Non-linear dynamics of semi-dilute PAAm solutions in a microfluidic 3D cross-slot flow geometry

Abstract

We have characterised the flow of semi-dilute PAAm solutions (3.3c* ≤ c ≤ 16.6c*) through a three-dimensional cross-slot device (width to depth aspect ratio 2: 1) over a range of Weissenberg (0.13 ≤ Wi ≤ 88.5) and Elasticity (1.5 ≤ El ≤ 58.4) numbers by means of micro-particle imaging velocimetry (μ-PIV) and pressure drop measurements. The flow regimes are mapped into a Wi−Re diagram. At intermediate Wi (12 ≤ Wi ≤ 45) we observe the formation of lip vortices in the inlet channels. At higher Wi (Wi ≥ 45) we observe the onset of an asymmetric flow regime, which occurs at a much higher Weissenberg number than previously reported in the literature. Increasing El in the asymmetric flow regime results in flow patterns that are markedly more time-dependent and unstable. The extensional rates measured along the centreline of the outlet channels are much lower than the corresponding nominal values. By means of an improved version of the numerical method that was used in our previous works, we have linked the measured velocity field with the “local Deborah number” field to quantify the spatial distribution of the deformation rate underwent by the polymer chains at high Wi flows near the stagnation point of the cross slot device. We measured the extensional viscosity and Trouton ratios of our polymer solutions over a range of 1 ≤ Wi ≤ 30. This work is of significance for the development of extensional rheometers for measuring the properties of low-viscosity fluids such as inks, blood, silk fibroin and protein solutions.