@article{FayzrakhmanovaStraubeShklyaev2011,
  author    = {Fayzrakhmanova, Irina S. and Straube, Arthur V. and Shklyaev, Sergey},
  title     = {Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis},
  series = {Physics of fluids},
  volume    = {23},
  journal   = {Physics of fluids},
  number    = {10},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1070-6631},
  doi       = {10.1063/1.3650280},
  pages     = {6},
  year      = {2011},
  abstract  = {We consider a sessile hemispherical bubble sitting on the transversally oscillating bottom of a deep liquid layer and focus on the interplay of the compressibility of the bubble and the contact angle hysteresis. In the presence of contact angle hysteresis, the compressible bubble exhibits two kinds of terminal oscillations: either with the stick-slip motion of the contact line or with the completely immobile contact line. For the stick-slip oscillations, we detect a double resonance, when the external frequency is close to eigenfrequencies of both the breathing mode and shape oscillations. For the regimes evolving to terminal oscillations with the fixed contact line, we find an unusual transient resembling modulated oscillations.},
  language  = {en}
}
@article{ShklyaevStraube2009,
  author    = {Shklyaev, Sergey and Straube, Arthur V.},
  title     = {The impact of bubble diffusivity on confined oscillated bubbly liquid},
  issn      = {1070-6631},
  doi       = {10.1063/1.3157237},
  year      = {2009},
  abstract  = {We consider the dynamics of monodisperse bubbly liquid confined by two plane solid walls and subject to small- amplitude high-frequency transverse oscillations. The period of these oscillations is assumed small in comparison with typical relaxation times for a single bubble but comparable with the period of volume eigenoscillations. The time- averaged description accounting for the two-way coupling between the liquid and the bubbles and for the diffusivity of bubbles is applied. We find nonuniform steady states with the liquid quiescent on average. At relatively low frequencies, accumulation of bubbles either at the walls or in planes parallel to the walls is detected. These one- dimensional states are shown to be unstable. At relatively high frequencies, this accumulation is found at the central plane and the solution is stable.},
  language  = {en}
}
@article{ShklyaevStraube2010,
  author    = {Shklyaev, Sergey and Straube, Arthur V.},
  title     = {Formation and evolution of bubbly screens in confined oscillating bubbly liquids},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.016321},
  year      = {2010},
  abstract  = {We consider the dynamics of dilute monodisperse bubbly liquid confined by two plane solid walls and subject to small-amplitude high-frequency oscillations normal to the walls. The initial state corresponds to the uniform distribution of bubbles and motionless liquid. The period of external driving is assumed much smaller than typical relaxation times for a single bubble but larger than the period of volume eigenoscillations. The time-averaged description accounting for the two-way coupling between the liquid and the bubbles is applied. We show that the model predicts accumulation of bubbles in thin sheets parallel to the walls. These singular structures, which are formally characterized by infinitely thin width and infinitely high concentration, are referred to as bubbly screens. The formation of a bubbly screen is described analytically in terms of a self-similar solution, which is in agreement with numerical simulations. We study the evolution of bubbly screens and detect a one-dimensional stationary state, which is shown to be unconditionally unstable.},
  language  = {en}
}
@article{ShklyaevStraube2010,
  author    = {Shklyaev, Sergey and Straube, Arthur V.},
  title     = {Superexponential droplet fractalization as a hierarchical formation of dissipative compactons},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.82.020601},
  year      = {2010},
  abstract  = {We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.},
  language  = {en}
}