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. An important step towards such understanding lies in determining the correct boundary conditions. The existence and the extend of boundary slip for a Newtonian liquid flowing over a solid surface has been debated over the past two centuries, but a convincing conclusion is still lacking. To rationalize this controversy, new highly sensitive and accurate experimental techniques are required. Recently we have developed a new method for direct studies of flows in the close proximity of a solid surface based on total internal reflection fluorescence cross-correlation spectroscopy (TIR-FCCS). 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 fluorescent signals from two confocal observation volumes that a laterally shifted in flow direction contains important 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.

As an initial test we applied the method to aqueous flow near a hydrophilic surface and evaluated a slip length smaller than 5 nm, and, within the limitations of the experiments and the model, indistinguishable from zero. Our studies show that when combine with proper data analysis the TIR-FCCS method can estimate the slip length with few nanometer accuracy.

• 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.
  Opt. Expr., 17, 21149(2009)
• 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.
  Phys.Rev. B, 84, 066306 (2011)