Superhydrophobic surfaces: stability of the Cassie-Baxter state and its effect on liquid water slippage

Transcription

1 Superhydrophobic surfaces: stability of the Cassie-Baxter state and its effect on liquid water slippage Mauro Chinappi Center for Life Nano Science

2 Talk outlines Talk 1: Solid Molecular Dynamics application to nanofluidics Water slippage on rough surfaces Water Effect of meniscus curvature on slippage Defected OTS-SAM Talk 2: Cassie-Wenzel transition Wetting on rough surfaces Cassie-Baxter/Wenzel transition Free-energy profile and transition mechanism

3 Molecular Dynamics application to nanofluidics Validity of continuum assumption at nanoscale Slippage on smooth hydrophobic surface Slippage on rough hydrophobic surfaces (Super Hydrophobic surfaces) Molecular dynamics (MD): each atom is modelled as a material point that interacts with other atoms via proper potentials. The time evolution of the system is provided by the solution of Hamilton equations.

4 Classical fluid-dynamics: continuum approach Stokes equation Principal assumptions: (small scale) Continuum External forcing Dynamic viscosity Single phase Negligible inertia (Low Reynolds number) 2 p=μ u+ f Incompressible Newtonian fluid (stress proportional to strain rate) Pressure gradient Velocity field + boundary conditions!!

5 Classical fluid-dynamics: continuum approach Does Stokes equation provide correct results at nanoscale? (what is the characteristic scale below which Stokes equation fails?) External forcing Dynamic viscosity 2 p=μ u+ f Pressure gradient Velocity field + boundary conditions!!

6 Validity of continuum approach Strategy: 1) For a specific system select an analytical result from Stokes equation 2) Perform MD simulations to check if the continuum prediction holds

7 Validity of continuum approach Strategy: 1) For a specific system select an analytical result from Stokes equation 2) Perform MD simulations to check if the continuum prediction holds The system: The prediction: The mass flow rate scales as the fourth power of the single* characteristic dimension d L d D y Φ f d x Periodic in x direction Axial-symmetric Free-slip boundary condition at the solid wall 4 Flow rate Pore diameter *all dimensions scale with d, e.g. D = a*d, L=b*d, etc

8 Validity of continuum approach Strategy: 1) For a specific system select an analytical result from Stokes equation 2) Perform MD simulations to check if the continuum prediction holds The system: MD set-up: F L d D y x Lennard-Jones atoms Solid modelled as a smooth confining potential No tangential force between wall and liquid atoms Periodic in x-direction Axialsymmetric Free-slip boundary condition

9 MD set-up Oxy view F y x Oyz view Molecule size d d~8σ d d~2σ Details Periodic in x LJ atoms Solid modelled as a smooth confining potential (No tangential force) NOTE: the atoms outside the pore are represented as points while the ones inside the pore as spheres. All the atoms are IDENTICAL

10 Validity of continuum approach MC, S. Melchionna et al. JCP (2008) Single file Flow rate Φ f d 3 4 Φ /( f d ) d/σ People involved: Simone Melchionna Carlo Casciola Sauro Succi (molecule size) Φ f d 4 Continuum

11 Liquid flow through a nanopore Message 1: Stokes equation is valid for simple liquid down to system of characteristic scale of 5-6 molecule sizes Message 2: For smaller diameter a single file regime sets in (mass flow rate scales with d3) F

12 Molecular Dynamics application to nanofluidics Validity of continuum assumption at nanoscale Slippage on smooth hydrophobic surface Slippage on rough hydrophobic surfaces

13 Boundary condition for micro and nanofluidics Stokes equation 2 p= u f + boundary conditions!! What is the proper boundary condition to employ?

