Elongational properties of liquids in contraction flow

What is it about?

Flows through contraction geometries (contraction flows) are found in many fields involving fluids, including physics, chemistry, biology, medicine, engineering, and industry, but they are poorly understood. The reason for this is that a contraction flow has two inseparable aspects: shear flow and elongational flow. Shear flow is easy to achieve in practice, and there are many methods for obtaining shear properties. By contrast, elongational flow is difficult to realize experimentally because it is usually associated with shear flow, and only a few methods for realizing elongational flow have been explored for a limited set of materials. However, if attention is restricted to the flow on the center line of a contraction geometry, then the shear flow vanishes because of the symmetry of the velocity profile in the plane containing the center line, leaving only the elongational component. Standing on this idea, we focused the flow on the center line of contraction geometry and clarified elongational properties of liquids.

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Why is it important?

We derived two types of velocity-equation; exponential contraction flow (ECF) type and linear contraction flow (LCF) type on the center line of the contraction geometry from only the continuity equation, not using any constitutive equation which describes the mechanical flow characteristic of liquids. This means that the derived equations hold irrespective of the kind of fluids, and in fact the equation of ECF- type agreed with the experimental results so far obtained for water, polymer solutions and polymer melts. On the other hand, the equation of LCF- type agreed with the data for limited dilute polymer solutions, which suggested that the equation of LCF-type is applicable to the fluid flow which generates association among stretched polymers. We showed that the ratio of elongational viscosity to shear viscosity is very high 103 -104 for dilute of PEO and PAA aqueous solutions, but the ratio is close to the prediction of Newtonian fluids even for non-dilute solutions of non-Newtonian flow property. We proposed a model of contraction flow and showed that ECF-type flow provides Newtonian fluid property, that is, the elongational stress is proportional to the elongational rate, which was confirmed with the experimental data so far reported for non-Newtonian fluids. We found that the exponent in exponential velocity of ECF-type is expressed as a linear relationship against 〖log〗_10RV, where RV is the relaxation velocity number which was newly proposed in the present paper. This means that contraction flow can be used to measure the elongational property of fluids. Furthermore, both equations of ECF and LCF-type flows are valid for the flow in melt spinning.

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