b ) h=1.7 nm (b )-6-4-20246R=6.3 nm θ=115.1 degX (nm)FIG.6.Pore depth affects the contact line pinning and nanobubble stability.(a)Time evolution of the simulation box height and the typical snapshots for final configurations.(b)The two-dimensional density distributions for the liquid molecules.nanobubble stability,we first determined the equilibrium gas concentration.For this purpose,we placed a solution slab of ∼10000molecules (with ∼500gas molecules)in the middle of the simulation box of 4.7×4.7×35.0nm 3.NP zz T-MD simulations were performed with periodic boundary condi-tions in all three directions.The Nosé-Hoover barostat with a time constant of 5ps was applied to maintain a pressure of p =5atm.We equilibrated the system with a 100ns simulation run and then performed another 100ns simulation run to determine the equilibrium gas concentration.The equilibriumgas molar fraction is found to be x egas=0.026in liquid phase and y egas=0.820in vapor phase.Thus,if the gas concentra-tion x gas >0.026,the gas-liquid solution is gas supersaturated.D.Nanobubbles in the gas-liquid mixtures at T <0We performed MD simulations to explore nanobubble stability in the gas-liquid mixtures as follow:at first,for the initial configuration shown in Fig.3(b)at T =0,∼1000solvent molecules were turned into gas molecules;next,the system was cooled down to T =−20K;then,a 200ns sim-ulation was carried out at a given x gas ;after that,we changed x gas and carried out other simulation runs of 200ns to inves-tigate the effect of gas supersaturation.In total,four simula-tion runs were sequentially performed at x gas =0.026,0.069,0.104,and 0.125.Figure 7(a)shows the time evolution of the simulation box height and the number of gas molecules.For x gas in the range of (0.026,0.104),both the simulation box height and the number of gas molecules reach their stable values within20232629050100150200700170027003700H (n m )x gas =0.026 x gas =0.069 x gas =0.104 x gas =0.125x gas(a)N u m b e r o f g a s m o l e c u l e st (ns)x gasFIG.7.(a)Time evolution of the simulation box height and the number of gas molecules at T =−20K.(b)Typical snapshots for final configurations corresponding to T =−20K and x gas =0.026(Cassie state),0.069(sta-ble nanobubble),and 0.104(stable nanobubble).In the last figure,the liquid molecules are hidden to show the gas enrichment in the vapor-liquid inter-face region.(c)Several typical snapshots during the liquid-to-vapor phase transition process at x gas =0.125and T =−20K.50ns,but at x gas =0.125the simulation box expands contin-uously.This observation can be interpreted from the behavior how the solution wets the rough substrate [see Figs.7(b)and 8].Typical snapshots for different values of x gas are given in Figs.7(b)and 7(c).At x gas =0.026,a Cassie state is found with an almost planar vapor-liquid interface,correspondingto the vapor-liquid equilibrium state (x egas=0.026).As x gas increases to 0.069and 0.104,the mixture becomes moder-ately gas supersaturated,and Fig.7(b)clearly indicates the existence of the stable nanobubbles.For x gas further increases to 0.125,however,the liquid-to-vapor phase transition is ob-served after the contact line depinning at about t =25ns [see Fig.7(c)].Figure 8gives the two-dimensional density distributions that are averaged over the later 100ns for solvent molecules and for gas molecules.From the figure,several characteris-tics for these stable nanobubbles are found.First,the curva-ture radius and the contact angle for the nanobubbles decrease as the increase of gas concentration in the solution,just like the increase of superheating in the pure fluids.The depen-dence of nanobubble contact angle on the level of supersatu-ration also agrees with the experimental observation by Zhang et al.29that the contact angle of nanobubbles decreases with691215(a)x gas =0.026R=∞y gas =0.810Z (n m )ρ (mol/L)(b )x gas =0.069R=14.5 nm θ=159.4 deg y gas =0.8860.0017.034.0-6-3036691215(c)x gas =0.104R=7.7 nm θ=133.0 deg y gas =0.918X (nm)Z (n m )-6-3036(d)x gas =0.104X (nm)0.004.509.00FIG.8.The two-dimensional density distributions of the liquid molecules corresponding to different values of x gas from 0.026to 0.104((a)-(c)),and that for the gas molecules at x gas =0.104(d).The temperature is set to T =−20K.increasing supersaturation.Second,the gas enrichment can be clearly found near the vapor-liquid interface [Figs.7(b)and 8(d)].The