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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimer: 2152-5102
ISSN En ligne: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v38.i1.40
pages 38-55

Unsteady Motion of a Single Rising Bubble in Low Reynolds Numbers: An Analytical Study

M. Jalaal
Department of Mechanical Engineering, University of Tabriz
Davood Ganji (D.D. Ganji)
Babol University


The rising behavior of bubbles is of fundamental importance in many natural and industrial phenomenon. In current study, the unsteady motion of a single spherical air bubble rising in a stationary viscose liquid has been studied for low Reynolds numbers region. Considered nonlinear equation of motion involved added-mass term and neglected the Basset term. An exact solution is derived for instantaneous velocity using homotopy perturbation method. Therefore, acceleration and position of the bubble were achieved. Equation was solved generally and for some practical conditions while air was assumed to be the gas phase and glycerin solutions with different concentrations were considered as liquid phases. Present investigation shows the effectiveness of HPM and exhibit a new application of it for nonlinear problems arising in two-phase flows. Current analytical expression for rising bubble can be used in different further investigations on rising bubbles.