Foam stability in gas injection foaming process
Xing Nan Liu
•
Yan Xiang Li
•
Xiang Chen
•
Yuan Liu
•
Xue Liu Fan
Received: 7 February 2010 / Accepted: 24 June 2010 / Published online: 13 July 2010
Ó Springer Science+Business Media, LLC 2010
Abstract Particle coverage ratio on bubble interface was
investigated by metallographic analysis when the foam is
critically stable in the gas injection foaming process. It is
found that the critical coverage ratio was almost the same
under different conditions, such as different particle
amount, particle size, or particle wettability. The particle
coverage ratio is proposed as the criterion to judge the
foam stability, and a criterion equation was deduced.
Adsorption coefficient of particles, effective coverage ratio
of a particle and critical coverage ratio on the bubble
interface are stability influencing parameters of the crite-
rion equation. Their determination methods were presented
and examined by air injection foaming of A356/Al
2
O
3
melt. The adsorption coefficient calculated by measuring
cross-section of foam cell wall gave values agreeing with
the experimental results. The effective coverage ratio,
which is about 0.9 in this article, can be calculated by
combining measurements on surface and on the cross-
section of the foam cell wall. The critical coverage ratio,
that is about 14% in this article, can be determined by
measuring the cross-section as well as the surface of the
foam cell wall.
List of symbols
A
b
Equator area of a bubble in Eq. 1 (cm
2
)
E
k
Adsorption coefficient of particles in Eq. 1
h Nozzle immersion depth in Eq. 1 (cm)
N
P
*
Critical number of particles required to stabilize
the bubble in Eq. 1
V
P
Volume of a single particle in Eq. 1 (cm
3
)
vol.% Particle volume percentage in Eq. 1 (%)
b
*
Critical foam stability parameter in Eq. 1 (cm)
A Coverage area of particles on the bubble
interface (mm
2
)
D Diameter of a bubble, or pore size
in the foam (mm)
d Diameter of particles (mm)
d
0
Two-dimensional diameter of particles
measured by metallographic analysis (mm)
d
a
Two-dimensional diameter of particles
on the bubble interface (measured
on the surface of the foam cell
wall by metallographic analysis) (mm)
d
l
Two-dimensional diameter of particles on the
bubble interface (measured on the cross-section
of the foam cell wall by metallographic
analysis) (mm)
d
1
,…,d
n
Diameter of different sections of particle when
measuring two-dimensional diameter of the
particle by metallographic analysis (mm)
E Effective coverage ratio of a particle, ‘‘effective
coverage ratio’’ for short
F
V
Volume percentage of particles in the melt (%)
F
Vf
Volume percentage of particles in the foam (%)
F
Vf
0
F
Vf
calculated by Eq. 13 (%)
F
Vf
00
F
Vf
calculated by Eq. 21 (%)
F
Vf1
Volume percentage of particles attached on the
gas/solid interface (%)
X. N. Liu Á Y. X. Li (&) Á X. Chen Á Y. Liu Á X. L. Fan
Department of Mechanical Engineering, Tsinghua University,
Beijing 100084, People’s Republic of China
e-mail: yanxiang@tsinghua.edu.cn
Y. X. Li Á X. Chen Á Y. Liu
Key Laboratory for Advanced Materials Processing Technology,
Ministry of Education, Beijing 100084,
People’s Republic of China
123
J Mater Sci (2010) 45:6481–6493
DOI 10.1007/s10853-010-4736-5