14 Liquid slippage: Navier boundary condition The usual boundary condition for fluids at macroscale is the no-slip condition* Slip velocity v(z) d v ( z) V s =L s dz Liquid Slip length Ls [1 nm 10μ m] Ls Solid (at rest) Relevance for micro-/nano-fluidics Flow rate Flow rate for no slip Q Q 0 Ls Q0 h Channel size *Well known violations of no-slip such as rarefied gases and triple line movement not addressed

15 Liquid slippage: intrinsic and apparent Smooth surface: intrinsic (or molecular) slippage Low affinity between solid and liquid molecules (e.g. hydrophobic solid) The molecules of the first liquid layer are in motion Rough surfaces: Apparent slippage Slippage observed on a scale larger than surface structures (e.g. roughness) Slippage due to vapor/gas bubbles

16 Intrinsic slippage on hydrophobic wall MD simulation for intrinsic slippage J. Koplik, J.R. Banavar, J.F. Willemsen 1997 P.A. Thompson and S.M. Troian 1999 J.L. Barrat, L. Bocquet: 2004 T.M. Galea, P. Attard 2008 Huang et al 2010 MC and C.M. Casciola 2011 MC and Gala el al T.A. Ho et al S.K. Kannam, et al 2013 X. Yong, L. T. Zhang 2013 D. Gentili, MC et al 2013 Sega et al... OTS are hydrophobic molecules able to selfassemble in compact layers OTS layer We employed Molecular Dynamics to estimate the slip length Ls for a technologically relevant case. Octedecyltrichlorosilane (OTS) layers

17 Intrinsic slippage on hydrophobic wall Technical details: MD protocol Surface characterization Equilibration (NPT flexible cell) Non equilibrium simulations (Couette flow) Velocity profiles are measured NVT Simulations with different droplet size and extrapolation of CA for large droplet to remove line tension effect Contact angle (CA) ~ 104 Methyl group (hydrophobic) Water OTS (octadeciltrichlorosilane) ~2.3 nm OTS layers are widely used in experiments

18 Intrinsic slippage on hydrophobic wall MD protocol System characterization Equilibration (NPT flexible cell) Non equilibrium simulations (Couette flow) Velocity profiles are measured Initial configuration Water NPT triperiodic equilibration Equilibrated configuration correct density no air bubbles Hydrophobic coating (OTS)

19 Intrinsic slippage on hydrophobic wall MD protocol System characterization Equilibration (NPT flexible cell) Non equilibrium simulations (Couette flow) Velocity profiles are measured Water Hydrophobic coating (OTS)

20 Intrinsic slippage on hydrophobic wall MD protocol System characterization Equilibration (NPT flexible cell) Non equilibrium simulations (Couette flow) Velocity profiles are measured Hydrophobic (OTS) wall Moving wall Slip length Ls ~ 1 nm

21 Intrinsic slippage and hydrophobicity 2 Ls (cos (θ c )+1) Slip Length Ls Huang et al. PRL (2008) MC, Gala et al Phil. Tran. Royal Soc (2011) MC, Casciola PoF (2010) Flow rate M. Sega et al. Arxiv (2013) If realistic model are used (e.g. proper wall fluctuations, correct atomic size) the result is robust to different protocols and different surface details Flow rate for no slip Q Q 0 Ls Q0 h Channel size

22 Experiments vs MD simulations MD results Ls ~ 1 nm Author Technique Value Cottin-Bizonne et al (2005) AFM ~ 20 nm Bouzigues et al (2008) Evanescent wave ~ 20 nm Joly et al (2006) Fluorescence corr. spectroscopy ~ 20 nm Li and Yoda (2010) MicroPIV ~ 10 nm Zhu, Attard, Neto (2011) AFM ~ 25 nm Attard (2013) (arxiv) AFM (same data of previous paper) ~ 2 nm Schaeffel (2013) Flourescence cross-corr spectr. ~ 0 (error 10 nm)

23 Molecular Dynamics application to nanofluidics Validity of continuum assumption at nanoscale Slippage on smooth hydrophobic surface Slippage on rough hydrophobic surfaces (Super-hydrophobic)

24 Liquid slippage: intrinsic and apparent Intrinsic (or molecular) slippage Low affinity between solid and liquid molecules (e.g. hydrophobic solid) The molecules of the first liquid layer are in motion Apparent slippage Slippage observed on a scale larger that surface structures (e.g. roughness) Slippage due to vapour/gas bubbles

