Rheology of thixotropic dispersions. Transient phenomena with increasing shear rate

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Abstract

A structural rheological model is used to describe the thixotropic dispersed system of silicon dioxide in oil. The model includes a kinetic equation of the processes of formation and destruction of particle aggregates and a rheological equation containing a structural parameter (the number of aggregated particles in a unit volume). The case of an equilibrium plastic flow, which corresponds to experimental flow curves, is considered. The coefficients of the rheological equation are calculated. For a stepwise increase in the shear rate from γ˙1 to γ˙2, the transient process is considered as a transition from one equilibrium state of the flow to another equilibrium state through a certain nonequilibrium state of the flow. The coefficient of deviation from equilibrium is introduced, and its dependence ζ(t) is calculated using exponential functions; the limiting value ζ0 is determined. The transient dependences τ1/2(t) are approximated.

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About the authors

V. N. Matveenko

M. V. Lomonosov Moscow State University; State Social and Humanitarian University

Author for correspondence.
Email: 13121946VNM@gmail.com

M. V. Lomonosov Moscow State University, Department of Chemistry

Russian Federation, Moscow; Kolomna, Moscow Region, 140411

E. A. Kirsanov

M. V. Lomonosov Moscow State University; State Social and Humanitarian University

Email: Kirsanov47@mail.ru

M. V. Lomonosov Moscow State University, Department of Chemistry

Russian Federation, Moscow; Kolomna, Moscow Region, 140411

References

  1. Barnes H.A. // J. Non-Newtonian Fluid Mech. 1997. V. 70. P. 1.
  2. Yufei Wei. Investigating and Modeling the Rheology and Flow Instabilities of Thixotropic Yield Stress Fluids. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Chemical Engineering). University of Michigan, 2019. 139 p.
  3. Mujumdar A., Beris A.N., and Metzner A.B. // J. of Non-Newtonian Fluid Mech. 2002. V. 102. P. 157.
  4. Cross M. // J. Colloid Sci. 1965. Vol. 20. P. 417.
  5. Кирсанов Е.А., Матвеенко В.Н. Неньютоновское течение дисперсных, полимерных и жидкокристаллических систем. Структурный подход: монография М.: Техносфера, 2016. 384 с. [Kirsanov E.A., Matveenko V.N. Non-Newtonian flow of dispersed, polymer and liquid crystal systems. Structural approach. Moscow: Technosphere, 2016, 384 p. (in Russ.)].
  6. Кирсанов Е.А., Матвеенко В.Н. Вязкость и упругость структурированных жидкостей: монография М.: Техносфера, 2022. 284 с. [Kirsanov E.A., Matveenko V.N. Viscosity and elasticity of structured liquids. Moscow: Technosphere, 2022, 284 p. (in Russ.)].

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2. Fig. 1. Schematic diagram of the transition process with a step-by-step increase in the shear rate from to : a — step-by-step increase in the shear rate; b — change in shear stress over time while maintaining the initial structure of the substance (thin solid line), decrease in stress during destruction of the structure after reaching the speed (dashed line), change in stress during destruction of the structure at the beginning of the transition interval (thick solid line).

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3. Fig. 2. Flow curves in the CR↑ mode of a thixotropic dispersion of silicon dioxide in oil at a volume concentration of 0.029 and a particle diameter of 16 nm: a — in double logarithmic coordinates; b — in root coordinates over the entire measurement range; c — in root coordinates over the range of low shear rates. The dotted line corresponds to the approximation from the high-velocity region.

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4. Fig. 3. Flow curves in the CR↓ mode of a thixotropic dispersion of silicon dioxide in oil at a volume concentration of 0.029 and a particle diameter of 16 nm: a — in double logarithmic coordinates; b — in root coordinates over the entire measurement range; c — in root coordinates over the range of low shear rates. The dotted line corresponds to the approximation from the high-velocity region.

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5. Fig. 4. Flow curves in the CS↓ mode of a thixotropic dispersion of silicon dioxide in oil at a volume concentration of 0.029 and a particle diameter of 16 nm: a - in double logarithmic coordinates; b - in root coordinates over the entire measurement range; c - in root coordinates over the range of low shear rates. The dotted line corresponds to the approximation from the high-velocity region.

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6. Fig. 5. Dependence of the shear stress on time with a stepwise increase in the shear rate from = 0.1 to = 5.0 s-1: a — dependence of the root of the shear stress on the logarithm of time; b — dependence of the root of the shear stress on time. The horizontal dotted lines correspond to the shear stress at equilibrium flow at a velocity (15 a) and the shear stress of nonequilibrium flow at the same velocity after the transition from to (15 b). The solid line is an approximation according to equation (15 d) using equation (17).

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7. Fig. 6. Dependence of the coefficient of deviation from equilibrium ζ on time with a stepwise increase in the shear rate from = 0.1 to = 5.0 s-1: a — dependence ζ(t) in double logarithmic coordinates; b — dependence ζ on time in the interval from zero to 20 s. ζ0 = 2.815. Circles — values ​​obtained from equation (18), solid line — approximation according to equation (17).

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8. Fig. 7. Dependence of the shear stress on time with a stepwise increase in the shear rate from = 0.1 to = 2.5 s-1: a — dependence of the root of the shear stress on the logarithm of time; b — dependence of the root of the shear stress on time. The horizontal dotted lines correspond to the shear stress at equilibrium flow at a velocity of (15a) and the shear stress of nonequilibrium flow at the same velocity after the transition from to (15b).

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9. Fig. 8. Dependences of the coefficient of deviation from equilibrium ζ on time with a stepwise increase in the shear rate from = 0.1 to = 2.5 s-1: a — dependence ζ(lg t); b — dependence ζ on time t. ζ0 = 2.404. Circles — values ​​obtained from equation (18), solid line — approximation according to equation (17).

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10. Fig. 9. Dependences of the shear stress and the coefficient of deviation from equilibrium on time with a step increase in the shear rate from = 0.1 to = 1.0 s-1: a - dependence of the root of the shear stress on the logarithm of time; b - dependence ζ(lg t). ζ0 = 1.845. The horizontal dotted lines correspond to the shear stress at equilibrium flow at a velocity (15a) and the shear stress of nonequilibrium flow at the same velocity after the transition from to (15b)

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11. Fig. 10. Dependence of the shear stress and the coefficient of deviation from equilibrium on time with a step increase in the shear rate from = 1.0 to = 9.0 s-1: a — dependence of the root of the shear stress on the logarithm of time; b — dependence ζ(lgt). ζ0 = 2.108. The horizontal dotted lines correspond to the shear stress at equilibrium flow at a velocity (15a) and the shear stress of nonequilibrium flow at the same velocity after the transition from to (15b).

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12. Fig. 11. Dependences of the root of shear viscosity on time with a stepwise increase in the shear rate from = 0.1 s-1 to the value indicated on the graph. The dashed lines show the viscosity values ​​at the beginning of the process of structure destruction and the viscosity values ​​after reaching equilibrium.

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