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

Abstract

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.

Linear stability analysis of a three-dimensional viscoelastic liquid jet surrounded by a swirling air stream

“…Those disturbances between the lower cutoff number and upper cutoff number are unstable. Similar results were reported by Brenn et al, Liu and Liu [12,22,23], who considered the viscoelastic liquid jet with axisymmetric and non-axisymmetric disturbances moving in an air stream without swirl.…”

“…(46) can be reduced to proper forms that agree with previous work [5,9,12,22,23,28,30] by setting specific parameters to zero. In this sense, the dispersion equation displayed above is a general one.…”

“…However, a more general investigation of the non-axisymmetric mode may offer a satisfactory explanation for the results of the experiments previously mentioned [6][7][8]. To determine the physical mechanism of a non-axisymmetric mode, some researchers established different theoretical models to predict its growing process [22][23][24][25][26][27][28][29]. Liu and Liu [22,23] carried out a linear stability analysis for viscoelastic liquid jets when the ambient gas medium was assumed to be inviscid.…”

“…To determine the physical mechanism of a non-axisymmetric mode, some researchers established different theoretical models to predict its growing process [22][23][24][25][26][27][28][29]. Liu and Liu [22,23] carried out a linear stability analysis for viscoelastic liquid jets when the ambient gas medium was assumed to be inviscid. For the parametric values considered in their paper, they found that the unstable growth rate of non-axisymmetric disturbances can exceed that of axisymmetric disturbances at high liquid Weber number.…”

Experimental and linear analysis for the instability of non‐Newtonian liquid jets issuing from a pressurized vibrating nozzle

“…Some authors have already carried out linear temporal analyses considering the expressions and similar assumptions to those that we will address once again here. [19][20][21] The way in which a jet evolves depends on the balance of forces acting on it. They are in general body forces (gravity, electromagnetic forces, and inertial effects), liquid pressure, stresses on the liquid-related mainly to the viscosity termand surface tension.…”