scholarly journals Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

2018 ◽  
Vol 847 ◽  
pp. 71-92 ◽  
Author(s):  
M. De Corato ◽  
V. Garbin
Keyword(s):  
Bubble Radius ◽  
Deformation Mode ◽  
Planar Interface ◽  
Capillary Waves ◽  
Periodic Force ◽  
Capillary Interactions ◽  
Point Forces ◽  
Analytical Formulas ◽  
Dynamic Forcing ◽  
Forcing Mechanisms

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominant deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non-monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

Nonlinear stability of Kelvin–Helmholtz waves in magnetic fluids stressed by a time-dependent acceleration and a tangential magnetic field

1996 ◽  
Vol 55 (2) ◽  
pp. 219-234 ◽  
Author(s):  
Yusry O. El-Dib
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Multiple Scales ◽  
Sufficient Conditions ◽  
Magnetic Fluids ◽  
Capillary Waves ◽  
Periodic Force ◽  
Weakly Nonlinear ◽  
Nonlinear Schrödinger ◽  
Periodic Acceleration

The nonlinear stability of surface waves propagating between two superposed streaming magnetic fluids is investigated. The fluids are stressed by a constant tangential magnetic field and a vertical periodic acceleration. The solution employs the method of multiple scales. Owing to the periodicity, resonant cases appear. Two parametrically nonlinear Schrödinger equations are derived for the resonant cases to describe the elevation of weakly nonlinear capillary waves. The standard nonlinear Schrödinger equation is satisfied for the non resonant cases. Necessary and sufficient conditions for stability are obtained. A formula for the surface elevation is obtained in each case. It is found that the magnetic field, the velocities and the frequency of the applied periodic force play dual roles in the resonant region. Investigation of the stability criterion by nonlinear perturbation shows that an increase in the acceleration frequency has a stabilizing effect. The stabilizing role of the frequency is due to the destabilizing effect of the amplitude of the periodic acceleration.

scholarly journals Capillary waves control the ejection of bubble bursting jets

2019 ◽  
Vol 867 ◽  
pp. 556-571 ◽  
Author(s):  
J. M. Gordillo ◽  
J. Rodríguez-Rodríguez
Keyword(s):  
Capillary Wave ◽  
Bubble Radius ◽  
Bond Number ◽  
Capillary Waves ◽  
Liquid Density ◽  
Ohnesorge Number ◽  
Capillary Suction ◽  
Lower Base ◽  
Capillary Pressures ◽  
The Moment

Here we provide a theoretical framework describing the generation of the fast jet ejected vertically out of a liquid when a bubble, resting on a liquid–gas interface, bursts. The self-consistent physical mechanism presented here explains the emergence of the liquid jet as a consequence of the collapse of the gas cavity driven by the low capillary pressures that appear suddenly around its base when the cap, the thin film separating the bubble from the ambient gas, pinches. The resulting pressure gradient deforms the bubble which, at the moment of jet ejection, adopts the shape of a truncated cone. The dynamics near the lower base of the cone, and thus the jet ejection process, is determined by the wavelength $\unicode[STIX]{x1D706}^{\ast }$ of the smallest capillary wave created during the coalescence of the bubble with the atmosphere which is not attenuated by viscosity. The minimum radius at the lower base of the cone decreases, and hence the capillary suction and the associated radial velocities increase, with the wavelength $\unicode[STIX]{x1D706}^{\ast }$. We show that $\unicode[STIX]{x1D706}^{\ast }$ increases with viscosity as $\unicode[STIX]{x1D706}^{\ast }\propto Oh^{1/2}$ for $Oh\lesssim O(0.01)$, with $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}R\unicode[STIX]{x1D70E}}$ the Ohnesorge number, $R$ the bubble radius and $\unicode[STIX]{x1D70C}$, $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D70E}$ indicating respectively the liquid density, viscosity and interfacial tension coefficient. The velocity of the extremely fast and thin jet can be calculated as the flow generated by a continuous line of sinks extending along the axis of symmetry a distance proportional to $\unicode[STIX]{x1D706}^{\ast }$. We find that the jet velocity increases with the Ohnesorge number and reaches a maximum for $Oh=Oh_{c}$, the value for which the crest of the capillary wave reaches the vertex of the cone, and which depends on the Bond number $Bo=\unicode[STIX]{x1D70C}gR^{2}/\unicode[STIX]{x1D70E}$. For $Oh>Oh_{c}$, the jet is ejected after a bubble is pinched off; in this regime, viscosity delays the formation of the jet, which is thereafter emitted at a velocity which is inversely proportional to the liquid viscosity.

