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Research Papers: Multiphase Flows

A Model for an Acoustically Driven Microbubble Inside a Rigid Tube

[+] Author and Article Information
Adnan Qamar

Mechanical Engineering Program,
Division of Physical Sciences and Engineering,
King Abdullah University of Science
and Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
e-mail: adnan.qamar@kaust.edu.sa

Ravi Samtaney

Mechanical Engineering Program,
Division of Physical Sciences and Engineering,
King Abdullah University of Science
and Technology (KAUST),
Thuwal 23955-6900, Saudi Arabia
e-mail: ravi.samtaney@kaust.edu.sa

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 14, 2014; final manuscript received August 14, 2014; published online September 10, 2014. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 137(2), 021301 (Sep 10, 2014) (9 pages) Paper No: FE-14-1021; doi: 10.1115/1.4028337 History: Received January 14, 2014; Revised August 14, 2014

A theoretical framework to model the dynamics of acoustically driven microbubble inside a rigid tube is presented. The proposed model is not a variant of the conventional Rayleigh–Plesset category of models. It is derived from the reduced Navier–Stokes equation and is coupled with the evolving flow field solution inside the tube by a similarity transformation approach. The results are computed, and compared with experiments available in literature, for the initial bubble radius of Ro = 1.5 μm and 2 μm for the tube diameter of D = 12 μm and 200 μm with the acoustic parameters as utilized in the experiments. Results compare quite well with the existing experimental data. When compared to our earlier basic model, better agreement on a larger tube diameter is obtained with the proposed coupled model. The model also predicts, accurately, bubble fragmentation in terms of acoustic and geometric parameters.

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Figures

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Fig. 1

Schematic of the proposed coupled model

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Fig. 2

Maximum bubble radius as a function of PNP of acoustics for (a) Ro = 1.5 μm and (b) Ro = 2 μm for two vessel diameters. The basic model is the one proposed in Ref. [34].

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Fig. 3

Maximum bubble radius as a function of vessel length for Ro = 1.5 and 2 μm. The basic model is the one proposed in Ref. [34].

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Fig. 4

Spatial evolution of (a) F and (b) G at various time instance in an acoustic cycle for Ro = 2 μm, D = 200 μm, and PNP = 325

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Fig. 5

Temporal evolution of F and G functions for (a) Ro = 1.5 μm, D = 12 μm, and PNP = 1350 kPa and (b) Ro = 1.5 μm, D = 200 μm, and PNP = 175 kPa

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Fig. 6

Temporal evolution of bubble interface velocity (VB) and shear stress (Cf) for (a) Ro = 2 μm, D = 200 μm, and PNP 175 kPa and (b) Ro = 1.5 μm, D = 6 μm, and PNP = 1350 kPa

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