interface enrichment of gas molecules is consid-ered to have a considerable impact on the surface tension.48,49Third,the nanobubbles is almost entirely occupied by gas molecules (y gas ∼90%),and the concentration increases with the gas supersaturation.We also demonstrated the importance of contact line pin-ning on the nanobubble stability in gas-liquid mixtures.We performed a simulation run at x gas =0.104but employed a smooth substrate.The time evolution of the pre-existing nanobubble is shown in Fig.5(b),which indicates that the nanobubble dissolves and disappears within 1ns,stressing that in the gas-liquid mixtures,the contact line pinning effect plays a crucial role for nanobubble stability.In general,we proved that at T <0,the generation of stable nanobubbles requires both contact line pinning and gas supersaturation.These stable nanobubbles are mainly made up of gas molecules and show the gas enrichment in the vapor-liquid interface region.More importantly,these nanobubbles exhibit the same behaviors as observed for nanobubbles in the pure fluids:they are stable within a suitable range of superheating/supersaturation and in the presence of contact line pinning;the curvature radius of vapor-liquid interface and the contact angle decrease as the level of superheat-ing/supersaturation increases;the contact angle are always greater than the microscopic contact angle for the liquid.E.Nanobubbles in the gas-liquid mixtures at T >0Although we have showed that the dissolved gas is not required for producing stable nanobubbles in superheated liq-uid,it is of particular interest to know how the dissolved gas influences nanobubbles when T >0.Here,we simulated nanobubbles in the gas-liquid mixtures at T =8K.It is important to note that if T >0,the equilibrium gas con-centration is 0.Thus,the gas-liquid solution with x gas >0is always gas supersaturated as long as T >0.The simu-lation details are similar to those in the gas-liquidmixtures691215(a)x gas =0R=16.4 nm θ=164.5 deg y gas =0Z (n m )(b )x gas =0.005R=11.5 nm θ=154.2 deg y gas =0.096-6-3036691215(c)x gas =0.010R=9.4nm θ=146.0degy gas =0.145X (nm)Z (n m )-6-3036ρ (mol/L)(d)x gas =0.020R=6.8 nm θ=123.7 deg y gas =0.277X (nm)0.0017.034.0FIG.9.Two-dimensional density distributions of the liquid molecules at T =8K and different values of x gas from 0to 0.020.at T =−20K,and five independent simulation runs were performed with x gas varying from 0to 0.025.Our simulation results show the presence of stable nanobubbles as long as x gas ≤0.020(see Fig.9for the density distributions of liq-uid molecules).For these stable nanobubbles,we found that (i)the curvature radius of vapor-liquid interface and the con-tact angle of nanobubbles decrease as x gas increases from 0to 0.020,just like the trend observed for nanobubble at T =−20K.But,the main difference between them is that at T >0(T >T b ),the nanobubble can survive even the gas concentration decreases to 0,while at T <0the nanobubblewill disappear if x gas <x egas(Figs.7and 8).(ii)The gas con-centration in the nanobubbles increases with x gas .But,differ-ent form the nanobubbles at T <0,these nanobubbles con-tain substantial number of solvent molecules when T >0(Fig.9).IV .CONCLUSIONIn this work,we applied the molecular dynamics (MD)simulations to explore stability of surface nanobubbles in both pure fluids and gas-liquid mixtures.Different from experi-ments,which usually includes some unknown factors or fac-tors that cannot be precisely controlled,e.g.,substrate het-erogeneity at the nanoscale (in our model 27),contamination (in the contamination model 23)and gas flow (in the dynamic equilibrium model 24),computer simulation is featured with well controllable input or independent variables.We demon-strated with MD simulations,for the first time,that surface nanobubbles can be stabilized in supersaturated solution by the contact line pinning effect caused by the surface hetero-geneity.The reproduction of stable nanobubbles with our MD simulations indicates that our model catches the main ingre-dients for nanobubble stability.Especially,we demonstrated that the stable nanobubbles can be generated in the super-heated pure fluids or gas-liquid mixture,predicting a possi-bility that has not been considered before and thus needs to prove experimentally.Then we unified the mechanisms for nanobubble stabil-ity for both cases,namely,stabilizing nanobubbles requires。
