Abstract
The effect of accumulation of reversible strains on the pressure head is analyzed theoretically for elastic and viscoelastic liquid flow from convergent channels. It is shown that, depending on the rheological features of the liquids, the pressure head can both increase and decrease as compared with the pressure determined by the Bernoulli formula. In particular, a situation in which a liquid flows out without any pressure head applied (paradox of “self-outflow”) is possible within the framework of the model. Transition to different viscoelastic liquid flow regimes as a function of the constitutive parameters is considered with reference to a channel with a sharp bottleneck (abrupt decrease in the cross-section).
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REFERENCES
Chang Dae Han, Rheology in Polymer Processing, Academic Press, New York (1976).
A. S. Lodge, Elastic Liquids, Academic Press, London-New York (1964).
R. G. Larson, "Instabilities of viscoelastic flows," Rheological Acta, 31, No. 3, 213 (1992).
A.V. Bazilevskii, V. M. Entov, and A.N. Rozhkov, "Elastic stresses in capillary jets of dilute polymer solutions," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 3 (1985).
R. P. Mun, J.A. Byars, and D.V. Boger, "The effect of polymer concentration and molecular weight on the breakup of laminar capillary jets," J. Non-Newtonian Fluid Mech., 74, 285 (1998).
Y. Christanti and L.M. Walker, "Surface tension driven jet break up of strain-hardening polymer solutions," J. Non-Newtonian Fluid Mech., 100, 9 (2001).
J.D. Mayer, A.V. Bazilevsky, and A.N. Rozhkov, "Effects of polymeric additives on thermal ink jets," in: Proc. IS&T's NIP13: Intern. Conference on Digital Printing Technologies, IS&T, Seattle, USA (1997), P. 675.
J.D. Mayer, A.V. Bazilevsky, and A.N. Rozhkov, "Effects of polymeric additives on thermal ink jets," in: E. Hanson (Ed.), Recent Progress in Ink Jet Technologies II, Series Editor: R. Eschbach, IS&T, (1999), P. 450.
O. L. Kulikov and K. Hornung, "A simple geometrical solution to the surface fracturing problem in extrusion processes," J. Non-Newtonian Fluid Mech., 98, 107 (2001).
Y. Tomita and T. Takahashi, "An anomalous phenomenon occurring in the flow of viscoelastic fluids out of ducts," Rheological Acta, 27, No. 5, 523 (1988).
T. Takahashi and Y. Tomita, "A study on an anomalous phenomenon occurring in the issuing of viscoelastic fluids from ducts (critical point of the anomalous phenomenon)," JSME Intern. J. Ser. II, 32, 348 (1989).
M. M. Denn, "Extrusion instabilities and wall slip," Ann. Rev. Fluid Mech., 33, 265 (2001).
E. J. Hinch, "Mechanical model of dilute polymer solutions in strong flows," Phys. Fluids, 20, No. 10, Pt. 2, S22 (1977).
P. G. De Gennes, "Coil-stretch transition of dilute flexible polymers under ultra high velocity gradients," J. Chem. Phys., 60, 5030 (1974).
A.V. Bazilevskii, S. I. Voronkov, V.M. Entov, and A.N. Rozhkov, "Orientation effects in breakup of jet and filaments of dilute polymer solutions," Dokl. Akad. Nauk SSSR, 257, 336 (1981).
A.N. Rozhkov, "Intensive flows of polymer solutions," Thesis for Degree of Candidate of Physico-Mathematical Sciences [in Russian], Moscow (1984).
V. M. Entov, Kh. S. Kestenboim, and A.N. Rozhkov, "On the flow of viscoelastic liquids from convergent channels," Dokl. Akad. Nauk SSSR, 282, 879 (1985).
V. M. Entov and A.N. Rozhkov, "Elastic effects in polymer solution flows through variable-cross-section channels and porous media," Inzh.-Fiz. J., 49, No. 3, 390 (1985).
V. M. Entov, V. I. Kordonskii, I.V. Prokhorov, A.N. Rozhkov, A. I. Toropov, Z. P. Shul'man, and A. L. Yarin, "Intensive extension of polymer solutions," Dokl. Akad. Nauk SSSR, 301, 867 (1988).
V. M. Entov, V. I. Kordonskii, I.V. Prokhorov, A.N. Rozhkov, A. I. Toropov, Z. P. Shul'man, and A. L. Yarin, "Intensive extension of moderate-concentration polymer solutions," Vysokomoleculyarn. Soedineniya. Ser. A., 30, 2486 (1988).
W. K. Lee and H. H. George, "Flow visualization of fiber suspensions," Polymer Eng. Sci., 18, 146 (1978).
A.Yu. Ishlinskii, "Rolling and drawing at high deformation rates," Prikl. Mat. Mekh., 7, 226 (1943).
A.N. Rozhkov, "Dynamics of filaments of polymer solutions," Inzh.-Fiz. J., 45, No. 1, 72 (1983).
V. M. Entov, V. I. Kordonskii, V.A. Kuz'min, Z. P. Shul'man, and A. L. Yarin, "Investigation of breakup of jets of rheologically complex liquids," Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 90 (1980).
V. M. Entov, S. M. Makhkamov, and K.V. Mukuk, "On one effect of normal stresses," Inzh.-Fiz. J., 34, No. 3, 514 (1978).
M. P. Brenner and D. Gueyffier, "On the bursting of viscous films," Phys. Fluids, 11, No. 3, 737 (1999).
V. M. Entov and Kh. S. Kestenboim, "On the mechanics of fiber drawing," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 26 (1987).
V. M. Entov, Kh. S. Kestenboim, S.V. Pokrovskii, and G.A. Shugai, "One-dimensional dynamics of jet flows of elastic fluids," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 3 (1997).
S. L. Bazhenov, I.A. Dukhovskii, P. I. Kovalev, and A.N. Rozhkov, "Breakup of an SVM aramide fiber during high-velocity transverse impact," Vysokomoleculyarn. Soedineniya. Ser. A., 43, 73 (2001).
G. Astarita and G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, etc. (1974).
A. L. Yarin, "Theoretical analysis of the process of intensive uniaxial extension of concentrated polymeric systems at a constant velocity of the gripping device," Vysokomoleculyarn. Soedineniya. Ser. A., 30, 2492 (1988).
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Rozhkov, A.N. Paradox of “Self-Outflow” of a Free Liquid Jet. Fluid Dynamics 38, 507–517 (2003). https://doi.org/10.1023/A:1026362309383
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DOI: https://doi.org/10.1023/A:1026362309383