Evolution and breaking of parametrically forced capillary waves in a circular cylinder

Abstract

We present results on parametrically forced capillary waves in a circular cylinder, obtained in the limit of large fluid depth, using two low-viscosity liquids whose surface tensions differ by an order of magnitude. The evolution of the wave patterns from the instability to the wave-breaking threshold is investigated in a forcing frequency range (f= ω/2π = 25–100 Hz) that is around the crossover frequency (ωot) from gravity to capillary waves (ωot/2≤ω/2≤4ωot). As expected, near the instability threshold the wave pattern depends on the container geometry, but as the forcing amplitude is increased the wave pattern becomes random, and the wall effects are insignificant. Near breaking, the distribution of random wavelengths can be fitted by a Gaussian. A new gravity–capillary scaling is introduced that is more appropriate, than the usual viscous scaling, for low-viscosity fluids and forcing frequencies <103Hz. In terms of these scales, a criterion is derived to predict the crossover from capillary- to gravity-dominated breaking. A wave-breaking model is developed that gives the relation between the container and the wave accelerations in agreement with experiments. The measured drop size distribution of the ejected drops above the breaking threshold is well approximated by a gamma distribution. The mean drop diameter is proportional to the wavelength determined from the dispersion relation; this wavelength is also close to the most likely wavelength of the random waves at drop ejection. The dimensionless drop ejection rate is shown to have a cubic power law dependence on the dimensionless excess acceleration ε′dan inertial–gravitational ligament formation model is consistent with such a power law.

Evidence of the harmonic Faraday instability in ultrasonic atomization experiments with a deep, inviscid fluid

“…(4) is consistent with previous atomization work in the capillary regime. [4][5][6][7] However, for larger drive amplitude this is not necessarily the case. Figure 1 shows the growth rates for the subharmonic and harmonic modes as a function of the nondimensionalized drive amplitude a.…”

“…Lang 6 and others 4,5,7 established that the rupture of capillary waves at the fluid surface is responsible for the ejected droplets. Due to this observation, the problem of predicting the ejected droplet size is reduced to the determination of the dominant capillary mode at the surface of the excited fluid.…”

Microparticle Response to Two-Dimensional Streaming Flows in Rectangular Chambers Undergoing Low-Frequency Horizontal Vibrations

“…It is to be noted that the actuation accelerations employed in the experiments are well below the threshold acceleration above which Faraday instability is observed; this threshold acceleration is given by [48] …”

Footprint geometry and sessile drop resonance

“…For both, typical observables are mode shapes [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], resonance frequencies [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and the evolution of surface waves with forcing amplitude [18,23,[29][30][31][33][34][35]. The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low.…”

“…The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low. However, an elevated acceleration triggers modes which oscillate at half the forcing frequency [15,18,19,21,[30][31][32], called half-frequency subharmonic modes.…”