Universal rescaling of flow curves for yield-stress fluids close to jamming

Abstract

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

Normal stress measurement in foams and emulsions in the presence of slip

“…to henceforth as "mobile" and "rigid" emulsions) [42]. The liquid volume fraction of the shaving foam was 9.2 ± 0.5 %, with a mean bubble radius of about 18 micrometers, in fair agreement with previously reported data on the same brand [43].…”

Scaling of flow curves: Comparison between experiments and simulations

“…As discussed above, flow curves above the critical jamming volume fraction can collapse into one master branch by plotting σ/|∆φ| ∆ vsγ/|∆φ| Γ [4,5]. Consistent with prior work, we find scaling collapse using ∆ ≈ 2.1 and Γ ≈ 3.8, see Figure 2c.…”

Merging fluid and solid granular behavior

“…Figure 11: Scaled pressure p * (a) and stress ratio µ (b) plotted against the volume fraction, for the proposed constitutive model (solid lines, Eqs. (12) and (16)), and the constitutive model of Chialvo et al [8] (dashed lines, Eqs. (22) and (23)).…”

“…4. Finally, Paredes et al [45] have presented a microscopic two-state theory for yield-stress fluids, elaborated in more detail by Dinkgreve et al [12] , to describe the transition between jammed and unjammed states. Yieldstress fluids are complex fluids composed of dispersions of one material (particles, drops or bubbles) in a liquid (or continuous phase), whose mechanical behavior is characterized by the emergence of a yield stress for volume fractions higher than some critical value (the jamming volume fraction) and Newtonian flow for lower volume fractions, with shear thinning in either case for high shear rates.…”