2012
DOI: 10.1017/jfm.2012.182
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Spatial modes of capillary jets, with application to surface stimulation

Abstract: AbstractSurface stimulation of any physical origin (electrohydrodynamic, thermocapillary, etc.) has the goal of generating localized perturbations on the free surface or the velocity field of a capillary jet. Among these perturbations, only the axisymmetric ones are determinant for the jet breakup. Often, the stimulation is weak enough for a linear model to be applicable. Then, the stimulation can be described by means of the Green functions for stresses, both normal and tangen… Show more

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Cited by 12 publications
(23 citation statements)
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“…A sketch of the 3D spatial modes in the complex k plane similar to that presented in Ref. [23] can be found in Fig. 1 for the sake of future reference.…”
Section: Capillary Advective Capillary Inertial Hydrodynamicmentioning
confidence: 90%
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“…A sketch of the 3D spatial modes in the complex k plane similar to that presented in Ref. [23] can be found in Fig. 1 for the sake of future reference.…”
Section: Capillary Advective Capillary Inertial Hydrodynamicmentioning
confidence: 90%
“…is the observer's frame of reference, which is solidary to the jet in the former case and to the laboratory in the latter case. Thus, the spatial analysis incorporates advection and leads to (i) natural modes in Doppler-type correspondence with those of the temporal analysis (capillary, hydrodynamic), and (ii) new modes (inertial, advective capillary) leading to nontrivial phenomena, such as the absolute instability responsible for the dripping regime [22,23]. The latter reference definitely clarified previous misconceptions about some of the spatial modes just appealing to the region (upstream or downstream) where each mode is living.…”
Section: Capillary Advective Capillary Inertial Hydrodynamicmentioning
confidence: 99%
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“…To characterize the transition from jetting to dripping from a purely theoretical point of view, Leib & Goldstein (1986) analyzed the growth and propagation of capillary perturbations on a purely cylindrical jet. These authors found that, for a given liquid and nozzle exit diameter, there exists a critical flow rate below which the spatial analysis (Keller et al 1972;Guerrero et al 2012) is not well posed since the flow is absolutely unstable (Landau 1946;Briggs 1964;Huerre & Monkewitz 1985) i.e., the perturbations grow in time without propagating and the jet formation process is thus inhibited. Nevertheless, the theoretically determined boundary separating the region where the jet is absolutely unstable from that in which it is convectively unstable, is only in order of magnitude agreement with the experimentally determined critical conditions for which the jetting to dripping transition takes place.…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, there are numerous numerical and experimental examples of initial non-exponential transients that show that a single mode is unable to couple the boundary conditions at the orifice with the subsequent evolution of the liquid jet. Recently, a rigorous modal analysis has revealed that, among the infinite modes that arise from the 3D dispersion relation, only two (but not less) are required to adequately describe the initial conditions in the temporal analysis [14], or the boundary conditions at the orifice in the spatial analysis [16,26]. In brief, the retained modes are those having non-negligible shape deformation and net axial flow, or, in mathematical terms, those surviving to a radial integration over any jet section.…”
Section: Introductionmentioning
confidence: 99%