25 Apparent slippage: continuum approaches Model assumption (typical): v(z) Flat meniscus Free-slip at liquid-gas interface No-slip (or intrinsic slip) at solid-liquid interface Uniform shear far from the wall Liquid Ls Solid (at rest) Air bubbles trapped (Cassie state) Gas-Liquid Free-slip Solid-Liquid No slip (or intrinsic slip)

26 Apparent slippage: open issues State of the art Continuum prediction for flat meniscus for a number of common surface pattern Meniscus shape and super-hydrophobic transition will be discussed in Talk2 Some recent analysis suggest a strong effect of meniscus curvature (continuum models and experiment at microscale) Continuum models need assumption for meniscus configuration and boundary condition Motivation Can continuum models be applied at nanoscale? What is the effect of meniscus curvature?

27 MD set-up: Pillars Pressure P estimated from spring forces Constrained on z (pressure measured here) Water Long chains Short chains Thermostatted Fixed Measure P, Measure Ls

28 Continuum set-up Model input Assign P Measure Ls Solid surface geometry Triple line pinned at surface corner Pressure P Meniscus curvature (from Laplace equation) Intrinsic slippage at solid-liquid (from dedicated MD simulation on smooth surface) Liquid Triple line Liquid-air interface Air Triple line

29 Apparent slippage: pillars P Squares: Continuum simulations Circles: MD simulations People involved: Daniele Gentili Guido Bolognesi Alberto Giacomello Carlo Casciola

30 Apparent slippage: local depletion Evidence: MD provides a Ls larger than continuum Local depletion at the pillars border Depletion layer Depletion layer -> Ls Three different values of Ls were used to define an effective Ls Blue diamond: local depletion included in continuum model (intrinsic slippage increase at solid-liquid interface) Smooth surface

31 Apparent slippage: partial filling Evidence: MD provide a slip length smaller than continuum Phenomenological explanation Filling Blue triangle: Filling included continuum model in

32 Apparent slippage: MD vs Continuum Summary: Atomistic simulations and continuum models provide different results This is associated with subtle effects at triple line Blue triangle Filling included in continuum model Take home message: Continuum models for prediction of slippage on super-hydrophobic surfaces fail at nanoscale. (not a problem of continuum assumption) Blue diamond local depletion included in continuum model Gentili et al Meccanica (2013) Gentili et al. Submitted to Micro and Nanofluidics

33 Molecular Dynamics application to nanofluidics Validity of continuum assumption at nanoscale Continuum assumption is valid for system 5 times larger than molecule size Slippage on smooth hydrophobic surface For hydrophobic smooth coating Ls ~ 1 nm Slippage on rough hydrophobic surfaces Continuum model may fail at nanoscale (triple line effect)

34 Talks outline Talk 1: Solid Molecular Dynamics application to nanofluidics Water slippage on rough surfaces Water Effect of meniscus curvature on slippage Talk 2: Thanks!! Defected OTS-SAM Cassie-Wenzel transition Wetting on rough surfaces Cassie-Baxter/Wenzel transition Free-energy profile and transition mechanism

35 Other research interests Particle motion on super-hydrophobic surfaces Daniela Pimponi Paolo Gualtieri Carlo Casciola Two-phase flows Francesco Magaletti Luca Marino Francesco Picano Carlo Casciola Protein translocation Marco Bacci Fabio Cecconi Daniele Di Marino Carlo Casciola Anna Tramontano

36 Flux vs Diameter Non-dimensional form 2 p= u f 2 t 0=d / ν u0 =ν / d 2 p0=ν ρ/ d 2 f 0=ν /d p=μ u + f 2 3 Φ= S u n ds=d ν ρ Φ u f Φ Φ f d 4 No additional length scale. (No-slip or free-slip boundary condition

37 Intrinsic slippage: effect of pressure P estimated from the spring forces Depletion layer = 1 w z Water bulk density B w s z B s dz Solid bulk density Gentili et al. Meccanica (2013)