Suspension models viscoelasticity

Tanner RI, Qi F (2005a) A comparison of some models for describing polymer crystallization at low deformation rate. J Non-Newtonian Fluid Mech 127 131-141 Tanner RI, Qi F (2005b) A phenomenological approach to suspensions with viscoelastic matrices. Korea-Australia Rheol J 17 149-156... 

Consequently, two major factors affect the rheological properties of the mixture during phase separation (i) the change of composition in the epoxy-rich matrix and (ii) the variation of viscoelastic behavior of the phase-separated blend. The authors employed a two-phase suspension model as proposed by Graebling and Palierne [52] to explain the effect of viscoelastic behavior on the phase-separated mixture ... 

Ramazani SAA, Ait-Kadi A, Grmela M (2001) Rheology of fiber suspensions in viscoelastic media experiments and model predictions. J Rheol 45 945-962 Rienacker G, Hess S (1999) Orientational dynamics of nematic liquid crystals under shear flow. 

The above model assumes that both components are dynamically symmetric, that they have same viscosities and densities, and that the deformations of the phase matrix is much slower than the internal rheological time [164], However, for a large class of systems, such as polymer solutions, colloidal suspension, and so on, these assumptions are not valid. To describe the phase separation in dynamically asymmetric mixtures, the model should treat the motion of each component separately ( two-fluid models [98]). Let Vi (r, t) and v2(r, t) be the velocities of components 1 and 2, respectively. Then, the basic equations for a viscoelastic model are [164—166]... 

As indicated above, such an agreement is perhaps expected. On the other hand, it is remarkable that a rather complex phenomenological theory postulated for an LC continuum can be reconciled with an even more complex molecular theory built on the concept of intermolecular potential. Perhaps the only other such happy instance is the agreement between the continuum Oldroyd-B model for viscoelastic liquids and the molecular model based on a dilute suspension of linear Hookean dumbbells in a Newtonian solvent. ... 

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

Several researchers reported viscoelastic behavior of yeast suspensions. Labuza et al. [9] reported shear-thinning behavior of baker s yeast (S. cerevisiae) in the range of 1 to 100 reciprocal seconds at yeast concentrations above 10.5% (w/w). The power law model was successfully applied. More recently, Mancini and Moresi [10] also measured the rheological properties of baker s yeast using different rheometers in the concentration range of 25 to 200 g dm. While the Haake rotational viscometer confirmed Labuza s results on the pseudoplastic character of yeast suspension, the dynamic stress rheometer revealed definitive Newtonian behavior. This discrepancy was attributed to the lower sensitivity of Haake viscometer in the range of viscosity tested (1.5 to 12 mPa s). Speers et al. [11] used a controlled shear-rate rheometer with a cone-and-plate system to measure viscosity of... 

More recently, a new, viscoelastic-plastic model for suspension of small particles in polymer melts was proposed [Sobhanie et al., 1997]. The basic assumption is that the total stress is divided into that in the matrix and immersed in it network of interacting particles. Consequently, the model leads to non-linear viscoelastic relations with yield function. The latter is defined in terms of structure rupture and restoration. Derived steady state and dynamic functions were compared with the experimental data. 

The arterial circulation is a multiply branched network of compliant tubes. The geometry of the network is complex, and the vessels exhibit nonlinear viscoelastic behavior. Flow is pulsatile, and the blood flowing through the network is a suspension of red blood cells and other particles in plasma which exhibits complex non-Newtonian properties. Whereas the development of an exact biomechanical description of arterial hemodynamics is a formidable task, surprisingly useful results can be obtained with greatly simplified models. 

Sarvestani, A. S., and Jabbari, E., Modeling the viscoelastic response of suspension of particles in polymer solution the effect of polymer-particle interactions, Macmmol. Theory Simul.,... 

Khalkhal and Carreau (2011) examined the linear viscoelastic properties as well as the evolution of the stmcture in multiwall carbon nanotube-epoxy suspensions at different concentration under the influence of flow history and temperature. Initially, based on the frequency sweep measurements, the critical concentration in which the storage and loss moduli shows a transition from liquid-like to solid-like behavior at low angular frequencies was found to be about 2 wt%. This transition indicates the formation of a percolated carbon nanotube network. Consequently, 2 wt% was considered as the rheological percolation threshold. The appearance of an apparent yield stress, at about 2 wt% and higher concentration in the steady shear measurements performed from the low shear of 0.01 s to high shear of 100 s confirmed the formation of a percolated network (Fig. 7.9). The authors used the Herschel-Bulkley model to estimate the apparent yield stress. As a result they showed that the apparent yield stress scales with concentration as Xy (Khalkhal and Carreau 2011). 

Feme J, Ausias G, Heuzey MC, Carreau PJ (2009) Modeling fiber interactions in semiconcentrated fiber suspensions. J Rheol 53 49—72 Ferrari A, Dumbser M, Toto EF, Armanini A (2009) A new 3D parallel SPH scheme for free surface flows. Comput Fluids 38 1203—1217 Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New York... 

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