The long-time motion of vortex sheets with surface tension

1997 ◽  
Vol 9 (7) ◽  
pp. 1933-1954 ◽  
Author(s):  
T. Y. Hou ◽  
J. S. Lowengrub ◽  
M. J. Shelley
Keyword(s):  
Surface Tension ◽  
Vortex Sheets ◽  
Time Motion ◽  
Long Time

scholarly journals Traveling waves from the arclength parameterization: Vortex sheets with surface tension

2013 ◽  
Vol 15 (3) ◽  
pp. 359-380 ◽  
Author(s):  
Benjamin Akers ◽  
David Ambrose ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Traveling Waves ◽  
Vortex Sheets

scholarly journals Capillary phenomena on a liquid surface

1970 ◽  
Vol 38 ◽  
pp. 45-51
Author(s):  
Mohammad Ali ◽  
Akira Umemura
Keyword(s):  
Surface Tension ◽  
Capillary Wave ◽  
Fluid Velocity ◽  
Liquid Sheet ◽  
Navier Stokes ◽  
Capillary Phenomena ◽  
Long Time ◽  
Propagation Of Waves ◽  
Tip Velocity ◽  
Low Pressures

Contraction of a liquid sheet of an incompressible Newtonian fluid in a passive ambient fluid is studied computationally to provide insights into the dynamics of capillary wave created during contraction. The problem composed of the Navier-Stokes system is associated with initial and boundary conditions that govern the time evolution of the capillary wave and the pressure and velocity fields within it. The correctness of the algorithm is verified with the data of experiment. It can be found that the prediction of the computation agrees well with the experiment. The algorithm is capable of capturing the capillary wave and therefore it is used to study the characteristic phenomena of that wave created on the surface of the liquid. Results show that the capillary wave is radiated from the tip of the liquid sheet caused by surface tension. The amplitude of the tip wave is much larger than any other waves and the asymptotic approach of the wave peaks can be observed during the propagation of waves. The tip wave contains the highest pressure and gradually the peak values of both high and low pressures decrease with the propagation of waves. Fluid velocity is motivated by both pressure due to surface tension and recirculation in peak and trough of the wave. During the contraction of the liquid sheet, the tip velocity is not uniform. Initially the length of the sheet increases a little and very soon the contraction occurs and continues. After long time, the gradient of tip velocity becomes very small. Keywords: Capillary wave, liquid sheet.DOI: 10.3329/jme.v38i0.900 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.45-51  

Linear and nonlinear stability of floating viscous sheets

2011 ◽  
Vol 683 ◽  
pp. 112-148 ◽  
Author(s):  
G. Pfingstag ◽  
B. Audoly ◽  
A. Boudaoud
Keyword(s):  
Surface Tension ◽  
Surface Forces ◽  
Two Dimensional ◽  
Buckling Mode ◽  
Geometrical Nonlinearities ◽  
Flat Sheet ◽  
Long Time ◽  
Classical Models ◽  
Linear And Nonlinear ◽  
The Stability

AbstractWe study the stability of a thin, Newtonian viscous sheet floating on a bath of denser fluid. We first derive a general set of equations governing the evolution of a nearly flat sheet, accounting for geometrical nonlinearities associated with moderate rotations. We extend two classical models by considering arbitrary external body and surface forces; these two models follow from different scaling assumptions, and are derived in a unified way. The equations capture two modes of deformation, namely viscous bending and stretching, and describe the evolution of thickness, mid-surface and in-plane velocity as functions of two-dimensional coordinates. These general equations are applied to a floating viscous sheet, considering gravity, buoyancy and surface tension. We investigate the stability of the flat configuration when subjected to arbitrary in-plane strain. Two unstable modes can be found in the presence of compression. The first one combines undulations of the centre-surface and modulations of the thickness, with a wavevector perpendicular to the direction of maximum applied compression. The second one is a buckling mode; it is purely undulatory and has a wavevector along the direction of maximum compression. A nonlinear analysis yields the long-time evolution of the undulatory mode.

