Normal stress emulsions

Concentrated emulsions can exhibit viscoelasticity, as can gelled foams and some suspensions. Compared with the previous equations presented, additional coefficients (including primary and secondary normal stress coefficients) are needed to characterize the rheology of viscoelastic fluids [376,382]. 

For a viscosity ratio M of order unity or less, r is the relaxation time of the droplet shape and of the resulting viscoelastic stress in the dispersion. Thus, for rjs I cP, F 10 dyn/cm, a (xm, we obtain t 10 sec, and the stress in the emulsion relaxes almost instantly after cessation of flow. However, when the fluid medium is more viscous and the droplets are bigger, say, rjg 100 P, a 10 jxm, with the same F, we obtain T 0.01 sec. Although this latter value of r corresponds to rather fast relaxation, it can produce appreciable normal stress differences at high shear rates thus (Choi and Schowalter 1975)... 

Han and King (22) had shown that concentrated emulsions can exhibit viscoelastic behavior even though the dispersed and the continuous phases are both Newtonian. For a given shear stress, the primary normal stress... 

Starting with cell model of creeping flow, Choi and Schowalter [113] derived a constitutive equation for an emulsion of deformable Newtonian drops in a Newtonian matrix. The authors characterized the interphase with an ill-defined interfacial tension coefficient, Vu, affecting the capillarity number, k = (Judfvu. The analysis indicated that depending on magnitude of /cy the emulsion may be elastic, characterized by two relaxation times. For the steady-state shearing, the authors expressed the relative viscosity of emulsions and the first normal stress difference as ... 

In the next paper, Vinckier et aL [279] fitted the viscosity and the first normal stress difference of the model PIB/PDMS emulsions to Eq. (2.18). A reasonable description of the rheological behavior was obtained for the diluted and semi-diluted concentrations with the viscosity ratios A = 1.5—4. The experiments were carefiilly conducted within the range of the capillarity numbers (k < Kcr) and ... 

Emulsion elasticity expressed by Eq. (2.18) as the first normal stress difference, Ni, originates from the deformability of the interphase thus it is present even in Newtonian liquid blends [113]. The relation predicts that Ni increases with vdthout bound. Since drops do not deform at high viscosity ratio, A > 4, as well as when the interfadal tension coefficient is high, the elasticity should decrease as the dispersed liquid viscosity or the interfacial tension coefficient became large. Similarly, G in Eq. (2.23) and its homologues depends on the R/V12 ratio [126], but here the prediction for both limiting values of V12 is the same. As in the case of viscosity, these two direct measures of elasticity are expected to differ due to different strains imposed in the steady-state and dynamic flow fields. 

Malkin, A.Ya. and Masalova, 1. (2007) Shear and normal stresses in flow of highly concentrated emulsions. J. Non-Newtonian Fluid Medt., 147 (1-2), 65-68. 

Another factor that may affect the rheology of emulsions is the viscosity of the disperse droplets. This is particularly the case when the viscosity of the droplets is comparable to or lower than that of the dispersions medium. This problem was considered by Taylor (17), who extended the Einstein hydrodynamic treatment for suspensions for the case of droplets in a liquid medium. Taylor (17) assumed that the emulsifier film around the droplets would not prevent the transmission of tangential and normal stresses form the continuous phase to the disperse phase and that there was no slippage at the o/w interface. These stresses produce fluid circulation within the droplets, which reduces the flow patterns around them. Taylor derived the following expression for 11 ... 

Particular examples of the first normal-stress difference Ni or its coefficient are shown in figures 12 - 29, where a comprehensive collection of examples is given for polymer solutions and melts, as well as an emulsion. These are compared with either the equivalent shear stress or the viscosity. All the different possible combinations of shear and normal-stress difference, and viscosity and normal-stress coefficient are displayed to show the way that results are presented in the rheological literature. The figures are set out to illustrate overall behaviour, with especial emphasis on low shear-rate and mid-range (i.e. power-law) behaviour. 

F ure 23 The viscosity (dotted line) and first normal-stress difference coefficient (1st NSD, solid line) as a function of shear rate at txxxn temperature for an emulsion of low-molecular weight polybutene in glyerol, at two levels of phase volume, [14]. 

Unsaturated polyesters for laminates Debye, light scattering of polymer solutions Flory, viscosity of polymer solutions Harkins, theory of emulsion polymerization Weissenberg, normal stresses in polymer flow Silicones... 

Some experimental facts should be stressed anyway for the present purpose. The delayed inversion of a normal emulsion along a change in composition toward a higher... 

Adhesive joints may be subjected to a variety of adverse service conditions, including elevated temperature, organic solvents, water and stress (see Durability fundamentals. Durability creep rupture). Solvent-based, emulsion and melt adhesives are normally based on thermoplastics with fairly low softening temperatures. If a loaded joint is subjected to elevated temperature, failure may occur because of Creep unless the adhesive is cross-linked. Likewise, attack by organic solvents can be minimized by cross-linking. Solvent-based, emulsion and hot melt systems are available that cross-Unk after the initial bonding has been carried out. These systems provide improved in-service performance. 

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