Frequency dispersion of small-amplitude capillary waves in viscous fluids

Optical coherence viscometry

We report a technique, named optical coherence viscometry (OCV), to measure the viscosity of Newtonian fluids in a noncontact manner. According to linear wave theory with small amplitudes, capillary waves are associated with fluid mechanical properties. To perform this measurement and avoid the overdamped effects of capillary waves in viscous fluids, transient acoustic radiation force was applied to generate capillary waves. Within a very limited field-of-view using optical coherence tomography, wave motion acquired in the time domain was analyzed using Fourier methods to study the wave velocity dispersion and attenuation relationships for capillary waves, which can reduce the fluid quantity drastically into tissue culture scale. We measure the viscosities of water, water-glycerol solutions with three concentrations, and biological plasma using the proposed OCV and compare the experimental results to theoretical calculations. OCV is sensitive to wave perturbations and can be a promising technique for measuring the viscosity of biological fluids and could be applied in future applications for measurements for lipid membranes in cell biology and tissue engineering investigation.

Oscillatory surface deformation of paramagnetic rare-earth solutions driven by an inhomogeneous magnetic field

The deformation of the free surface of a paramagnetic liquid subjected to a nonuniform magnetic field is studied. A transient deformation of the surface caused by the interplay of gravity, magnetic field, and surface tension is observed when a permanent magnet is moved vertically downward to the free surface of the liquid. Different concentrations of rare-earth-metal salt (DyCl_{3}) are used and different magnet velocities are studied. The deformation of the interface is followed optically by means of a microscope and recorded with a high-speed camera. The experimental results are compared and discussed with complementary numerical simulations. Detailed results are given for the static shape of the deformed surface and the temporal evolution of the surface deformation below the center of the magnet. The frequency of the surface oscillations is found to depend on the concentration of the salt and is compared with analytical findings. Finally, a potential application of the effects observed is presented.

Transient structures in rupturing thin films: Marangoni-induced symmetry-breaking pattern formation in viscous fluids

In the minutes immediately preceding the rupture of a soap bubble, distinctive and repeatable patterns can be observed. These quasistable transient structures are associated with the instabilities of the complex Marangoni flows on the curved thin film in the presence of a surfactant solution. Here, we report a generalized Cahn-Hilliard-Swift-Hohenberg model derived using asymptotic theory that describes the quasielastic wrinkling pattern formation and the consequent coarsening dynamics in a curved surfactant-laden thin film. By testing the theory against experiments on soap bubbles, we find quantitative agreement with the analytical predictions of the nucleation and the early coarsening phases associated with the patterns. Our findings provide fundamental physical understanding that can be used to (de-)stabilize thin films in the presence of surfactants and have important implications for both natural and industrial contexts, such as the production of thin coating films, foams, emulsions, and sprays.

Resonance excitation of surface capillary waves to enhance material removal for laser material processing

The results of detailed experiments and high fidelity modeling of melt pool dynamics, droplet ejections and hole drilling produced by periodic modulation of laser intensity are presented. Ultra-high speed imaging revealed that melt pool oscillations can drive large removal of material when excited at the natural oscillation frequency. The physics of capillary surface wave excitation is discussed and simulation is provided to elucidate the experimental results. The removal rates and drill through times as a function of driving frequency is investigated. The resonant removal mechanism is driven by both recoil momentum and thermocapillary force but the key observation is the latter effect does not require evaporation of material, which can significantly enhance the efficiency for laser drilling process. We compared the drilling of holes through a 2 mm-thick Al plate at modulation frequencies up to 20 kHz. At the optimal frequency of 8 kHz, near the resonant response of the melt pool, the drilling efficiency is greater than 10x with aspect ratio of 12:1, and without the collateral damage that is observed in unmodulated CW drilling.

Linear motion of multiple superposed viscous fluids

In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that can be inverted numerically. The derived equations also contain the general normal mode equations, which can be used to determine the asymptotic growth rates of the systems directly. After derivation, the equations are used to study two different problems involving three fluid layers. The first problem is the effect of initial phase difference on the development of a Rayleigh-Taylor instability and the second is the damping effect of a thin, highly viscous, surface layer.

Marangoni effect on small-amplitude capillary waves in viscous fluids

We derive a general integro-differential equation for the transient behavior of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.