(519d) Modeling the Transient Shear Flow of a Carbon Black Soft Colloidal System Using a Scalar Structural Parameter Thixotropic Model

Authors: 
Armstrong, M., United States Military Academy
Beris, A. N., University of Delaware
Recent work using small angle neutron scattering under flow has identified the existence of a microstructure that is dependent on flow conditions [1,2] in soft colloidal systems. On the other hand, over the last twenty years or so, a large number of empirically based thixotropic rheological models has been developed that involve, albeit phenomenologically, a single scalar structural parameter, lambda [3-6]. These models involve the combination of a lambda-dependent decomposition of the shear stress to an elastic and a viscous contribution with a relaxation-based evolution equation for lambda. The rich behavior of the soft colloidal systems is primarily due to the interaction of the structure and the hydrodynamic force and this can be particularly enhanced applied through in transient flow, and/or large amplitude oscillatory shear flow.

Applying large amplitude oscillatory shear (LAOS) to complex fluids induces nonlinear rheological responses, that, with proper modeling, can be used to sensitively probe the underlying microstructure and its dynamics. We demonstrate this for several concentrated colloidal suspensions using a newly developed semi-empirical, thixotropic master-equation developed around a scalar internal structural parameter, and the best features of several published thixotropic constitutive equations [3,4,5,6]. We examine two soft colloidal systems, all involving collective phenomena of yield stress and thixotropy. The systems are a 3.23vol% carbon black in napthenic oil [7,8,9], a thermo-reversible, adhesive hard sphere system, 30 nm silica particles in n-tetradecane [2].

The new master equation uses the structure parameter with a constitutive equation to model the elastic and viscous components of rheological responses to shear rate. Both steady state and time-dependent shear experimental data are fit using a recently developed robust numerical method that stochastically and effectively searches for the global optimum of a suitably forced least squares residual in the allowed parameter space [9]. With the best fit model parameters large amplitude oscillatory shear is predicted and compared to LAOS experimental data. The quality of the model is evaluated by comparing the difference between prediction and experimental LAOS data that are system dependent, and predicting strain rate frequency superposition [10]. While the master equation has been found to be able to qualitatively fit the experimental data, important quantitative are still were observed. The advantages and disadvantages of the new rheological model limitations of are going to be discussed focusing on the elucidation of the limitations of generic single scalar internal structural parameter models. These results and model comparisons are used to identify areas for improvement in thixotropic suspension modeling. Limitations of single scalar structural modeling will be shown.

Reference

[1] C.R. Lopez-Barron, A.K. Gurnon, A.P.R. Eberle, L. Porcar, and N.J. Wagner. Physical Review 89, 042301 (2014), 1-11.

[2] J. M. Kim. PhD thesis, University of Delaware, 2013.

[3] J. Mewis and N. J. Wagner, Colloidal Suspension Rheology, Cambridge Univ. Press, 2012.

[4] P. de Souza Mendes and R. Thompson. Rheol. Acta (2013) 52:673-694.

[5] A. Mujumbdar, A. N. Beris and A. B. Metzner. J. Non-Newtonian Fluid Mech. 102 (2002) 157-178.

[6] C.J. Dimitriou, R.H. Ewoldt and G.H. McKinley. J. Rheol. 571(1), 27-70.

[7] K. Dullaert and J. Mewis. Rheol. Acta (2005) 45: 23-32.

[8] K. Dullaert and J. Mewis. JNNFM 139 (2006) 21-30.

[9] M.J. Armstrong, PhD Thesis, University of Delaware (2015).

[10] H.M. Wyss, K. Mikayzaki, J. Mattsson, A. Hu, D.R. Reichman and D.A. Weitz. PRL 98, 238303 (2007).

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