Uniaxial extensional flows in liquid bridges

Bänsch, Eberhard; Berg, Christian; Ohlhoff, A.

doi:10.1017/s0022112004001193

Cited by 15 publications

(3 citation statements)

References 25 publications

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“…For details see Bänsch (2001). The code has been successfully validated in many applications, see Davis and Bänsch (2002), Bänsch et al (2004Bänsch et al ( , 2006 and Krahl et al (2008).…”

Section: Comparison With Direct Numerical Simulationsmentioning

confidence: 99%

On the stability of an evaporating liquid surface

Krahl

Bänsch

2012

Fluid Dyn. Res.

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The stability of the interface between a volatile liquid and a gaseous phase has been studied in this paper. We consider the case when the liquid volume is not a film and thus the thin-film approximation might not be valid. A linear stability analysis leads to the Orr-Sommerfeld equation for the stream function and a second-order differential equation for the temperature. This system is solved semi-analytically. A parameter study shows that surface tension is stabilizing, while viscosity is destabilizing the liquid surface. The capillary number is identified as the most significant factor. The analytical results were compared with the growth of an initial perturbation for the full system by direct numerical simulations, and excellent agreement was observed.

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Section: Comparison With Direct Numerical Simulationsmentioning

confidence: 99%

On the stability of an evaporating liquid surface

Krahl

Bänsch

2012

Fluid Dyn. Res.

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“…This methodology was introduced by Dziuk [3] and later applied to ow calculations in the ALE framework by B ansch and coworkers [4][5][6], Sashikumaar and Tobiska [7], and Matthies [8]. Some work has also been done in the context of Eulerian ÿxed grids; with level sets by Gro et al [9] and with front tracking by Minev and coworkers [10].…”

Section: Semi-implicit Time Integrationmentioning

confidence: 99%

A new implicit surface tension implementation for interfacial flows

Hysing

2006

Numerical Methods in Fluids

128

144

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SUMMARYA new implementation of surface tension e ects in interfacial ow codes is proposed which is both fully implicit in space, that is the interface never has to be reconstructed, and also semi-implicit in time, with semi-implicit referring to the time integration of the surface tension forces. The main idea is to combine two previously separate techniques to yield a new expression for the capillary forces. The ÿrst is the continuum surface force (CSF) method, which is used to regularize the discontinuous surface tension force term. The regularization can be elegantly implemented with the use of distance functions, which makes the level set method a suitable choice for the interface-tracking algorithm. The second is to use a ÿnite element discretization together with the Laplace-Beltrami operator, which enables simple reformulation of the surface tension term into its semi-implicit equivalent. The performance of the new method is benchmarked against standard explicit methods, where it is shown that the new method is signiÿcantly more robust for the chosen test problems when the time steps exceed the numerical capillary time step restriction. Some improvements are also found in the average number of nonlinear iterations and linear multigrid steps taken while solving the momentum equations.

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“…In the linear regime, the eigenfrequencies of cylindrical 7 and axisymmetric 8 shapes have been calculated for arbitrary capillary numbers semianalytically and numerically, respectively. There is a considerable body of literature dealing with the theoretical analysis of nonlinear phenomena in liquid bridges, such as the free and forced oscillations, 9 the steady streaming flow due to high-frequency vibration, 10 the uniaxial extensional flows, 11 and the breakup process. 12 Experimental studies of the dynamical behavior of isothermal liquid bridges have been relatively scarce probably due to the high spatial and temporal resolutions required to analyze the experiments under normal gravity conditions.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a liquid bridge in a coaxial gas flow

et al. 2011

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The dynamical response of an isothermal liquid bridge to a coaxial gas stream is examined from axisymmetric numerical simulations of the Navier-Stokes equations. The simulation method is previously validated by calculating the temporal evolution of the first oscillation mode in both cylindrical and axisymmetric liquid bridges. The comparison with other theoretical approaches and experiments shows good agreement in most cases, although significant discrepancies are found between the simulation and the experimental values of the damping rate for hexadecane. The simulation of a liquid bridge in a coaxial gas stream shows that a recirculation cell always appears in the liquid driven by the gas viscous stress on the free surface. The recirculation cell speed depends quasilinearly on the gas velocity for the range of gas flow rates considered. If the gas stream and gravity have the same direction, then the speed of the recirculation cell increases considerably due to the free surface deformation of the liquid bridge at equilibrium. This effect does not occur when gravity has the opposite direction because viscous dissipation in the liquid increases in this case. If the gas stream and gravity point downward, the liquid bridge shrinks at the upper part and bulges at the lower owing to the accumulation of momentum there. The same occurs for zero gravity, but noncylindrical liquid bridges deform more than cylindrical shapes with the same slenderness. If one inverts the direction of the gravity force, the interface deformation caused by the gas stream is the opposite, and its magnitude is smaller. The magnitude of the free surface deformation depends almost linearly on the gas stream velocity for both zero and normal gravity conditions.

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Uniaxial extensional flows in liquid bridges

Cited by 15 publications

References 25 publications

On the stability of an evaporating liquid surface

On the stability of an evaporating liquid surface

A new implicit surface tension implementation for interfacial flows

Numerical simulation of a liquid bridge in a coaxial gas flow

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