TWO-DIMENSIONAL TEMPORAL INSTABILITY OF A VISCOELASTIC LIQUID SHEET OF A PARABOLIC VELOCITY PROFILE

2017 ◽  
Vol 27 (5) ◽  
pp. 423-438
Author(s):  
Run-ze Duan ◽  
Zi-yue Wang ◽  
Zhi-ying Chen ◽  
Lian-sheng Liu
Keyword(s):  
Velocity Profile ◽  
Liquid Sheet ◽  
Viscoelastic Liquid ◽  
Two Dimensional ◽  
Temporal Instability ◽  
Parabolic Velocity Profile

Instability of a liquid sheet of parabolic velocity profile

1998 ◽  
Vol 10 (4) ◽  
pp. 1034-1036 ◽  
Author(s):  
E. A. Ibrahim
Keyword(s):  
Velocity Profile ◽  
Liquid Sheet ◽  
Parabolic Velocity Profile

Effect of velocity profile on instability of the viscoelastic liquid sheet

2014 ◽  
Vol 229 (11) ◽  
pp. 2031-2044 ◽  
Author(s):  
Runze Duan ◽  
Zhiying Chen ◽  
Liansheng Liu
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Liquid Sheet ◽  
Viscoelastic Liquid ◽  
Rheological Parameters ◽  
Liquid Sheets ◽  
Elasticity Number

A linear analysis method has been used to investigate the instability behavior of the viscoelastic liquid sheets moving in the surrounding ambient gas. The gas boundary layer thickness and the liquid sheet velocity profile were taken into account. The effects of gas and liquid viscosity on the growth rate were revealed. The governing equations were obtained through analysis of the liquid and gas domain and solved using the spectral method. The viscoelastic rheological parameters and some flow parameters have been tested to investigate their influences on the instability of the viscoelastic liquid sheets. The results reveal that the disturbances grow faster for the viscoelastic liquid sheet than Newtonian one with identical viscosity. Moreover, the increases of Weber number, elasticity number, gas Reynolds number, and momentum flux ratio can accelerate the breakup of the viscoelastic liquid sheet. However, the increases of time constant ratio, boundary layer thickness, and liquid Reynolds number have the opposite effects.

DUAL-MODE LINEAR ANALYSIS OF TEMPORAL INSTABILITY FOR POWER-LAW LIQUID SHEET

2016 ◽  
Vol 26 (4) ◽  
pp. 319-347 ◽  
Author(s):  
Han-Yu Deng ◽  
Feng Feng ◽  
Xiao-Song Wu
Keyword(s):  
Power Law ◽  
Linear Analysis ◽  
Liquid Sheet ◽  
Dual Mode ◽  
Temporal Instability

scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

Effect of Velocity Profile on the Stability of Liquid Sheet

2014 ◽  
Vol 694 ◽  
pp. 288-291
Author(s):  
Run Ze Duan ◽  
Zhi Ying Chen ◽  
Li Jun Yang
Keyword(s):  
Growth Rate ◽  
Velocity Profile ◽  
Linear Analysis ◽  
Liquid Sheet ◽  
Wave Number ◽  
Flat Plates ◽  
Chebyshev Spectral Collocation ◽  
The Stability ◽  
The Relationship ◽  
Temporal Growth Rate

An electrified liquid sheet injected into a dielectric moving through a viscous gas bounded by two horizontal parallel flat plates of a transverse electric field is investigated with the linear analysis method. The liquid sheet velocity profile and the gas boundary layer thickness are taken into account. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The effects of the velocity profile on the stability of the electrified liquid sheet were revealed for both sinuous mode and varicose mode. The results show that the growth rate of the electrified Newtonian liquid is greater than that of corresponding Newtonian one under the same condition, and the growth rate of the sinuous mode is greater than that of the varicose mode. Keywords: instability; planar liquid sheet; velocity profile;spectral method;linear analysis

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