Macroscopic rheology of non-Brownian suspensions at high shear rates: the influence of solid volume fraction and non-Newtonian behaviour of the liquid phase

Abstract

Abstract Modelling the macroscopic rheology of non-Brownian suspensions is complicated by the non-linear behaviour that originates from the interaction between solid particles and the liquid phase. In this contribution, a model is presented that describes suspension rheology as a function of solid volume fraction and shear rate dependency of both the liquid phase, as well as the suspension as a whole. It is experimentally validated using rotational rheometry ( $$\varphi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> ≤ 0.40) and capillary rheometry (0.55 ≤ $$\varphi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> ≤ 0.60) at shear rates &gt; 50 s −1 . A modified Krieger-Dougherty relation was used to describe the influence of solid volume fraction on the consistency coefficient, $$K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> , and was fitted to suspensions with a shear thinning liquid phase, i.e. having a flow index, $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> , of 0.50. With the calculated fit parameters, it was possible to predict the consistency coefficients of suspensions with a large variation in the shear rate dependency of the liquid phase ( $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> = 0.20–1.00). With increasing solid volume fraction, the flow indices of the suspensions were found to decrease for Newtonian and mildly shear thinning liquid phases ( $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> ≥0.50), whereas they were found to increase for strongly shear thinning liquid phases ( $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> ≤0.27). It is hypothesized that this is related to interparticle friction and the relative contribution of friction forces to the viscosity of the suspension. The proposed model is a step towards the prediction of the flow curves of concentrated suspensions with non-Newtonian liquid phases at high shear rates.