Wall Slip of Soft-Jammed Systems: A Generic Simple Shear Process

From well-controlled long creep tests, we show that the residual apparent yield stress observed with soft-jammed systems along smooth surfaces is an artifact due to edge effects. By removing these effects, we can determine the stress solely associated with steady-state wall slip below the material yield stress. This stress is found to vary linearly with the slip velocity for a wide range of materials whatever the structure, the interaction types between the elements and with the wall, and the concentration. Thus, wall slip results from the laminar flow of some given free liquid volume remaining between the (rough) jammed structure formed by the elements and the smooth wall. This phenomenon may be described by the simple shear flow in a Newtonian liquid layer of uniform thickness. For various systems, this equivalent thickness varies in a narrow range ($35\pm 15\mathrm{nm}$).

Figure 1

(a) View of a heap of emulsion after some motion (from the top left) on a smooth inclined surface. (b) Schematic aspect of the sample cross section close to the contact line showing the different flow regions and their microstructural origin (suspended elements in dark or light gray, interstitial liquid in white).

Figure 2

Direct concentrated emulsion (82%): flow curve (with rough surfaces) (solid squares) and apparent flow curve in the presence of wall slip along one smooth surface (open circles). The inset shows creep test data for the latter case. The numbers correspond to stress values in Pascals. The dotted lines mark the transition to slip (lower line) and the bulk yielding (upper line).

Figure 3

Flow curve of a thixotropic clay-water suspension for fully rough (solid stars) and partially smooth (open stars) surface conditions. The insets show creep curves for rough (top) and smooth (bottom) surfaces. The data shown as gray stars (for 27 Pa) correspond to the jump in the apparent steady state observed for a stress between 24 and 27.5 Pa (see the bottom inset).

Figure 4

Apparent flow curves of an emulsion (82%) for the same gap and different plate diameters: 9 cm (squares), 6 cm (triangles), 4 cm (diamonds), 3 cm (stars), 3 cm with oil film at the sample periphery (half-filled stars), and 2 cm (circles). Hexagons show data with two rough plate surfaces. Several tests carried out by changing the sample while keeping the same surface are shown for each diameter in order to appreciate the reproducibility. Note that, in order to remove the impact of the sample shape at the periphery, which increases when sample $R$ decreases, $\tau$ has been rescaled by a factor of around 1 to get the same stress values for ${\dot{\gamma }}_0$ (see [24]). The bottom inset shows the stress minus the residual yield stress vs shear rate. The dotted line of slope 1 is a guide for the eye. The top inset shows ${\tau }_c^{\prime }$ (in Pascals) values as a function of $R$ (in centimeters).

Figure 5

Wall slip velocity for various materials (see [27] for detailed data) as a function of slip stress: emulsions at different concentrations on silicon surface (blue squares), emulsions with different surfactants and solid surfaces (blue circles), emulsion with a water-glycerol solution (with a viscosity 15 times that of water) as interstitial liquid (light blue solid square), bentonite suspensions at different concentrations (brown diamonds), inverse emulsions (dark yellow inverse triangles) (here using $1.5\mu$; see [27]), Carbopol gels (green pentagons), ketchup (red solid stars), mustard (red open stars), foam (crosses), and direct emulsion (82%) over a Teflon surface (black cones). The dashed lines correspond to the equation ${\tau }_S=\mu V_S/\delta$ with $\delta =30\mathrm{nm}$ and $\delta =50\mathrm{nm}$.