The evolution of a viscous thread pulled with a prescribed speed

2016 ◽  
Vol 795 ◽  
pp. 380-408 ◽  
Author(s):  
J. J. Wylie ◽  
B. H. Bradshaw-Hajek ◽  
Y. M. Stokes
Keyword(s):  
Surface Tension ◽  
Critical Exponent ◽  
Large Time ◽  
Asymptotic Form ◽  
Numerical Solutions ◽  
Long Wavelength ◽  
Asymptotic Expressions ◽  
Different Types ◽  
Long Time ◽  
Special Case

We examine the extension of an axisymmetric viscous thread that is pulled at both ends with a prescribed speed such that the effects of inertia are initially small. After neglecting surface tension, we derive a particularly convenient form of the long-wavelength equations that describe long and thin threads. Two generic classes of initial thread shape are considered as well as the special case of a circular cylinder. In these cases, we determine explicit asymptotic solutions while the effects of inertia remain small. We further show that inertia will ultimately become important only if the long-time asymptotic form of the pulling speed is faster than a power law with a critical exponent. The critical exponent can take two possible values depending on whether or not the initial minimum of the thread radius is located at the pulled end. In addition, we obtain asymptotic expressions for the solution at large times in the case in which the critical exponent is exceeded and hence inertia becomes important. Despite the apparent simplicity of the problem, the solutions exhibit a surprisingly rich structure. In particular, in the case in which the initial minimum is not at the pulled end, we show that there are two very different types of solution that exhibit very different extension mechanics. Both the small-inertia solutions and the large-time asymptotic expressions compare well with numerical solutions.

Determination of equilibrium surface tension values by extrapolation via long time approximations

1997 ◽  
Vol 122 (1-3) ◽  
pp. 269-273 ◽  
Author(s):  
A.V. Makievski ◽  
V.B. Fainerman ◽  
R. Miller ◽  
M. Bree ◽  
L. Liggieri ◽  
...  
Keyword(s):  
Surface Tension ◽  
Equilibrium Surface ◽  
Equilibrium Surface Tension ◽  
Long Time

scholarly journals Well-posedness of 3D vortex sheets with surface tension

2007 ◽  
Vol 5 (2) ◽  
pp. 391-430 ◽  
Author(s):  
David M. Ambrose ◽  
Nader Masmoudi
Keyword(s):  
Surface Tension ◽  
Well Posedness ◽  
Vortex Sheets

Nano-Sized Ceramic Inks for Drop-on-Demand Ink-Jet Printing in Quadrichromy

2008 ◽  
Vol 8 (4) ◽  
pp. 1979-1988 ◽  
Author(s):  
Davide Gardini ◽  
Michele Dondi ◽  
Anna Luisa Costa ◽  
Francesco Matteucci ◽  
Magda Blosi ◽  
...  
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Ceramic Tiles ◽  
Nozzle Clogging ◽  
Ink Jet Printing ◽  
Drop On Demand ◽  
Wide Range ◽  
Ink Jet ◽  
Long Time ◽  
Jet Printing

Nano-sized ceramic inks suitable for ink-jet printing have been developed for the four-colours CMYK (cyan, magenta, yellow, black) process. Nano-inks of different pigment composition (Co1–xO, Au0, Ti1–x–ySbxCryO2, CoFe2O4) have been prepared with various solid loadings and their chemico-physical properties (particle size, viscosity, surface tension, ζ-potential) were tailored for the ink-jet application. The pigment particle size is in the 20–80 nm range. All these nano-suspensions are stable for long time (i.e., several months) due to either electrostatic (high ζ-potential values) or steric stabilization mechanisms. Both nanometric size and high stability avoid problems of nozzle clogging from particles agglomeration and settling. Nano-inks have a Newtonian behaviour with relatively low viscosities at room temperature. More concentrated inks fulfil the viscosity requirement of ink-jet applications (i.e., <35 mPa˙s) for printing temperatures in between 30 and 70 °C. Surface tension constraints for ink-jet printing are fulfilled by nano-inks, being in the 35–45 mN˙m–1 range. The nano-sized inks investigated behave satisfactorily in preliminary printing tests on several unfired industrial ceramic tiles, developing saturated colours in a wide range of firing temperatures (1000–1200 °C).

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