Scaling laws for the flow of generalized Newtonian suspensions

It has been observed that flow curves (viscosity vs shear rate) of spherical solid inclusions suspended in a generalized Newtonian fluid medium can be rescaled so as to collapse onto the flow curve of the fluid medium. This result is surprising given the range of values and the spatial heterogeneity of local shear rates and viscosity in such systems. We consider such scaling for the cases of shear thinning, Newtonian, and shear-thickening fluid media. Results from experiment and computational modeling are presented that examine the microscopic origins of this scaling behavior. Over a wide range of volume fractions (5–50%), it is shown that the distribution of local shear rates can be collapsed onto a single universal curve. The parameters for rescaling the shear rate distributions can be analytically related to the macroscopic rescaling parameters for the viscosity. As a result of this rescaling capability, one may measure the properties of the fluid medium and predict the macroscopic behavior of the susp...

[1]  David Turnbull,et al.  Molecular Transport in Liquids and Glasses , 1959 .

[2]  N. Phan-Thien,et al.  Normal stress differences behavior of polymeric particle suspension in shear flow , 2014 .

[3]  Thomas J. Dougherty,et al.  A Mechanism for Non‐Newtonian Flow in Suspensions of Rigid Spheres , 1959 .

[4]  Didier Lootens,et al.  A smoothed particle hydrodynamics-based fluid model with a spatially dependent viscosity: application to flow of a suspension with a non-Newtonian fluid matrix , 2010 .

[5]  Sangtae Kim.  Chapter 6 – Transient Stokes Flows , 1991 .

[6]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[7]  R. Tanner,et al.  Viscometric functions of semi-dilute non-colloidal suspensions of spheres in a viscoelastic matrix , 2013 .

[8]  Nicos Martys,et al.  Study of a dissipative particle dynamics based approach for modeling suspensions , 2005 .

[9]  Peter V. Coveney,et al.  Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics , 1997 .

[10]  R. Tanner,et al.  Viscometric functions of concentrated non-colloidal suspensions of spheres in a viscoelastic matrix , 2014 .

[12]  S. Manenti.  A Smoothed Particle Hydrodynamics : Basics and Applications , 2009 .

[13]  G. McKinley,et al.  The normal stress behaviour of suspensions with viscoelastic matrix fluids , 2002 .

[14]  D. Sundstrom.  Viscosity of suspensions in polymeric solutions , 1983 .

[15]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[16]  John F. Brady,et al.  Rheology and microstructure in concentrated noncolloidal suspensions , 2002 .

[17]  W. Gleissle,et al.  Validity of the Cox–Merz rule for concentrated suspensions , 2003 .

[18]  T. Kitano,et al.  Viscosity of particle filled polymer melts , 1978 .

[19]  D. Highgate,et al.  Rheological properties of suspensions of spheres in non-Newtonian media , 1970 .

[20]  Pep Español,et al.  Smoothed dissipative particle dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  See-Eng Phan,et al.  Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Nicos Martys,et al.  Velocity Verlet algorithm for dissipative-particle-dynamics-based models of suspensions , 1999 .

[23]  R. Tanner,et al.  A differential approach to suspensions with power-law matrices , 2010 .

[24]  Howard A. Barnes,et al.  A REVIEW OF THE RHEOLOGY OF FILLED VISCOELASTIC SYSTEMS , 2003 .

[25]  G. Jarzebski.  On the effective viscosity of pseudoplastic suspensions , 1981 .

[26]  R. Roscoe.  The viscosity of suspensions of rigid spheres , 1952 .