Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets

Liu, Zhengbai; Brenn, Günter; Durst, F.

doi:10.1016/s0377-0257(98)00060-3

Cited by 63 publications

(51 citation statements)

References 24 publications

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“…A corotational model is used by Bird, Armstrong & Hassager (1977), Park & Lee (1995), Goren & Gottlieb (1982), Liu, Brenn & Durst (1998), and many others for describing the viscoelastic liquid state. The following linearized equations are obtained after neglecting the nonlinear terms:…”

Section: Liquid Phase Velocity and Pressure Distributionmentioning

confidence: 99%

Linear analysis of three-dimensional instability of non-Newtonian liquid jets

Liu

Liu²

2006

J. Fluid Mech.

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The instability behaviour of non-Newtonian liquid jets moving in an inviscid gaseous environment is investigated theoretically for three-dimensional disturbances. The corresponding dispersion relation between the wave growth rate and the wavenumber is derived. Results for axisymmetrical non-Newtonian jets, the Newtonian jets, and the inviscid jets are recovered, and it is shown that two-dimensional disturbances are the most dangerous for the considered set of parameters.

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Section: Liquid Phase Velocity and Pressure Distributionmentioning

confidence: 99%

Linear analysis of three-dimensional instability of non-Newtonian liquid jets

Liu

Liu²

2006

J. Fluid Mech.

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“…Liu et al 9 studied the linear instability of two-dimensional viscoelastic sheets; they found that-similar to Newtonian liquid sheets-the instability of viscoelastic sheets also has two modes, i.e., the sinuous and the varicose modes. The effects of Weber number, Reynolds number, and gas-to-liquid density ratio are similar to those of Newtonian liquid sheets.…”

Section: Introductionmentioning

confidence: 99%

“…An increase of elasticity, or a reduction of time constant ratio (the ratio of the deformation retardation time to the stress relaxation time), enhances instability. Brenn et al 10 extended the linear stability analysis of Liu et al, 9 to one with three-dimensional disturbances. They found that the three-dimensional disturbances are less unstable than the two-dimensional counterpart.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear instability of planar viscoelastic sheets

et al. 2015

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A second-order weakly nonlinear analysis has been made of the temporal instability for the linear sinuous mode of two-dimensional planar viscoelastic liquid sheets moving in an inviscid gas. The convected Jeffreys models including the corotational Jeffreys model, Oldroyd A model, and the Oldroyd B model are considered as the rheology model of the viscoelastic fluid of the sheet. The solution for the secondorder gas-to-liquid interface displacement has been derived, and the temporal evolution leading to the breakup has been shown. The second-order interface displacement of the linear sinuous mode is varicose, which causes the sheet to fragment into ligaments. First-order constitutive relations of the three rheology models become identical after linearization, so the linear instability results are also the same. For the second-order weakly nonlinear instability, the second-order constitutive relation varies among the corotational Jeffreys model, Oldroyd A model, and the Oldroyd B model, but although they have different disturbance pressures, their disturbance velocities and interface displacements are the same, and therefore, the sheets of the corotational Jeffreys fluid, Oldroyd A fluid, and the Oldroyd B fluid have the same instability behavior characterized by the wave profile and breakup time. The reason for the identical instability behavior is that the effect of different codeformations of the corotational frame, covariant frame, and the contravariant frame is counteracted by the corresponding change in the second-order disturbance pressure, leaving no influence on the second-order velocity. At wavenumbers with maximum instabilities, an increase in the elasticity, or a reduction of the deformation retardation time, leads to a larger linear temporal growth rate, greater second-order disturbance amplitude, and shorter breakup time, thereby enhancing instability. The mechanism of linear instability has been examined using an energy approach, which shows that the main cause of instability is the aerodynamic force. C 2015 AIP Publishing LLC.

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“…In 1975, Crapper et al [9] studied surface wave growth on thin sheets of nonNewtonian fluids. In 1998, Liu et al [10] succeeded in applying the method of analyzing the instability of planar Newtonian sheets to that of planar non-Newtonian sheets. They investigated breakup instability for both symmetric and antisymmetric disturbances and effects of various parameters on the instability of viscoelastic fluids.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Instability Analysis of Power-Law Sheets

Liu¹,

Yang²,

Liu³

et al. 2017

Topical Problems of Fluid Mechanics 2017

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Research on nonlinear instability of Power-law plane sheets has been conducted using Carreau law. Combined with asymptotic expansion and long wave assumption, the governing equations and boundary conditions were performed using integral transform. The first-order dimensionless dispersion relation between unstable growth rate and wavenumber was obtained and the second-order interface disturbance amplitude was calculated. By comparison and analysis of components of the second-order interface disturbance amplitude, the effects of power-law index n (n<1) were investigated and the condition under which the shear-thinning effect can be evident was concluded, thus contributing to theoretical basis and technological means to improve atomization of power-law sheets.

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Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets

Cited by 63 publications

References 24 publications

Linear analysis of three-dimensional instability of non-Newtonian liquid jets

Linear analysis of three-dimensional instability of non-Newtonian liquid jets

Weakly nonlinear instability of planar viscoelastic sheets

Nonlinear Instability Analysis of Power-Law Sheets

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