scholarly journals Об инкрементах неустойчивости волн различной симметрии на движущейся относительно материальной среды объемно заряженной струе

2019 ◽  
Vol 89 (8) ◽  
pp. 1176
Author(s):  
А.И. Григорьев ◽  
С.О. Ширяева ◽  
Г.Е. Михеев
Keyword(s):  
Deformation Mode ◽  
Incompressible Material ◽  
Dielectric Medium ◽  
Capillary Waves ◽  
Dielectric Fluid ◽  
Axisymmetric Mode ◽  
Volume Charge Density ◽  
Bending Mode ◽  
Wave Numbers ◽  
Aerodynamic Instability

The increments of instability of capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers ) on the surface of a volume charged cylindrical jet of an ideal incompressible dielectric fluid moving relative to an ideal incompressible material dielectric medium are investigated. It is shown that at not too high velocities of the jet motion, with an increase in the volume charge density, the axisymmetric mode ( m=0) becomes unstable first, then the bending mode ( m=1), and then the bending-deformation mode (m=2 ).This sequence of realization of the instability of azimuthal modes and determines the patterns of fragmentation of charged jets in the experiments. At jet speeds comparable to the critical for the realization of aerodynamic instability, the first loses stability mode whis . For all azimuthal modes, the dependences of the maximum increments on the wave numbers are determined.

Effects of capillary waves on the thickness of wetting layers

1988 ◽  
Vol 49 (4) ◽  
pp. 675-680 ◽  
Author(s):  
S. Chatterjee ◽  
E.S.R. Gopal
Keyword(s):  
Capillary Waves ◽  
Wetting Layers

A Tilting Procedure to Enhance Compositional Contrast and Reduce Residual Bragg Contrast in EFTEM Imaging of Planar Interfaces

2000 ◽  
Vol 6 (S2) ◽  
pp. 156-157
Author(s):  
K.T. Moore ◽  
E.A. Stach ◽  
J.M. Howe ◽  
D.C. Elbert ◽  
D.R. Veblen
Keyword(s):  
Electron Scattering ◽  
Planar Interface ◽  
Zone Axis ◽  
Crystalline Material ◽  
Energy Losses ◽  
Inelastic Electron ◽  
Diffraction Contrast ◽  
Background Removal ◽  
Intensity Changes ◽  
Elemental Maps

When acquiring energy-filtered TEM (EFTEM) images of a crystalline material, the detrimental effects of diffraction contrast can often be seen in raw energy-filtered images (EFI) (i.e., pre-edge and post-edge images), jump-ratio images and elemental maps as residual diffraction contrast. Residual diffraction contrast occurs in raw EFI because of plural scattering (i.e., inelastic-elastic and elastic-inelastic electron scattering) and in jump-ratio images and elemental maps because background removal procedures often are unable to completely account for intensity changes due to dynamical effects (elastic scattering) that occur between pre-edge and post-edge images acquired at different energy losses.It is demonstrated in these experiments that, when examining a planar interface, EFTEM images have increased compositional contrast and decreased residual diffraction contrast when the sample is oriented so that the interface is parallel to the electron beam, but not directly on a zone axis.

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

scholarly journals Universal Stokes’s nanomechanical viscometer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Komal Chaudhary ◽  
Pooja Munjal ◽  
Kamal P. Singh
Keyword(s):  
Electric Field ◽  
Real Time ◽  
Sample Volume ◽  
Capillary Waves ◽  
Small Sample ◽  
Medical Applications ◽  
Rapid Measurement ◽  
Single Lens ◽  
Universal Applicability ◽  
Small Sample Volume

AbstractAlthough, many conventional approaches have been used to measure viscosity of fluids, most methods do not allow non-contact, rapid measurements on small sample volume and have universal applicability to all fluids. Here, we demonstrate a simple yet universal viscometer, as proposed by Stokes more than a century ago, exploiting damping of capillary waves generated electrically and probed optically with sub-nanoscale precision. Using a low electric field local actuation of fluids we generate quasi-monochromatic propagating capillary waves and employ a pair of single-lens based compact interferometers to measure attenuation of capillary waves in real-time. Our setup allows rapid measurement of viscosity of a wide variety of polar, non-polar, transparent, opaque, thin or thick fluids having viscosity values varying over four orders of magnitude from $$10^{0}{-}10^{4}~\text{mPa} \, \text{s}$$ 10 0 - 10 4 mPa s . Furthermore, we discuss two additional damping mechanisms for nanomechanical capillary waves caused by bottom friction and top nano-layer appearing in micro-litre droplets. Such self-stabilized droplets when coupled with precision interferometers form interesting microscopic platform for picomechanical optofluidics for fundamental, industrial and medical applications.

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