TY - JOUR
T1 - Minimal formulation of the linear spatial analysis of capillary jets
T2 - Validity of the two-mode approach
AU - González, H.
AU - Vazquez, P. A.
AU - García, F. J.
AU - Guerrero, J.
N1 - Funding Information:
This work was supported by two Spanish public organizations: by the Ministerio de Economía, Industria y Competitividad, under Contract No. FIS2014-25161 and by the Junta de Andalucía under Contract No. P11-FQM-7919.
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/4/18
Y1 - 2018/4/18
N2 - A rigorous and complete formulation of the linear evolution of harmonically stimulated capillary jets should include infinitely many spatial modes to account for arbitrary exit conditions [J. Guerrero, J. Fluid Mech. 702, 354 (2012)JFLSA70022-112010.1017/jfm.2012.182]. However, it is not rare to find works in which only the downstream capillary dominant mode, the sole unstable one, is retained, with amplitude determined by the jet deformation at the exit. This procedure constitutes an oversimplification, unable to handle a flow rate perturbation without jet deformation at the exit (the most usual conditions). In spite of its decaying behavior, the other capillary mode (subdominant) must be included in what can be called a "minimal linear formulation." Deformation and mean axial velocity amplitudes at the jet exit are the two relevant parameters to simultaneously find the amplitudes of both capillary modes. Only once these amplitudes are found, the calculation of the breakup length may be eventually simplified by disregarding the subdominant mode. Simple recipes are provided for predicting the breakup length, which are checked against our own numerical simulations. The agreement is better than in previous attempts in the literature. Besides, the limits of validity of the linear formulation are explored in terms of the exit velocity amplitude, the wave number, the Weber number, and the Ohnesorge number. Including the subdominant mode extends the range of amplitudes for which the linear model gives accurate predictions, the criterion for keeping this mode being that the breakup time must be shorter than a given formula. It has been generally assumed that the shortest intact length happens for the stimulation frequency with the highest growth rate. However, we show that this correlation is not strict because the amplitude of the dominant mode has a role in the breakup process and it depends on the stimulation frequency.
AB - A rigorous and complete formulation of the linear evolution of harmonically stimulated capillary jets should include infinitely many spatial modes to account for arbitrary exit conditions [J. Guerrero, J. Fluid Mech. 702, 354 (2012)JFLSA70022-112010.1017/jfm.2012.182]. However, it is not rare to find works in which only the downstream capillary dominant mode, the sole unstable one, is retained, with amplitude determined by the jet deformation at the exit. This procedure constitutes an oversimplification, unable to handle a flow rate perturbation without jet deformation at the exit (the most usual conditions). In spite of its decaying behavior, the other capillary mode (subdominant) must be included in what can be called a "minimal linear formulation." Deformation and mean axial velocity amplitudes at the jet exit are the two relevant parameters to simultaneously find the amplitudes of both capillary modes. Only once these amplitudes are found, the calculation of the breakup length may be eventually simplified by disregarding the subdominant mode. Simple recipes are provided for predicting the breakup length, which are checked against our own numerical simulations. The agreement is better than in previous attempts in the literature. Besides, the limits of validity of the linear formulation are explored in terms of the exit velocity amplitude, the wave number, the Weber number, and the Ohnesorge number. Including the subdominant mode extends the range of amplitudes for which the linear model gives accurate predictions, the criterion for keeping this mode being that the breakup time must be shorter than a given formula. It has been generally assumed that the shortest intact length happens for the stimulation frequency with the highest growth rate. However, we show that this correlation is not strict because the amplitude of the dominant mode has a role in the breakup process and it depends on the stimulation frequency.
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U2 - 10.1103/PhysRevFluids.3.044802
DO - 10.1103/PhysRevFluids.3.044802
M3 - Article
AN - SCOPUS:85047070035
SN - 2469-990X
VL - 3
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 4
M1 - 044802
ER -