A nonequilibrium thermodynamics perspective of thixotropy

Abstract

We propose a new description of elasto-viscoplastic fluids by relating the notion of thixotropy directly to internal viscoelasticity and network structures through a general, thermodynamically consistent, approach. By means of non-equilibrium thermodynamics, a thermodynamically-admissible elasto-viscoplastic model is derived which introduces self-consistently and effortlessly thixotropic effects and reproduces at both low and high shear rates experimental data usually fitted with empirical constitutive equations, such as the Bingham and Herschel-Bulkley models. The predictions of the new model are in very good agreement with available steadystate shear rheological data for soft colloidal pastes and blood, i.e. systems exhibiting a yield stress, and with time-dependent rheological data for blood, i.e. during a triangular time-dependent change in shear rate, exhibiting a hysteresis. The proposed approach is expected to provide the means to improve our understanding of thixotropic fluids.

A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

“…By employing a NET formalism 34,[39][40][41] we are assured that the constitutive model is, by construction, consistent with the laws of thermodynamics by imposing restrictions to the model parameters. 34,[39][40][41] Up to date, several micro-structured systems, such as liquid crystals, 57,58 immiscible complex fluids, 34,[38][39][40][41][42]44,[46][47][48][49][50][51]55,56,59 aggregating low-Ht blood, 33 polymer melts and solutions, 34,[39][40][41][60][61][62][63] polymer nanocomposites, [64][65][66][67] micellar systems 68,69 drilling fluids, 70 and thixotropic fluids 71 have been addressed through NET, a fact attesting to its usefulness and applicability.…”

Elucidating the rheological implications of adding particles in blood

“…We have recently proposed (Stephanou 2020 ) that to accomplish this we need to employ one additional scalar structural variable, , to properly characterize the network formed by RBCs. When the network is fully formed, then =1, while in a completely broken state, i.e., when only single RBCs remain, it vanishes (Mewis and Wagner 2009 ; Stephanou and Georgiou 2018 ). Next, we consider particles as rigid spheroids; to describe the average particle orientation, we consider the orientation tensor defined (Stephanou et al 2014 ; Stephanou 2015 ) as where is the particle’s director vector and is the orientational distribution function for the vector at position and time .…”

“…In this work, we will employ non-equilibrium thermodynamics (NET) to develop a sophisticated mathematical model addressing the rheological behavior of nanoblood. To accomplish this, we will develop the model using the generalized bracket formalism (Beris and Edwards 1994 ) of NET (Beris and Edwards 1994 ; Grmela and Öttinger 1997 ; Öttinger and Grmela 1997 ; Edwards et al 2003 ; Öttinger 2005 ), by means of which several microstructured systems have been addressed up to date, such as, but not limited to, immiscible complex fluids (Edwards and Dressler 2003 ; Dressler and Edwards 2004 ; Dressler et al 2008 ; Grmela et al 2014 ; Mwasame et al 2017 ), polymer melts and solutions (Beris and Edwards 1994 ; Grmela and Öttinger 1997 ; Öttinger and Grmela 1997 ; Öttinger 2005 ; Stephanou et al 2009 , 2016 , 2020b ), polymer nanocomposites (Rajabian et al 2005 ; Eslami et al 2010 ; Stephanou et al 2014 ; Stephanou 2015 ), micellar systems (Germann et al 2013 ; Stephanou et al 2020a ), blood (Tsimouri et al 2018 ; Stephanou 2020 ; Stephanou and Tsimouri 2020 ), drilling fluids (Stephanou 2018 ), and thixotropic fluids (Stephanou and Georgiou 2018 ). The use of a NET formalism has the compelling advantage, over other approaches, that the constitutive model as a whole is guaranteed consistency with the laws of thermodynamics (as extended for beyond equilibrium systems).…”

On the consistent modeling of shear-thickening polymer solutions

“…To accomplish this, we will develop the model using the Generalized bracket formalism 28 of NET, [28][29][30][31] by means of which several microstructured systems have been addressed, such as polymer melts and solutions, [28][29][30]32,33 polymer nanocomposites, 34,35 micellar systems, 36,37 blood, [38][39][40] drilling fluids, 41 and thixotropic fluids. 42 Thus, we guarantee that the model derived will be consistent with the law of thermodynamics as extended for beyond equilibrium systems. Also, we guarantee that the coupling between the various variables is accomplished self-consistently.…”