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Dynamics of rising bubbles in initially quiescent liquids that are later on disturbed by falling drops

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Abstract

Three-dimensional dynamics of rising bubbles in initially quiescent liquids that are later on disturbed by falling drops has been numerically investigated. The effects of various parameters such as Eotvos number (Eo), Morton number (M), size of the falling drop, single and multiple falling drops on the dynamics of three different cases represented as single bubble rising, inline bubbles rising and offset bubbles rising are investigated. From the results, it is observed that the final bubble rise velocity in disturbed liquid (with Eo = 38.8 and M = 9.71 × 10−4) due to the impact of falling drop with 0.01 m diameter is increased by 84.21% when compared to the rising bubble in undisturbed quiescent liquid. The same decreases with an increase in the diameter of falling drop up to 0.02 m and 0.03 m, respectively. For inline and offset bubbles, the disturbance caused by the falling drops reduces the final rise velocity by 110% and 113.4%. For Eo = 10.0 and M = 9.71 × 10−8, the low fluids internal resistance causes the bubble to rise faster and reach the liquid surface quickly. However, in the case of inline and offset rising bubbles, the bubbles reach the liquid surface even before the falling drop impacts.

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Abbreviations

D :

Diameter (m)

Eo:

Eotvos number

f :

Force vector (kg m s−2)

g :

Acceleration due to gravity (m s−2)

H :

Height (m)

k :

Curvature (m−1)

L :

Length (m)

M :

Morton number

p :

Pressure (kg m−1 s−2)

Re:

Reynolds number

t :

Time (s)

U :

Velocity vector (m s−1)

W :

Width (m)

α :

Volume fraction

µ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

σ :

Surface tension (kg s−2)

\({\varvec{\uptau}}\) :

Viscous stress tensor (N m−2)

\({\varvec{\uptau}}_{\text{t}}\) :

Turbulent stress tensor (N m−2)

b:

Bubble

d:

Drop

eq:

Equivalent

g:

Gas

l:

Liquid

r:

Relative

T:

Terminal

z :

Vertical direction (direction of bubble rise)

1:

Lighter fluid (gas)

2:

Heavier fluid (liquid)

2D:

Two-dimensional

3D:

Three-dimensional

VOF:

Volume of fluid

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  1. Center for Advanced Energy Studies, Koneru Lakshmaiah Educational Foundation, Vaddeswaram, Andhra Pradesh, India

    Rajesh Nimmagadda

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  1. Rajesh Nimmagadda
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Correspondence to Rajesh Nimmagadda.

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Nimmagadda, R. Dynamics of rising bubbles in initially quiescent liquids that are later on disturbed by falling drops. J Braz. Soc. Mech. Sci. Eng. 42, 526 (2020). https://doi.org/10.1007/s40430-020-02612-y

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