Dynamical role of slip heterogeneities in confined flows

We demonstrate that flows in confined systems are controlled by slip heterogeneities below a certain size. To show this we image the motion of soft glassy suspensions in microchannels whose inner walls impose different slip velocities. As the channel height decreases, the flow ceases to have the symmetric shape expected for yield-stress fluids. A theoretical model accounts for the role of slip heterogeneities and captures the velocity profiles. We generalize these results by introducing a length scale, valid for all fluids, below which slip heterogeneities dominate the flow in confined systems. General implications of this notion, concerning the interplay between slip and confinement, are presented.

Figure 1

(a) Shear stress versus shear rate for $C=0.016$ g/g: closed gray circles, macroscopic measurements; open black squares, data extracted from the velocity profiles shown in Figs. 2–2; and solid line, best fit to the Herschel-Bulkley equation (σ${}_y$ = 11.2 Pa, $n$ = 0.50, and $k$ = 4.1 Pa s${}^{1/2}$). The inset shows variations of the slip velocity with the reduced stress σ/σ${}_y$ at the hydrophilic (closed blue circles) and hydrophobic surfaces (closed red squares) of an asymmetric channel ($h$ = 75 μm); solid lines show linear fits. (b) Experimental setup. (c) Sketch of the focal plane in the microchannel.

Figure 2

Velocity profiles $V$ corrected from the slip velocity $V_{s,\min }$ for various heights, boundary conditions, and reduced stress σ/σ${}_y$ = 9 (dark cyan), 8 (purple), 6 (gray), 5 (blue), 4 (red), and 3 (green). The solid lines are the best fits to the theoretical expression of the velocity profiles calculated in the asymmetric Herschel-Bulkley flow model Eq. (3).

Figure 3

Representation of an asymmetric velocity profile (top) and the corresponding stress variation across the microchannel (bottom).

Figure 4

(a) Asymmetry parameter $S$ and velocity ratio α versus slip number ${\overline{U}}_s$ for different confinements 7 μm (★), 20 μm (■), 50 μm (▲), 75 μm (▶), and 100 μm ($•$); boundary conditions 20°-20° (blue open symbols), 20°-70° (green half-full symbols), and 20°-110° (red closed symbols); and microgel concentrations 0.016 g/g (symbols without a dot) and 0.022 g/g (dotted symbols). (b) Detail of velocity profiles near the low-slip hydrophobic surface showing slip-induced fluidization. Velocity profiles are scaled by the central plug velocity. The black dots point to the crossover between the central plug and the fluidized layers.