Free surface definitions in the trough cross-section.
Boger fluid matrix rheology. The viscosity is nearly constant at 2.16 Pa s, and the first normal stress difference obeys a square law in shear rate [see Eq. (6) ].
For 30% volume fraction the free surface is a circular arc. This contrasts with the intersecting planes for a Newtonian matrix [ Dai et al. (2013) ].
The fitted circular free surface shape for the 30% suspension. The radius of curvature is 55 mm and hm = 1.632 mm.
The viscosity as a function of shear rate. The lack of shear-thinning at higher concentrations was also found by Zarraga et al. (2001) , and Scirocco et al. (2005) found mild shear-thickening. The zero shear rate viscosities, estimated from the results for the lowest shear rates, are shown as horizontal lines. For the 40% suspension the differences between the mean results shown, and the other replicate runs were less than 3%, so the humped shapes are reproducible.
Relative viscosities at 10 s−1 and comparison with the results of Zarraga et al. (2001) for a similar matrix. Here and fitted line for our results represents Eq. (9) . The Einstein relation is also shown. Triangles, present work; circles, Zarraga et al. (2001) at two different shear rates; solid line, Eq. (9) ; dashed line, [ Zarraga et al. (2001) ].
versus for concentrations (5–40%). Two methods of finding were used: open symbols, circular arc fitting; filled symbols, used data directly from the profile.
from parallel-plate measurements for the lower volume fractions (0, 5, 10, 20, and 25%). Since the shear rate range of most interest is 0–30 s−1, we have used the quadratic fits shown (see Table II ).
from parallel-plate measurements for the higher volume fractions (30, 35, and 40%). Here the quadratic fits for were used (see Table II ).
The ratio changes sign at . This agrees qualitatively with the results of Aral and Kalyon (1997) . Circles, experimental data; line, fitting.
Experimental results for , , , and at various .
N 1 and N 2 behaviour from different workers. The percentage volume fraction ranges are listed in the Matrix fluid column.
Showing the fit of data to theories.
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