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Flow near surface, Slip



The dynamics of flow in confined geometries, such as in micro-fluidic and nano-fluidic devices, can be accurately described only if the physics of the flow at the interface between the fluid and the solid is thoroughly understood. The question of whether and how a Newtonian fluid is able to slip over a solid surface has arisen with the development of theoretical models for fluid motion at the beginning of the 19th century. Because of its high fundamental and technological importance, it has been continuously studied and controversially debated over the past two centuries, but a convincing conclusion is still lacking. To rationalize this controversy, new highly sensitive and accurate experimental approaches are needed. By using very small fluorescent tracers dispersed in the liquid and applying the sensitive technique of fluorescence correlation spectroscopy (FCS) we are able to obtain flow velocity profiles and quantify the slip for water flowing on both smooth hydrophobic and structured super hydrophobic surfaces.

Slip on smooth hydrophobic surfaces

Following Navier, slippage is typically characterized by the slip length b, relating velocity u, and stress at the surface via the boundary condition u=b(∂u/∂n) with n being the normal to the surface. Most theoretical studies predict a slip length b < 100 nm for water flowing on smooth, hydrophobic surfaces. In order to address such small values we study the flow in the very close proximity of the solid surface using total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS).

The TIR-FCCS principle: An evanescent wave that extends only ~ 100 nm from the glass wall of a micro-channel is used to excite fluorescent tracers (quantum dots) flowing with the liquid. The cross-correlation function of the fluorescence intensity signals (I1(t), I2(t)) from two small observation volumes that a laterally shifted in flow direction contains information on the tracer’s and hence flow velocity.

In order to extract this information in an accurate and quantitative way we performed detailed theoretical modeling of the phenomena in close cooperation with B. Duenweg from AK-Kremer. Firstly, Brownian Dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Secondly, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum values of the slip length and shear rate and their statistical error bars.



Left: typical experimental correlation curves (symbols) and the corresponding fits (lines); Right: the best fit parameters combination for shear rate and slip length. To determine precisely the real slip length ≈ 8 nm, first the shear rate (3730 s-1) was measured independently by using confocal FCS to map the flow profile across the entire micro-channel.

Our studies show that when combine with proper data analysis the TIR-FCCS method can estimate the slip length with few nanometer accuracy. We applied the method to study flow of water over glass coated with a layer of PDMS (advancing contact angle Q=108°) or perfluorosilane (Q=113°). We found a slip length less than 15 nm on all studied surfaces.



 

Slip on structured superhydrophobic surfaces

While the intrinsic slip on smooth, hydrophobic surfaces is too small to affect most applications, presumably much larger and therefore technologically much more relevant effective slip is expected on rough surfaces.

Left: schematic representation of structured surface on which the water is in the Cassie state. Right: scanning electron microscopy image of a pillar of our model surfaces.

This type of slip is due to a fluid being in the Cassie state; i.e., for typical superhydrophobic surfaces, air is entrapped underneath the water in surface indentations. In this case, slip may be considered on two length scales: (i) Effective slip that represents the inhomogeneous surface by an averaging parameter and thereby characterizes the flow far from the surface. Most experiments to date are limited to this global viewpoint, e.g., by measuring a net drag reduction. (ii) Local, intrinsic slip, considered at the length scale of the surface inhomogeneities. It is difficult to address this local slip experimentally and thus it is typically treated in strongly idealized way.

We used confocal fluorescence correlation spectroscopy, to perform detailed measurements of the local flow field and slip length for water in the Cassie state on a microstructured superhydrophobic surface.


Schematic of the experimental setup for measuring local flow profiles



Left: Confocal microscopy image of the air-water interface (blue color corresponds to strong reflection signal) and the coated pillars (black). Measurement positions are indicated in a pillar referred coordinate system. Right: FCS-measured local slip length (μm).


  • Zhao X, Best A, Liu WD, Koynov K, Butt HJ, Schonecker C:
    Irregular, nanostructured superhydrophobic surfaces: Local wetting and slippage monitored by fluorescence correlation spectroscopy
    Physical Review Fluids, 2021, 6, 054004 (doi 10.1103/PhysRevFluids.6.054004
  •  D. Schaeffel, K. Koynov, D. Vollmer, H.-J. Butt, C. Schoenecker:
    Local Flow Field and Slip Length of Superhydrophobic Surfaces.
    Physical Review Letters, 2016, 116, 134501 (doi 10.1103/PhysRevLett.116.134501)

  • D. Schaeffel, S. Yordanov, M. Schmelzeisen, T. Yamamoto, M. Kappl, R. Schmitz, B. Dünweg, H.-J. Butt, K. Koynov:
    Hydrodynamic boundary condition of water on hydrophobic surfaces.
    Physical review E, 2013, 87, 051001(R) (doi 10.1103/PhysRevE.87.051001)

  • R. Schmitz, S. Yordanov, H.-J. Butt, K. Koynov, B. Duenweg:
    Studying flow close to an interface by total internal reflection fluorescence cross-correlation spectroscopy: Quantitative data analysis.
    Physical Review E, 2011, 84, 066306 (doi 10.1103/PhysRevE.84.066306)

  • S. Yordanov, A. Best, H.-J. Butt, K. Koynov:
    Direct studies of liquid flows near solid surfaces by total internal reflection fluorescence cross-correlation spectroscopy.
    Optics Express, 2009, 17, 21149-21158 (doi 10.1364/OE.17.021149)