The Influence of Gravity on The Temporal Instability of Viscoelastic Liquid Curved Jets
A liquid curved jet has many applications in different industrial and engineering processes, such as the prilling process for generating small spherical pellets (fertilizer or magnesium). The liquids used are usually molten and contain small quantities of polymers and therefore can be modelled as non-Newtonian liquids. In this paper, we model the viscoelastic liquid jet by using the Oldroyd- B model. An asymptotic analysis has been used to simplify the governing equations. Furthermore, the trajectory and a linear temporal stability in the presence of gravity and rotation have been determined.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087326Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1562
 Ardekani, A. M., Sharma, V., and Mckinley, G. H., 2010, Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J. Fluid Mech. 665, 46-56
 Ashgriz, N. and Mashayek, F., 1995. Temporal analysis of capillary jet breakup. J. Fluid Mech. 291, 163-190.
 Cheong, B. S., Howes, T., 2004, Capillary jet instability under influence of gravity, Chemmical Engineering Science, 59, 2145-2157
 Clasen, C., Eggers, J., Fonlelos, M. A., Li, j., and Mckinley, G. H., 2006, The beads-on-string structure of viscoelastic threads. J. Fluid Mech., 556, 283-308
 Cooper-White, J. J., Fagan, J. E., Tirtaatmadja, V., Lastert, D. R., and Boger, D. V., 2002, Drop formation dynamics of constant low-viscosity, elastic fluids, J. Non-Newtonian fluid Mech., 106,29-59
 Davidson, M. R., Harvie, J. E., and Cooper-White, J. J., 2006, Simulation of pendant drop formation of a viscoelastic liquid, Korea-Australia Rheology Journal, 18, (2), 41-49
 Decent, S. P., King, A. C. and Wallwork, I. M., 2002, Free jets spun from a prilling tower, Journal of Engineering Mathematics, 42, 265-282
 Decent, S. P., King, A. C., Simmons, M. H., P˘ar˘au, E. I., Wong, D. C. Y., Wallwork, I. M., Gurney, C., and Uddin, J., 2007, The trajectory and stability of a spiralling liquid jet: Part II. Viscous Theory, Appl. Math. Modelling, 33, (12), 4283-4302
 Eggers, J., 1997. Nonlinear dynamics and breakup of free surface flows. Rev. Mod. Physis, 69, (3), 865-929.
 Goldin, M., Yerushalmi, J., Pfeffer, R., and Shinner, R., 1969, Breakup of a viscoelastic fluid. J. Fluid Mech. 38, 689-711.
 Grant, R. P., and Middleman, S., 1965, Newtonian jet stability. A. I. Ch. E. Journal, 2, 669.
 Larson, R. G., 1992, Instabilities in viscoelastic flows, Rheol., Acta,31
 Liu, Z., and Liu, Z., 2008, Instability of a viscoelastic liquid jet with axisymmetric and asymmetric disturbance, International Journal of Multiphase Flow, 34, 42-60
 Mageda, J. J., and Larson, R. G., 1988, Atransition occurring in ideal elastic liquids during shear flow, J. Non-Newtonian Fluid Mech., 30,1-19
 Middleman, S., 1965, Stability of a viscoelastic jet, Chem. Eng. Sci. 20, 1037-1040.
 Morrison, N. F., Harlen, O. G. 2010, Viscoelasticity in inkjet printing, Rheol., Acta, 49, 619-632
 Papageorgiou, D. T., 1995, On the breakup of viscous liquid threads, Phys. Fluids, 7, 1529 Nonlinear travelling waves on a spiralling liquid jet, Wave Motion, 43, 599-613.
 P˘ar˘au, E. I., Decent, S. P., Simmons, M. J. H., Wong, D. C. Y. and King, A. C., 2007, Nonlinear viscous liquid jets from a rotating orifice, J. Of Eng. Maths., 57, 159-179
 Rayleigh, W. S., 1878, On the instability of jets, Proc. Lond. Math. Soc 10,4.
 Renardy, M., 1995, A numerical study of the asymptotic evolution and breakup of Newtonian and viscoelastic jets, J. Non-Newtonian Fluid Mech., 59, 267-282
 Renardy, M., 2008, Stability of viscoelastic shear flows in the limit of high Weissenberg and Reynolds numbers, J. Non-Newtonian Fluid Mech., 155, 124-129
 Uddin, J., 2007. An investigation into methods to control breakup and droplet formation in single and compound liquid jets. PhD thesis, University of Birmingham.
 Uddin, J., and Decent, S. P., 2010, Instability of non-Newtonian liquid jets curved by gravity. Mathematics in industry, 15, 597-602.
 Wallwork, I. M., 2002a, The trajectory and stability of a spiralling liquid jet, Ph.D. Thesis, University of Birmingham, Birmingham.
 Wallwork, I. M., Decent, S.P., King, A. C. and Schulkes, R. M. S., 2002b, The trajectory and stability of a spiralling liquid jet. Part 1, Inviscid Theory, J. Fluid Mech., 459,43-65. Math. Mech, 11, 136-154.
 Weber, C., 1931, Zum Zerfall eines Flussigkeitsstrahles. Z. Angew.