Asymmetric Drainage in Foam Films N4.1

1994 ◽  
Vol 366 ◽  
Author(s):  
Jean-Luc Joye ◽  
George J. Hirasak ◽  
Clarence A. Miller
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hydrodynamic Instability ◽  
Surface Tension Gradient ◽  
Radius Of Curvature ◽  
Surface Viscosity ◽  
Foam Films ◽  
Surface Diffusivity

ABSTRACTDrainage of circular foam films is much more rapid when the drainage is asymmetric. The same basic mechanism is responsible for asymmetric drainage of thin circular films and marginal regeneration. A linear stability analysis showed that these phenomena are caused by a hydrodynamic instability that is produced by a surface-tension-driven flow and stabilized by surface viscosity, surface diffusivity and system length scale. A criterion for the onset of this instability was derived. Experiments performed on small circular films of aqueous solutions of SDS and SDS:l-dodecanol demonstrated the strong stabilizing effect of surface viscosity. Experimental results were found to be in good agreement with the predictions of the linear stability analysis. Finite difference simulations demonstrate the validity of the linear stability analysis for when the radius of curvature of the “barrier ring” is large compared to the transverse wave length of the instability. These simulations also show the circulation cells that relax the surface tension gradient and thus accelerate the drainage of the film.

scholarly journals Shear instability of an axisymmetric air–water coaxial jet

2018 ◽  
Vol 843 ◽  
pp. 575-600 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Antoine Delon ◽  
Alain Cartellier
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Scaling Laws ◽  
Shear Instability ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Instability Waves

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

Washing wedges: capillary instability in a gradient of confinement

2016 ◽  
Vol 790 ◽  
pp. 619-633 ◽  
Author(s):  
Ludovic Keiser ◽  
Rémy Herbaut ◽  
José Bico ◽  
Etienne Reyssat
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Linear Stability Analysis ◽  
Theoretical Description ◽  
Oil Droplets ◽  
Bulk Viscous ◽  
Open Question ◽  
Wetting Liquid

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

scholarly journals Dynamical properties of forced shear layers in an annular geometry

2000 ◽  
Vol 402 ◽  
pp. 255-289 ◽  
Author(s):  
K. BERGERON ◽  
E. A. COUTSIAS ◽  
J. P. LYNOV ◽  
A. H. NIELSEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Landau Equation ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Radius Of Curvature ◽  
Simulation Code ◽  
Annular Geometry

Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr–Sommerfeld operator for plane, circular Couette flow is calculated, and it is found to be insensitive to perturbations.The numerical simulation code is a highly accurate de-aliased spectral method which utilizes banded operators to increase the computational efficiency. Viscous dissipation terms enter the code directly from the equations of motion. The results from the simulation code at low Reynolds numbers are compared with the results from linear stability analysis and are used to give predictions for the coefficients of the Landau equation describing the saturation behaviour near the critical Reynolds number. Numerical results at higher Reynolds numbers demonstrate the effects of spin-up and spin-down, including the experimentally observed hysteresis. The properties of two- dimensional shears at high Reynolds numbers, at which temporal states are formed, are also addressed.

Effects of interaction between Marangoni and double-diffusive instabilities

1995 ◽  
Vol 303 ◽  
pp. 1-21 ◽  
Author(s):  
J. Tanny ◽  
C. C. Chen ◽  
C. F. Chen
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vertical Temperature ◽  
Onset Of Convection ◽  
Bottom Region ◽  
The Stability ◽  
Double Diffusive ◽  
Effect Of Surface

The effect of surface tension on the onset of convection in horizontal double-diffusive layer was studied both experimentally and by linear stability analysis. The experiments were conducted in a rectangular tank with base dimension of 25×13 cm and 5 cm in height. A stable solute (NaCl) stratification was first established in the tank, and then a vertical temperature gradient was imposed. Vertical temperature and concentration profiles were measured using a thermocouple and a conductivity probe and the flow patterns were visualized by a schlieren system. Two types of experiments were carried out which illustrate the effect of surface tension on the onset of convection. In the rigid–rigid experiments, when the critical thermal Rayleigh number, RT, is reached, large double-diffusive plumes were seen simultaneously to rise from the heated bottom and descend from the cooled top. In the rigid–free experiments, owing to surface tension effects, the first instability onset was of the Marangoni type. Well-organized small plumes were seen to emerge and persist close to the top free surface at a relatively small RTM (where subscript M denotes ‘Marangoni’). At larger RTt > RTM (where subscript t denotes ‘top’) these plumes evolved into larger double-diffusive plumes. The onset of double-diffusive instability at the bottom region occurred at a still higher RTb > RTt (where subscript b denotes ‘bottom‘). A series of stability experiments was conducted for a layer with an initial top concentration of 2 wt% and different concentration gradients. The stability map shows that in the rigid–free case the early Marangoni instability in the top region reduces significantly the critical RT for the onset of double-diffusive convection. Compared with the rigid–rigid case, the critical RT in the top region is reduced by about 60% and in the bottom region by about 30%. The results of the linear stability analysis, which takes into account both surface tension and double-diffusive effects, are in general agreement with the experiments. The analysis is then applied to study the stability characteristics of such a layer as gravity is reduced to microgravity level. Results show that even at 10 −4g0, where g0 is the gravity at sea level, the double-diffusive effect is of equal importance to the Marangoni effect.

Spiralling Liquid Jets

2002 ◽  
Author(s):  
Andrew King ◽  
Stephen Decent ◽  
Iain Wallwork ◽  
Emilian Parau ◽  
Mark Simmons ◽  
...  
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Rotation Rate ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Leading Order ◽  
Temporal And Spatial ◽  
Exit Speed

We examine the dynamics of a spiralling slender liquid jet which emerges from a rotating cylindrical drum. Such jets arise in the manufacture of fertiliser and magnesium pellts in the prilling process. Exploiting the slenderness of the jet we determine the steady trajectory of the jet, and find that at leading-order it is a function of the rotation rate of the drum, the surface tension and density of the liquid, the exit speed and exit radius of the jet, the radius of the cylinder, but not of the viscosity of the liquid. We carry out a linear stability analysis of the steady solution, using both inviscid and viscous perturbations, and considering both temporal and spatial stability. We compare our results to experiments, obtaining favourable agreement.

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