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Differential analysis of capillary breakup rheometry for Newtonian liquids

  • Louise L. McCarroll (a1), Michael J. Solomon (a2) and William W. Schultz (a1) (a3)

Abstract

We present a Newtonian, one-dimensional, differential analysis for capillary breakup rheometry (CBR) to determine the surface tension to viscosity ratio $\unicode[STIX]{x1D6FC}$ . Our local differential analysis does not require specific assumptions for the axial force to preclude its measurement. Our analysis indicates that measuring gradients in filament curvature is necessary to accurately determine $\unicode[STIX]{x1D6FC}$ when axial force is not measured. CBR experiments were performed on five silicone oils ( $0.35~\text{Pa}~\text{s}<\unicode[STIX]{x1D707}<10~\text{ Pa}~\text{s}$ ), three sample volumes, and three strains to evaluate the operating range of the differential analysis and compare its performance to that of a standard integral method from literature. We investigate the role of filament asymmetry, caused mainly by gravity, on the performance of the differential method for the range of conditions studied. Experimental and analytical details for resolving gradients of curvature are also given.

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Corresponding author

Email address for correspondence: schultz@umich.edu

References

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Anna, S. L. & Mckinley, G. H. 2001 Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol. 45 (1), 115138.
Bazilevsky, A. V., Entov, V. M. & Rozhkov, A. N. 1990 Liquid filament microrheometer and some of its applications. In Third European Rheology Conference and Golden Jubilee Meeting of the British Society of Rheology, pp. 4143. Springer.
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., Mckinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6 (8), 625631.
Brenner, M. P., Lister, J. R. & Stone, H. A. 1996 Pinching threads, singularities and the number 0.0304.... Phys. Fluids 8 (11), 28272836.
Canny, J. 1986 A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (6), 679698.
Eggers, J. 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71 (21), 34583460.
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69 (3), 865930.
Kolte, M. I. & Szabo, P. 1999 Capillary thinning of polymeric filaments. J. Rheol. 43 (3), 609625.
Liang, R. & Mackley, M. 1994 Rheological characterization of the time and strain dependence for polyisobutylene solutions. J. Non-Newton. Fluid Mech. 52 (3), 387405.
Matta, J. & Tytus, R. 1990 Liquid stretching using a falling cylinder. J. Non-Newton. Fluid Mech. 35 (2–3), 215229.
Mckinley, G. H. & Tripathi, A. 2000 How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44 (3), 653670.
Padday, J. F., Pitt, A. R. & Pashley, R. M. 1975 Menisci at a free liquid surface: surface tension from the maximum pull on a rod. J. Chem. Soc. Faraday Trans. 1 71, 19191931.
Papageorgiou, D. T. 1995 On the breakup of viscous liquid threads. Phys. Fluids 7 (7), 15291544.
Renardy, M. 1994 Some comments on the surface-tension driven break-up (or the lack of it) of viscoelastic jets. J. Non-Newton. Fluid Mech. 51 (1), 97107.
Schultz, W. W. & Davis, S. 1982 One-dimensional liquid fibers. J. Rheol. 26 (4), 331345.
Spiegelberg, S. H., Ables, D. C. & Mckinley, G. H. 1996 The role of end-effects on measurements of extensional viscosity in filament stretching rheometers. J. Non-Newton. Fluid Mech. 64 (2‐3), 229267.
Tirtaatmadja, V. & Sridhar, T. 1993 A filament stretching device for measurement of extensional viscosity. J. Rheol. 37 (6), 10811102.
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Differential analysis of capillary breakup rheometry for Newtonian liquids

  • Louise L. McCarroll (a1), Michael J. Solomon (a2) and William W. Schultz (a1) (a3)

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