In-phase and out-of-phase break-up of two immersed liquid threads under influence of surface tension

Gunawan, Agus Yodi; Molenaar, Jaap; Ven, van de Aaf Fons

doi:10.1016/s0997-7546(02)01187-1

Cited by 9 publications

(11 citation statements)

References 16 publications

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“…Fluids 24, 012102 (2012) Similar results as those obtained by Gunawan et al 22 are found: for small separations, the inphase configuration has the largest growth rate, and for large separations, and the out-of-phase behavior. The case for R/W ¼ 0.1 can be considered the unconfined situation.…”

Section: -15supporting

confidence: 71%

“…The case for R/W ¼ 0.1 can be considered the unconfined situation. For this, Gunawan et al 22 found a critical thread distance of 3.14, which they suspected to be p exactly. The current results show a critical separation just below 3.…”

Section: -15mentioning

confidence: 94%

“…Depending on the distance between the threads, threads can either break up in-phase or out-ofphase; threads that are close together break up in-phase, and larger separations lead to out-ofphase breakup, where the critical distance is a function of the viscosity ratio. Analysis by Knops et al 21 and Gunawan et al 22 showed the critical distance to be about 3 thread radii for a viscosity ratio of unity, and with increasing the viscosity ratio, the critical separation distance increases. Hagedorn et al…”

Section: Introductionmentioning

confidence: 98%

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Stability and breakup of confined threads

2012

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A boundary-integral method for periodic arrays of drops, threads or sheets between parallel walls is presented. The Green's functions take the form of a far-field HeleShaw description, which is used to generate periodic Green's functions for the parallel-wall configuration. The method is applied to study the effect of confinement on the breakup of threads. A comparison is made with classical Tomotika's theory and growth rates parallel and perpendicular to the walls are determined as a function of confinement ratio. Contrary to existing belief, we find that confined threads are not stable, but that the time for breakup increases with confinement and viscosity ratio, at least for threads whose diameter is smaller than the wallspacing. We also show the in-phase and out-of-phase breakup for an array of threads, as well as the stabilizing effect of shear flow.

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Section: -15supporting

confidence: 71%

Section: -15mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 98%

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Stability and breakup of confined threads

2012

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“…Numerically, we show that the stability analysis in the Stokes regime can be reduced to a generalized eigenproblem whose solutions are the growth modes, which is easily tractable even for large numbers of layers. Like several previous authors (Tomotika 1935;Stone & Brenner 1996;Gunawan et al 2002Gunawan et al , 2004, we begin by considering the Stokes (low-Reynolds) regime, which is consistent with the high viscosities found in drawn-fibre devices Deng et al 2008). In Appendix C, we generalize the analysis to the full incompressible Navier-Stokes problem, which turns out to be a relatively minor modification once the Stokes problem is understood, although it has the complication of yielding an unavoidably nonlinear eigenproblem for the growth modes.…”

Section: Introductionmentioning

confidence: 52%

Linear stability analysis of capillary instabilities for concentric cylindrical shells

et al. 2011

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Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier-Stokes problem. Generalizing previous work by Tomotika (N = 2), Stone & Brenner (N = 3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateaustyle geometrical arguments that only axisymmetric instabilities need be considered. We show that the N = 3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N = 2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional Stokes-flow simulations. Many N > 3 cases remain to be explored, and as a first step we discuss two illustrative N → ∞ cases, an alternating-layer structure and a geometry with a continuously varying viscosity.

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“…In Gunawan et al [16,17], we studied the stability of liquid threads immersed in a fluid in an unconfined region and driven by surface tension. It was shown that the instability of the threads is determined by the wave number k of the perturbations, the viscosity ratio µ of the two fluids and the distance b between the threads.…”

Section: Introductionmentioning

confidence: 99%