Viscoelastic phase separation

Explicit forms for the stress tensors d1 are deduced from the microscopic expressions for the component stress tensors and from the scheme of the total stress devision between the components [164]. Within this model almost all essential features of the viscoelastic phase separation observable experimentally can be reproduced [165] (see Fig. 20) existence of a frozen period after the quench nucleation of the less viscous phase in a droplet pattern the volume shrinking of the more viscous phase transient formation of the bicontinuous network structure phase inversion in the final stage. 

This problem is beyond our scope here, as are the subtleties which arise when the two crmstituents of a binary mixture have vastly different viscosities (viscoelastic phase separation [12]). 

Tanaka H (2000) Viscoelastic phase separation. J Phys Condens Matter 12 R207-R264... 

The SPH method provides an efficient way for the numerical simulations of the phase-separation phenomena in polymer blends. For instance, Okuzono used this approach to simulate a specific type of phase separation - the so-called viscoelastic phase separation - experimentally found in polymer solutions and dynamically asymmetric mixtures. Examining the effect of stress relaxation time on morphology of domains, it was shown that the more viscous phase forms network-like domains when the stress relaxation time is large. 

From the above considerations it is clear that our discussion of spinodal decomposition in terms of a generaUzed nonlinear diSusion equation (Eq. (5)) was very incomplete, since there it was tacitly assumed that the concentration field c(x, t) is the only relevant slow variable in the problems while in reality a second slow variable, the velocity field v(x, t), needs to be included, even if the fluid on average is at rest. A particularly interesting comphca-tion arises for fluids exposed to shear flow, where the direction of (relative to the flow direction) matters [11], while for fluids at rest S(k, t) is isotropic. This problem is beyond our scope here, as are the subtleties which arise when the two constituents of a binary mixture have vastly different viscosity (viscoelastic phase separation [12]). 

Abstract Phase separation in isotropic condensed matter has so far been believed to be classified into solid and fluid models. When there is a large difference in the characteristic rheological time between the components of a mixture, however, we need a model of phase separation, which we call viscoelastic model . This model is likely a general model that can describe all types of isotropic phase separation including solid and fluid model as special cases. We point out that this dynamic asymmetry between the components is quite common in complex fluids, one of whose components has large internal degrees of freedom. We also demonstrate that viscoelastic phase separation in such dynamically asymmetric mixtures can be characterized by the order-parameter switching phenomena. The primary order parameter switches from the... 

Here, we consider the characteristic features of the viscoelastic model of phase separation. Further, we demonstrate that these special features of a viscoelastic model lead to a novel phenomenon of order-parameter switching during viscoelastic phase separation, although it is always driven by a single thermodynamic driving force. 

In the viscoelastic model, the phase-separation mode can be switched between the fluid mode and elastic gel mode . The dynamic process of viscoelastic phase separation is schematically drawn in Fig. 1. It is characterized by the switching of phase-separation modes between fluidlike and elastic gel-like ones [4]. This switching is likely caused by the change in the coupling between stress fields and velocity fields, which is described by Eq. (6) According to Eq. (6), the two extreme cases, namely, (i) fluid model (xfj const.) and (ii) elastic gel model (G(t), K t) const.), correspond to and t[Pg.180]

Fig. 1 Schematic figure of pattern-evolution process during viscoelastic phase separation, (a)-(d) correspond to the elastic regime, (f) to the hydrodynamic fluid regime, and (e) to the viscoelastic relaxational regime. The first order-parameter switching occurs around (a), while the second one around (e). The phase-separation process during (a)-(d) is probably essentially the same as that of elastic gel...

Viscoelastic phase separation is expected to be universal in any mixture having asymmetry in elementary molecular dynamics between its components. The possible candidates for dynamic asymmetry are (1) slow dynamics in complex fluids such as polymer solutions and surfactant solutions, coming from their complex internal degree of freedom (e.g., entanglement effects in polyers) and (2) that near-glass transition. We hope that more examples of viscoelastic phase separation will be found in the family of complex fluids in the near future. 

A numerical study of viscoelastic phase separation in polymer solutions... 

Abstract A numerical model is constructed for the viscoelastic phase separation in polymer solutions based upon the two-fluid model using the method of the smoothed-particle hydrodynamics. Computer simulations are carried out with this model in two dimensions and efiects of the stress relaxation time on morphology of domains are examined. It is observed that the more... 

Key words Viscoelastic phase separation - dynamical asymmetry - two-fluid model - smoothed-particle hydrodynamics... 

Recently, a new type of phase separation called viscoelastic phase separation was observed in polymer solutions or dynamically asymmetric fluid mixtures [1-3]. It is an interesting feature of this phenomenon that network-like domains of more viscous phase emerge in a transient regime. It has little been understood what ingredient of physics is crucial to this phenomenon. Various numerical approaches have been made for the phase separation phenomena in binary fluid systems in the last decade [4-6]. Most of these studies have been concerned with classical fluids and have not involved viscoelasticity. A new numerical model was recently proposed by the author [7] based upon the two-fluid model [8,9] using the method of smoothed-particle hydrodynamics (SPH) [10,11]. In this model the Lagrangian picture for fluid is adopted and the viscoelastic effect can easily be incorporated. In this paper we carry out a computer simulation for the viscoelastic phase separation in polymer solutions with this model. 

In a system with a phase inversion structure, the complex viscosity of a blend system can be described by the Einstein equation (Eq. (4.11)). During viscoelastic phase separation, in which the interfadal tension plays a minor effect, the change in curing conversion is quite low and the viscosity difference between thermoplas-tics-rich matrix and dispersed thermoset-rich (low conversion and molecular weight) is very large and increases with the phase-separation process. When the viscosity of the dispersed thermoset-rich phase was neglected, the viscosity of the blend can be simplified as that of the thermoplastic-rich phase. 

Tanaka, H. (2009) Formation of network and cellular structures by viscoelastic phase separation. Adv. Mater., 21 (18), 1872-1880. 

The viscoelastic behavior of polymer solutions leads to many unusual flow phenomena, such as viscoelastic phase separation [227]. There is also a second level of complexity in soft matter systems, in which a colloidal component is dispersed in a solvent, which is itself a complex fluid. Examples are spherical or rod-like colloids dispersed in polymer solutions. Shear flow can induce particle aggregation and alignment in these systems [228]. 

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