The links-nodes-blobs model for shear-thinning-yield-stress fluids

A new model based on fractal and percolation concepts is proposed to explain the rheological behavior of shear-thinning yield-stress fluids. Suspension particles of the fluids are described in terms of the links-nodes-blobs (L-N-B) model. The complex suspension rheology can be interpreted via the similarity of the L-N-B model to the Rouse chain model. Consequently, the empirically universal relationship between the dimensionless shear stress, T, and the dimensionless shear rate, Γ, which was recently suggested by Coussot as T = 1+KΓ ⁿ at Γ<0.3 and approaches Newtonian behavior at Γ>50, can be derived in terms of microscopic properties of a suspension of the force-free particles, fractal dimensions of the percolation system, and the critical lengths of the percolation system. According to our study, a more precise and more general universal relationship, which fits experimental data well over a wide range from Γ = 10⁻⁷10³, is proposed as T = 1+Γ+KΓ ⁿ . The parameter K in the universal equation can be expressed as a function of the dimensionless cross-section of the blobs, the distribution of links, and fractal dimensions of the percolation system, while the exponent n in the universal equation is a function of the fractal dimensions only. The transition point of a shear-thinning yield-stress fluid from shear-thinning to Newtonian behavior was explicitly interpreted. Received: 22 March 1999 Accepted in revised form: 1 June 1999