Extensional flow of polymer solutions

Extensional deformation of polymer solutions is applied technically in the so-called dry spinning of polymer fibres. The literature data in this field are not as numerous as in the field of shear viscosity, so that only a qualitative picture can be given here. 

For concentrated polymer solutions, the behaviour in extensional deformation shows a great correspondence to that of polymer melts. At low rates of deformation the extensional viscosity has the theoretical value of three times the shear viscosity. At higher rates of deformation, the experimental results show different types of behaviour. In some cases, the extensional viscosity decreases with increasing rate of extension in the same way as the shear viscosity decreases with increasing shear rate. In other cases, however, a slight increase of the extensional viscosity with increasing rate of extension was observed. 

By contrast, quite different results have been obtained with dilute polymer solutions. Here the extensional viscosity may be as much as thousand times the shear viscosity. Measurement of extensional viscosity of such mobile liquids is far more difficult than shear viscosity, or even impossible. According to Barnes et al. (General references, 1993) The most that one can hope for is to generate flow which is dominated by extension and then to address the problem of how best to interpret the data in terms of material functions that are Theologically meaningful . An example of the difficulties that arise with the measurement of extensional viscosity is shown In Fig. 16.21 for a Round Robin test 

21 Apparent or transient extensional viscosity of the round robin test fluid Ml as a function of Hencky strain, measured in many different devices (lames and Walters, 1993). The various instruments are spin line Binding et al. Ferguson and Hudson Ngyuen et al. horizontal spin line Oliver open siphon Binding et al. stagnation flow. Laun and Hingmann Schweitzer et al. contraction flow. Binding et al.  

Boger and Binnington converging flow James et al. falling pendant drop Jones et al. falling cylinder  

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W.H. Talbott and J.D. Goddard, Streaming birefringence in extensional flow of polymer solutions, Rheol. Acta, 18, 507 (1979). 

If we regard that the flow pattern produced by the disturbance represents a kind of extensional flow, it is possible to infer that the extensional viscosity of polymer solution acts on the GGrtler vortices. Thus by adding the polymer a large extensional viscosity acts on the GCrtler vortices and the stable size of vortices is increased for a given flow field. 

Muller AJ, Odell JA, Carrington S (April 1991) In Degradation of polymer solutions in extensional flow, Proceedings of the polymer physics a Conference to mark the retirement of A Keller, Bristol UK 3-5... 

James DF, Saringer JH (1980) Extensional flow of dilute polymer solutions Fluid Mech 97 655... 

James DF, McLean BD, Saringer JH (1987) Presheared extensional flow of dilute polymer solutions J Rheol 31 453... 

J. Plucinski, R.K. Gupta and S. Chakrabarti, Shear and Extensional Rheology of Mayonnaises, presented at the Second International Conference on Extensional and Shear Flow of Polymer Fluids from the Solution to the Melt, St. Andrews, Scotland, June 19-22, 1994. 

Polymer melts and solutions show pronounced non-Newtonian flow behavior. In rotational flows, polymer solutions typically show a shear-thinning behavior (2i, 22) where the apparent viscosity reduces as the shear rate is increased. In extensional, or stretching flows, however, polymer solutions often show a marked increase in viscosity as the shear rate is increased, termed dilatancy (23-26), Stretching flows are of considerable importance and generally occur in flows through orifices, filters, porous media, constrictions in pipes, and in any flow possessing turbulence or vorticity, in fact as a component of most real flow systems. 

Larson R G, Magda J J (1989). Coil-stretch transitions in mixed shear and extensional flows of dilute polymer solutions. Macromo. 22(7) 3004-3010. 

Odell JA, Muller AJ, Narh KA, KcUct A (1990) Degradation of polymer-solutions in extensional flows. Macromolecules 23 3092—3103... 

Knudsen KD, Cifre JGH, de la Torre JG (1997) Ixacture of flexible polymer chains in dilute solution under transient extensional flow. Colloid Polym Sci 275 1001—1009... 

Serveral authors [1 - 3] describe the non-Newtonian flow behaviour of dilute polymer solutions in porous media as an increase of extensional viscosity based on finitely extensible, nonlinear-elastic dumbbells (FENE-dumbbell — theory [4]). Conformity between theory and experiment is partially so good that the relationships found can be used for characterization of polymer solutions. A few significant examples are demonstrated in the following with the aid of selected polymer-solvent-temperature systems. 

Weinberger, C.B. and Goddard, J.D. (1974) Extensional flow behaviour of polymer solutions and particle suspensions in a spinning motion, Int.. Multiphase Flow, 1,465-86. 

N. V. Orr and T. Sridhar. Probing the dynamics of polymer solutions in extensional flow using step strain rate experiments. J. Non-Newtonian Fluid Mech., 82 (1999), 203-232. 

To reach steady state, the residence time of the fluid in a constant stretch rate needs to be sufficiently long. For some polymer melts, this has been attained however, for polymer solutions this has proved to be a real challenge. It was not until the results of a world wide round robin test using the same polymer solution, code named Ml, became available that the difficulties in attaining steady state in most extensional rheometers became clearer. The fluid Ml consisted of a 0.244% polyisobutylene in a mixed solvent consisting of 7% kerosene in polybutene. The viscosity varied over a couple of decades on a logarithmic scale depending on the instrument used. The data analysis showed the cause to be different residence times in the extensional flow field... 

C. A. Cathey and G. G. Fuller, The optical and mechanical response of flexible polymer solutions to extensional flow, J. Non-Newt. Fluid Mech., 34,63 (1990). 

P. N. Dunlap and L. G. Leal, Dilute polystyrene solutions in extensional flow birefringence and flow modification, J. Non-Newt. Fluid Mech., 23, 5 (1987). E. Geffroy and L. G. Leal, Flow birefringence studies of a concentrated polystyrene solution in a two-roll mill. 1. Steady flow and start-up of steady flow, J. Polym. Sci., Polym. Phys., 30,1329 (1992). 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

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