Browsing by Author "Khismatullin, D. B."

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    Inertia-induced breakup of highly viscous drops subjected to simple shear
    Khismatullin, D. B.; Renardy, Yuriko Y.; Cristini, V. (AIP Publishing, 2003-05)
    We investigate the inertia-driven breakup of viscous drops suspended in a less viscous liquid under simple shear. For Stokes flow, it is known that there is a critical value of the viscosity ratio, beyond which breakup does not occur. We find that for viscosity ratios larger than this, inertia can be used as a mechanism of breakup. Inertia increases the angle of tilt of the drops and effectively leads to emulsification for a wider range of viscosity ratios than in Stokes flow. (C) 2003 American Institute of Physics.
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    Radial oscillations of encapsulated microbubbles in viscoelastic liquids
    Khismatullin, D. B.; Nadim, A. (American Institute of Physics, 2002-10)
    The small-amplitude radial oscillations of a gas microbubble encapsulated by a viscoelastic solid shell and surrounded by a slightly compressible viscoelastic liquid are studied theoretically. The Kelvin-Voigt and 4-constant Oldroyd models are used to describe the viscoelastic properties of the shell and liquid, respectively. The equation for radial oscillation is derived using the method of matched asymptotic expansions. Based on this equation, we present the expressions for damping coefficients and scattering cross sections at the fundamental frequency and at twice that frequency. The numerical maximization of the amplitude-frequency response function shows that the resonance frequency for the encapsulated microbubble highly depends on viscous damping, and therefore, significantly differs from the undamped natural frequency. The effects of the shell and liquid parameters on the resonance frequency and scattering cross sections are analyzed.
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    Sound-ultrasound interaction in bubbly fluids: Theory and possible applications
    Khismatullin, D. B.; Akhatov, I. S. (American Institute of Physics, 2001-12)
    The interaction between sound and ultrasound waves in a weakly compressible viscous liquid with gas bubbles is considered. Using the method of multiple scales one- and two-dimensional nonlinear interaction equations are derived. The degeneracy of the interaction is found in bubbly fluids. This phenomenon lies in the fact that the interaction coefficients vanish at a certain frequency of ultrasound. We demonstrate that the integrable Davey-Stewartson I (DSI) system of equation can describe the two-dimensional sound-ultrasound evolution. The DSI equations are remarkable by their solutions referred to as dromions. In bubbly fluids the dromion represents the localized focused ultrasound wave which can alter the direction of its motion under changes in the boundary conditions for the sound wave. The condition of singular focusing of ultrasound in bubbly fluids is obtained. By numerical analysis of the interaction models, we reveal such processes as intensification of ultrasound by sound, nonlinear instability of a sound profile, and prove the validity of the singular focusing condition. Finally, possible applications of the results are outlined.