Concentrated colloidal suspensions, in which the primary particles associate at rest into aggregates, or flocs, which, however, are broken apart upon an applied flow deformation, often exhibit a complex thixotropic rheological behavior characterized by yield stress and a deformation history dependent rheology[1-4]. Recently, well defined rheological measurements on a model thixotropic suspension [2,6-7] have been 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 [5]. In [5], this extended data set has been used to test a new structure-based model developed by extending the Delaware thixotropic model [8]. A similar, scalar structural parameter-based, model has also been recently developed to describe the thixotropic behavior of another aggregating colloidal system, human blood [9]. However, the LAOS-based work [8] has shown the inherent limitation of the new as well as other, phenomenological, single structural-parameter based models to unidirectional shear flows, in that they cannot account for the reversal of flow directionality inherent in LAOS flow. The present work attempts to circumvent that limitation by systematically developing a new, multiscale thixotropy model where a structural scalar parameter model, developed from the model coarsening of a microscopic population balance analysis [10], is combined with two internal tensor structure parameters that are introduced through a thermodynamically consistent formulation [11] to describe the orientation and deformation under flow of free and interacting aggregates, respectively. The resultant model is demonstrated to quantitatively capture the key rheological signatures observed in the experimental data on thixotropic suspensions with distinctly superior predictions when compared to current thixotropy models. More specifically, the multiscale tensor model arising from this work is shown to offer substantially better predictions to the model thixotropic suspension of Dullaert and Mewis [6] than the single scalar parameter models that have been tested before[7,9]. An additional advantage of the new formulation is the capability to model the system’s rheology under general flow deformation.
In summary, we have developed a multiscale tensor model that incorporates microscopic information at the particle level into a two structural tensors-based, thermodynamically consistent, macroscopic description of soft aggregating colloidal particles in a thixotropic suspension that displays a yield stress. The good agreement with rheological experiments on a model thixotropic suspension provides additional confidence in the results arising from the multiscale framework adopted in this modeling effort.
References:
[1] J. Mewis, J. J. Non-Newtonian Fluid Mech., 6, 1 (1979).
[2] K. Dullaert, K., J. Mewis. J. of Colloid and Interface Science, 287, 542 (2005).
[3] J. Mewis, N. J. Wagner, Adv. Colloid and Interface Science, 147-148, 214 (2009).
[4] J. Mewis, N. J. Wagner, Colloidal Suspension Rheology, Cambridge U. Press, New York, 2012.
[5] M. J. Armstrong, A. N. Beris, S. A. Rogers and N. J. Wagner, J. Rheol., in press (2016).
[6] K. Dullaert, J. Mewis, Rheol. Acta, 45, 23 (2005).
[7] K. Dullaert, J. Mewis, J. Non-Newtonian Fluid Mech., 139, 21 (2006).
[8] A. Mujumbdar, A. .N. Beris , A. B. Metzner, J. Non-Newtonian Fluid Mech., 102, 157 (2002).
[9] A. J. Apostolidis, M. J. Armstrong, A. N. Beris, J. Rheol., 59, 275 (2015).
[10] P.M. Mwasame, A.N. Beris, R.B. Diemer and N. J. Wagner, AIChE Journal, 63(2), 517-531, (2017).
[11] A. N. Beris, B. J. Edwards, Thermodynamics of Flowing Systems, Oxford UP, New York, 1992.
