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Bubble Formation at a Submerged Orifice in High-Speed Horizontal Oscillation

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Abstract

Reducing the cell size of aluminum foams is always a hot and difficult topic in the fabrication of aluminum foams by gas injection route. There lacks theoretical guidance for the bubble size reduction when foaming by the dynamic gas injection method. For the convenience of observation, the aqueous bubbles from small-sized orifice in the high-speed horizontal oscillation were investigated in this paper. A bubble formation and detachment model in the high-speed horizontal oscillation system was proposed. The high-speed system with horizontal simple harmonic oscillation could reduce the average bubble size of aqueous foam effectively. The regularity of bubble formation and the influence of experimental parameters on average bubble size can be predicted by the theoretical model, and the experimental results agree well with the theoretical calculation. The results have shown that bubbles generally detach from the orifice at deceleration periods of the simple harmonic oscillation, and there exist several fixed sizes of bubbles with the fixed experimental parameters due to the effects of periodic forces. The average bubble size decreases with the increase of oscillation frequency and amplitude, and it roughly increases with the increase of gas flow rate. Using the high-speed horizontal oscillation method to prepare aluminum foams, the cell size can be reduced to about 1 mm. Moreover, the cell sizes of aluminum foam can be well predicted by this theoretical model.

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Abbreviations

a :

Acceleration of the orifice (m/s2)

a d :

Orifice acceleration at the end of the detachment stage (m/s2)

\( \bar{a} \) :

Average liquid acceleration across the bubble (m/s2)

A :

Oscillation amplitude (mm)

C D :

The overall drag coefficient

d 0 :

Contact diameter between the bubble and orifice(m)

d d :

Equivalent diameter of the bubble at the end of detachment stage (m)

d i :

The inner diameter of orifice (mm)

D N :

The diameter of tube for flowing liquid, namely the width of flowing liquid in a tube along the bubble growth direction (m)

f :

Oscillation frequency (Hz)

F σx :

Horizontal component of surface tension force (N)

F σx0 :

Horizontal component of surface tension in static condition (N)

F D :

Viscous force (N)

F I :

Inertial force (N)

M :

Effective mass of the bubble (kg)

Q :

Gas flow rate (m3/s)

Q T :

The gas flow rate at the temperature of T in orifice (m3/s)

r :

Equivalent spherical radius of the bubble (m)

r e :

Equivalent radius of the bubble at the end of the expansion stage (m)

r d :

Equivalent radius of the bubble at the end of the detachment stage (m)

Re :

Reynolds number

s :

The oscillation displacement of orifice (m)

t :

Oscillation time (s)

t 0n :

The initial moment of the nth bubble (s)

t dn :

The detachment moment of the nth bubble (s)

T :

The temperature of orifice (K)

v :

Velocity of the orifice (m/s)

v d :

Orifice velocity at the end of the detachment stage (m/s)

\( \bar{v} \) :

Average liquid velocity across the bubble (m/s)

V :

Volume of the bubble (m3)

α :

The assistant angle at upstream half of the bubble as shown in Figure 3(b) (Rad)

β :

The assistant angle at downstream half of the bubble as shown in Figure 3(b) (Rad)

θ :

Contact angle at any position of the contact line (Rad)

θ 0 :

Equilibrium contact angle of system (Rad)

θ a :

Advancing contact angle when the bubble tilt (Rad)

\( \theta_{a}^{\prime } \) :

Advancing contact angle at the end of expansion stage (Rad)

θ r :

Receding contact angle when the bubble tilt (Rad)

μ :

The dynamic viscosity of the liquid (Pa s)

μ m :

The viscosity of the aluminum alloy melt (Pa s)

μ r :

The viscosity of the melt after adding Al2O3 particles (Pa s)

ρ g :

Density of air (kg/m3)

ρ l :

Density of the liquid (kg/m3)

σ :

Surface tension of the liquid (N/m)

φ :

Horizontal projection angle of the vibration motor with circular motion (Rad)

φ p :

Volume fraction of particles

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Acknowledgment

This work is supported by the International Cooperation Project of Ministry of Science and Technology of China (Grant No. 2013DFR50330).

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Correspondence to Xiang Chen.

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Manuscript submitted April 22, 2016.

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Wang, N., Chen, X., Yuan, J. et al. Bubble Formation at a Submerged Orifice in High-Speed Horizontal Oscillation. Metall Mater Trans B 47, 3362–3374 (2016). https://doi.org/10.1007/s11663-016-0776-9

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