Publication de 12 numéros par an
ISSN Imprimer: 1044-5110
ISSN En ligne: 1936-2684
IF:
1.2
5-Year IF:
1.8
Immediacy Index:
0.3
Eigenfactor:
0.00095
JCI:
0.28
SJR:
0.341
SNIP:
0.536
CiteScore™::
1.9
H-Index:
57
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INITIAL CONDITIONS TO STUDY THE TEMPORAL BEHAVIOR OF A VISCOELASTIC LIQUID JET UNDER PERTURBATION
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RÉSUMÉ
We study the behavior of a viscoelastic liquid jet. To that end, we carry out a temporal stability analysis. The eigenvalue problem has already been solved and is reported in Cottier et al. (2019), but does not provide a complete description of the jet's behavior. In this paper, we propose two different sets of initial conditions to close the corresponding initial-value problem. These conditions are determined by formulating the different quantities that can be imposed over the base flow, and making a correspondence with the expression of these quantities found by solving the eigenvalue problem, evaluated at the initial time. Here the imposed quantities are considered to hold on the jet's surface position, on the axial flow velocity, and on the axial normal extra stress within the flow. After giving a general formulation of the three initial conditions, two different initial configurations are distinguished: the pure deformation and the pure impulse configuration. A linearization of the conditions leads us to the determination of the analytical expressions of the first-order flow quantities in function of control parameters determining the choice of the initial configuration. The reduction of the initial conditions to the Newtonian case is valid and does not induce any physical change at the initial time. An application of the initial conditions is made upon a given liquid jet and the visualization of the flow quantities allows a comparison between the pure deformation and the pure impulse configuration.
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Bhat, P.P., Appathurai, S., Harris, M.T., Pasquali, M., McKinley, G.H., and Basaran, O.A., Formation of Beads-on-a-String Structures during Break-Up of Viscoelastic Filaments, Nature Phys., vol. 6, no. 8, pp. 625-631,2010.
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Brenn, G., Analytical Solutions for Transport Processes: Fluid Mechanics, Heat and Mass Transfer, New York: Springer, pp. 14-15,2017.
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Cottier, L., Brenn, G., and Renoult, M.C., Weakly Nonlinear Instability of a Viscoelastic Liquid Jet, ILASSEurope 2019, 29th Conference on Liquid Atomization and Spray System, Paris, France, 2019.
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Garcia, F.G. and Gonzalez, H., Normal-Mode Linear Analysis and Initial Conditions of Capillary Jets, J. Fluid Mech, vol. 602, pp. 81-117,2008.
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Goldin, M., Yerushalmi, J., Durst, F., and Shinnar, R., Breakup of a Laminar Capillary Jet of a Viscoelastic Fluid, J. Fluid Mech, vol. 38, no. 4, pp. 689-711,1969.
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Oliveira, M.S. and McKinley, G.H., Iterated Stretching and Multiple Beads-on-a-String Phenomena in Dilute Solutions of Highly Extensible Flexible Polymers, Phys. Fluids, vol. 17, no. 7, p. 071704,2005.
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Rayleigh, L., On the Instability of Jets, Proc. Lond. Math. Soc., vol. 10, no. 1, pp. 4-13,1878.
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Rayleigh, L., On the Instability of a Cylinder of Viscous Liquid under Capillary Force, Phil. Mag, vol. 34, no. 27, pp. 145-154,1892.
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Renoult, M.-C., Brenn, G., Plohl, G., andMutabazi, I., Weakly Nonlinear Instability of a Newtonian Liquid Jet, J. Fluid Mech, vol. 856, pp. 169-201,2018.