Rheological analysis of particle aggregation in a colloidal suspension of carbon black particles

다국어 초록 (Multilingual Abstract)

We examine scaling theories to estimate microstructural parameters of fractal aggregates in a colloidal suspension. The scaling theories are based on fractal theories and rheological properties of the colloidal suspension. Rheological measurement in oscillatory and steady shear modes is performed for colloidal suspensions of 56 nm carbon black particles in Newtonian ethylene glycol at the particle volume fractions φ ranging from 0.005 to 0.05. Elastic modulus G’ of the colloidal suspension at φ = 0.02-0.05 in the state of colloidal gel is used to estimate fractal dimension df of the aggregates. Steady-shear measurement gives yield stress τy as a function of φ. Shear dependence of the aggregate radius R is given by a power-law scaling, i.e., R∝S−m, where S is the shear rate. The power-law exponent m is estimated from df and a scaling relation between τy and φ. The estimation gives df = 2.14 and m = 0.33. The parameters df and m which can be determined by either direct measurement or theoretical calculation are used to establish a microrheological model for predicting shear viscosity of aggregated suspension as a function of φ and S. Both the concentration dependence and the shear dependence of aggregates are combined to obtain an expression for the shear viscosity. Hydrodynamic interaction effect among the aggregates is roughly considered in calculating average shear stress on the aggregate. It is found that this consideration critically contributes to behavior similarity with experimental result. It is shown that the predictions by the model reasonably agree with the experimental result.

참고문헌 (Reference)

1 Buscall, R., "The rheology of strong-flocculated suspensions" 24 : 183-202, 1987

2 Batchelor, G.K., "The determination of the bulk stress in a suspension of particles to order c2" 56 : 401-427, 1972

3 Sonntag, R.C., "Structure and breakup of flocs subjected to fluid stresses: I. Shear experiments" 113 : 399-413, 1986

4 Piau, J.-M., "Shear elasticity and yield stress of silica-silicone physical gels: Fractal approach" 43 : 305-314, 1999

5 Buscall, R., "Scaling behavior of the rheology of aggregate networks formed from colloidal particles" 84 : 4249-4260, 1988

6 Shih, W.-H., "Scaling behavior of the elastic properties of colloidal gels" 42 : 4772-4779, 1990

7 Quemada, D., "Rheology of concentrated disperse systems and minimum energy dissipation principle: 1. Viscosity-concentration relationship" 16 : 82-94, 1977

8 Casson, N., "Rheology of Disperse Systems" Pergamon Press 84-104, 1959

9 김단비, "Prediction of shear viscosity of a zinc oxide suspension with colloidal aggregation" 한국유변학회 30 (30): 67-74, 2018

10 Potanin, A.A., "On the model of colloidal aggregates and aggregating colloids" 96 : 9191-9200, 1992

11 Potanin, A.A., "On the computer simulation of the deformation and breakup of colloidal aggregates in shear flow" 157 : 399-410, 1993

12 Smith, T.L., "Intrinsic viscosities and other rheological properties of flocculated suspensions of nonmagnetic and magnetic ferric oxides" 72 : 13-26, 1979

13 Snabre, P., "I. Rheology of weakly flocculated suspensions of rigid particles" 6 : 1811-1834, 1996

14 Seto, R., "Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics" 84 : 041405-, 2011

15 Eggersdorfer, M.L., "Fragmentation and restructuring of soft-agglomerates under shear" 342 : 261-268, 2010

16 Meakin, P., "Fractal aggregates" 28 : 249-331, 1987

17 Lee, B., "Estimation of microstructure of titania particulate dispersion through viscosity measurement" 266 : 16-21, 2014

18 van der Aerschot, E., "Equilibrium properties of reversibly flocculated dispersions" 69 : 15-22, 1992

19 Mewis, J., "Colloidal Suspension Rheology" Cambridge Press 2012

20 Conchuir, B.O., "Analytical model of fractal aggregate stability and restructuring in shear flows" 53 : 9109-9119, 2014

21 이후인, "Analysis of fractal aggregates in a colloidal suspension of carbon black from its sedimentation and viscosity behavior" 한국유변학회 28 (28): 267-273, 2016

22 Jullien, R., "Aggregation and Fractal Aggregates" World Scientific 1987

23 Krieger, I.M., "A mechanism for non-Newtonian flow in suspensions of rigid spheres" 3 : 137-152, 1959

24 Patel, P.D., "A mean field theory for rheology of phase separated or flocculated dispersions" 31 : 355-383, 1988