Browsing by Author "Beris, Antony N."

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    A polydisperse model for thixotropic elasto-viscoplastic suspensions of aggregating particles using population balances
    (AIChE Journal, 2023-09-18) Jariwala, Soham; Song, Rong; Hipp, Julie B.; Diemer, R. Bertrum; Wagner, Norman J.; Beris, Antony N.
    An improved population balance-based rheological constitutive framework for polydisperse aggregating suspensions is derived by incorporating detailed models for orthokinetic and perikinetic aggregation and shear breakage processes. The framework accounts for critical properties such as dynamic arrest, viscoelasticity, kinematic hardening, thixotropy, and yield stress to generate a full range of thixotropic elasto-viscoplastic (TEVP) response. Additionally, the model is thermodynamically consistent because the dynamics and timescales are completely determined by internal structural and kinetic variables. The model connects the rheological response to the structural descriptors such as the size distribution of agglomerates, mean sizes, fractal dimension, and agglomerate volume fraction. Predictions are compared against a wide range of shear rheology measurements data for model thixotropic suspensions of fumed silica and carbon black, including large amplitude oscillatory shear (LAOS), as well as ultra-small angle neutron scattering under steady shear (Rheo-uSANS).
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    Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional
    (Physics of Fluids, 2024-01-04) Beris, Antony N.; Edwards, Brian J.
    We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.
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    Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments
    (The Society of Rheology, 2016-03-29) Armstrong, Matthew J.; Beris, Antony N.; Rogers, Simon A.; Wagner, Norman J.; Matthew J. Armstrong, Antony N. Beris, Simon A. Rogers, and Norman J. Wagner; Armstrong, Matthew J.; Beris, Antony N.; Rogers, Simon A.; Wagner, Norman J.
    Rheological measurements on a model thixotropic suspension by Dullaert and Mewis [J. Non-Newtonian Fluid Mech. 139(1–2), 21–30 (2006); Rheol. Acta 45, 23–32 (2005)] are extended to include large amplitude oscillatory shear (LAOS) flow, shear flow reversal, and a novel unidirectional LAOS flow to provide an extended rheological data set for testing constitutive models. We use this extended data set to test a new structure-based model developed by improving the Delaware thixotropic model [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102, 157–178 (2002); A. J. Apostolidis et al., J. Rheol. 59, 275–298 (2015)]. Model parameters are determined from steady, small amplitude oscillatory, and step shear rate tests. Holding those parameters fixed, model predictions are compared to LAOS experiments. Similar comparisons are made for three contemporary models from the literature. Two of these models use a scalar internal structural parameter and include the modified Jeffreys model proposed by de Souza Mendes and Thompson [Rheol. Acta 52, 673–694 (2013)]. The third model is based on fluidity additivity [F. Bautista et al., J. Non-Newtonian Fluid Mech. 80, 93–113 (1999)]. A common weakness in all models is shown to be the use of scalar order parameters that cannot account for the reversal of flow directionality inherent in LAOS flow. This is further illustrated by comparison with flow reversal and unidirectional LAOS experiments.
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    Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments
    (The Society of Rheology, 2016-03-29) Armstrong, Matthew J.; Beris, Antony N.; Rogers, Simon A.; Wagner, Norman J.; Matthew J. Armstrong, Antony N. Beris, Simon A. Rogers, and Norman J. Wagner; Armstrong, Matthew J.; Beris, Antony N; Rogers, Simon A.; Wagner, Norman J.
    Rheological measurements on a model thixotropic suspension by Dullaert and Mewis [J. Non-Newtonian Fluid Mech. 139(1–2), 21–30 (2006); Rheol. Acta 45, 23–32 (2005)] are extended to include large amplitude oscillatory shear (LAOS) flow, shear flow reversal, and a novel unidirectional LAOS flow to provide an extended rheological data set for testing constitutive models. We use this extended data set to test a new structure-based model developed by improving the Delaware thixotropic model [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102, 157–178 (2002); A. J. Apostolidis et al., J. Rheol. 59, 275–298 (2015)]. Model parameters are determined from steady, small amplitude oscillatory, and step shear rate tests. Holding those parameters fixed, model predictions are compared to LAOS experiments. Similar comparisons are made for three contemporary models from the literature. Two of these models use a scalar internal structural parameter and include the modified Jeffreys model proposed by de Souza Mendes and Thompson [Rheol. Acta 52, 673–694 (2013)]. The third model is based on fluidity additivity [F. Bautista et al., J. Non-Newtonian Fluid Mech. 80, 93–113 (1999)]. A common weakness in all models is shown to be the use of scalar order parameters that cannot account for the reversal of flow directionality inherent in LAOS flow. This is further illustrated by comparison with flow reversal and unidirectional LAOS experiments.
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    Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions
    (The Society of Rheology, 2016-01-14) Mwasame, Paul M.; Wagner, Norman J.; Beris, Antony N.; Paul M. Mwasame, Norman J. Wagner, and Antony N. Beris; Mwasame, Paul M.; Wagner, Norman J.; Beris, Antony N.
    The present study develops an extension of the approach pioneered by Farris [Trans. Soc. Rheol. 12, 281–301 (1968)] to model the viscosity in polydisperse suspensions. Each smaller particle size class is assumed to contribute to the suspension viscosity through a weighting function in two ways: first, indirectly, by altering the background viscosity, and second, directly, by increasing the contribution of the larger particles to the suspension viscosity. The weighting functions are developed in a consistent fashion as a power law with the exponent, h, a function of the relative volume fraction ratio and the base, g, a function of the solid particle size ratio. The model is fit to available theoretical and experimental results for the viscosity of several binary suspensions and shows good to excellent agreement depending on the functions g and h chosen. Once parameterized using binary suspension viscosity data, the predictive capability to model the viscosity of arbitrary continuous size distributions is realized by representing such distributions with equivalent ternary approximations selected to match the first six moments of the actual size distribution. Model predictions of the viscosity of polydisperse suspensions are presented and compared against experimental data.