Fluorescence cross-correlation spectroscopy for time dependent flows: a numerical investigation

We have previously addressed experimentally blood fluidodynamics in microcapillaries by coupling optical microscopy to pixelated detection. By computing the Cross-Correlation Function (CCF) of signals coming from pixels at a distance along the flow we obtained information on the flow speed and direction. The extension of these experiments to more complex systems with high branching of capillaries and/or inverted flows needs a theoretical investigation that we present here. We focus first on straight capillaries and harmonic flows between a minimum V min ≠ 0 and a maximum V max flow speed. The CCF shows multiple peaks at lag times that correspond closely to the maximum and minimum flow speeds. The general analytical expression of the CCF is given, the position of its maxima are discussed by means of geometrical considerations and numerical analysis and an experimental validation are presented. The second case that we study is the flow in the branches of a y-shaped junction in a microcapillary. By simply modeling the branching in laminar flow (low Reynold numbers) and assuming a smooth transition of speeds along the branches we derive a simple numerical model to compute the trajectories of micro-beads. We estimate the flow speed in the branches by computing the CCFs between linear regions of interest set perpendicular to the axes of the branches.