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Towards a scaling theory of drag reduction

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  • De Gennes, P.G.

Abstract

Flexible polymers in dilute solution enhance the viscosity in slow flows. But in strong, rapidly varying, shear fields, they behave elastically. A turbulent cascade (from large to small scales) should thus be deeply modified when the elastic stresses become comparable to the Reynold's stress. A (tentative) scaling picture for these effects has been proposed by M. Tabor and the present author1): it involves one unknown exponent n relating polymer deformation (λ) and spatial scales (r) in the cascade. We now show that, depending on the control parameters (turbulent power; polymer concentration and molecular weight) the cascade may proceed according to two “scenarios”. In the first scenario1) the smallest Kolmogorov eddy occurs when the chains are only partly strectched. In the second scenario, the smallest eddies display nearly full chain extension: polymer degradation is expected to be much more serious in the latter case.

Suggested Citation

  • De Gennes, P.G., 1986. "Towards a scaling theory of drag reduction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 9-25.
    • Handle: RePEc:eee:phsmap:v:140:y:1986:i:1:p:9-25
    DOI: 10.1016/0378-4371(86)90200-1
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