A review of the stability of disconnected equilibrium capillary surfaces

Alexander, J. Iwan D.; Slobozhanin, Lev A.

doi:10.1007/bf02870947

Cited by 6 publications

(7 citation statements)

References 36 publications

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“…The smallest eigenvalue of the above problem (3.3) with (3.4) corresponds to the minimum value of the second variation of the potential energy of the system. Thus the equilibrium is stable if , and is unstable if (Alexander & Slobozhanin 2004).…”

Section: Stability Analysismentioning

confidence: 99%

Capillary surfaces in and around exotic cylinders with application to stability analysis

Zhang

Zhou

2019

J. Fluid Mech.

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Section: Stability Analysismentioning

confidence: 99%

Capillary surfaces in and around exotic cylinders with application to stability analysis

Zhang

Zhou

2019

J. Fluid Mech.

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“…Relation between the stability of a solitary drop to fixed-pressure perturbations and the stability of connected drops to fixed-volume perturbations Alexander & Slobozhanin (2004) reviewed methods suggested by Gillette & Dyson (1974), Orel (1974), Maddocks (1987) and Lowry & Steen (1995) to examine the stability of systems with multiple free surfaces. Orel (1974) must be given credit for first recognizing the importance of fixed-pressure stability of single surface systems to the stability of fixed liquid volumes with coupled free surfaces.…”

Section: 2mentioning

confidence: 99%

“…This means that collectively, two pendant drops may be more unstable than either of the two drops considered separately and with a constant volume constraint. This is the distinctive feature of systems with disconnected free surfaces (see, for example, Alexander & Slobozhanin 2004).…”

Section: Introductionmentioning

confidence: 99%

The stability of two connected drops suspended from the edges of circular holes

Slobozhanin

Alexander

2006

J. Fluid Mech.

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The stability of an equilibrium system of two drops suspended from circular holes in a horizontal plate is examined. The drop surfaces are the disconnected axisymmetric surfaces pinned to the edges of the holes. The holes lie in the same horizontal plane and the two drops are connected by a liquid layer that lies above the plate. The total liquid volume is constant. For identical pendant drops pinned to holes of equal radii, axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a solitary pendant drop. A bifurcation analysis shows that the loss of stability leads to a continuous transition from a critical system of identical drops to a stable system of axisymmetric non-identical drops. With increasing total protruded liquid volume this system of non-identical drops reaches its own collective stability limit (to axisymmetric perturbations) which gives rise to dripping or streaming from the holes. Critical volumes and heights for non-identical drops have been calculated as functions of the dimensionless hole radius (associated with the Bond number). For unequal hole radii, there are three intervals of the larger dimensionless hole radius, $R_{1}^{0}$, with qualitatively different bifurcation patterns which in turn can depend on the smaller dimensionless hole radius, $R_2 ^0$. Loss of stability may occur when the drop suspended from the larger hole reaches its stability limit (to non-axisymmetric perturbations) as a solitary drop or when the system reaches the collective stability limit (to axisymmetric perturbations). Typical situations are illustrated for selected values of $R_1 ^0$, and then the basic characteristics of the stability for a dense set of $R_1 ^0$ are presented.

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“…To do so, experimental (Seebeck measurements), analytical (scaling considerations) and numerical (a quasi-steady state 2D pseudo-spectral model) information has been simultaneously used for the analysis of two Sn-Bi alloys. Agreement was reported for a characteristic concentrational decay time as a function of the inverse of the solutal cut-off pulsation of the problem, but analytical predictions significantly overpredict the variation of the induced composition drop as a function of the modified g-dose [6][7][8][9].…”

Section: Introductionmentioning

confidence: 96%