<p>Although the second normal stress difference <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({N}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> is connected to several critical flow phenomena, it has received relatively little attention in literature, mainly due to the difficulty of accurately measuring this material function. Even for highly viscous polymeric solutions or melts, a trustworthy <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({N}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> measurement is still a challenge, and only a few rheologists tackled this problem for lower viscous materials, mainly due to the sensitivity limits of current experimental setups. In this paper, we re-evaluate a technique that received less attention due to the relatively large sample volumes needed: the normal stress-induced deformation of the free surface of a fluid flowing through a tilted trough. We introduce a new design that derives <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({N}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> from the deformation of an interface between a viscoelastic and a Newtonian fluid flowing through a closed pipe.</p>

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Second normal stress difference measurement via interfacial deformation of stratified flow into a closed-channel

  • Luca Passaro,
  • Eugene Pashkovski,
  • Christian Clasen

摘要

Although the second normal stress difference \({N}_{2}\) N 2 is connected to several critical flow phenomena, it has received relatively little attention in literature, mainly due to the difficulty of accurately measuring this material function. Even for highly viscous polymeric solutions or melts, a trustworthy \({N}_{2}\) N 2 measurement is still a challenge, and only a few rheologists tackled this problem for lower viscous materials, mainly due to the sensitivity limits of current experimental setups. In this paper, we re-evaluate a technique that received less attention due to the relatively large sample volumes needed: the normal stress-induced deformation of the free surface of a fluid flowing through a tilted trough. We introduce a new design that derives \({N}_{2}\) N 2 from the deformation of an interface between a viscoelastic and a Newtonian fluid flowing through a closed pipe.