Chemistry Reference
In-Depth Information
curvature and differential bubble pressure, is the theoretical principle of
measurement (Loglio et al. 1996, 2001, Kovalchuk et al. 2001, Miller et al.
2000, Rusanov and Prokhorov 1996, Neumann and Spelt 1996, Cheu et al.
1998).
In order to describe a liquid meniscus and hence to obtain the interfacial
tension from the shape of a drop or bubble the Laplace equation is used.
This equation describes the mechanical equilibrium of two homogeneous
fluids separated by an interface (Rusanov and Prokhorov 1996, Neumann
and Spelt 1996) and relates the pressure difference across the interface to
the surface tension and the curvature of the interface
§
¨
·
¸
'
11
J
P
(1)
RR
1
2
Here
R
1
and
R
2
are the two principal radii of curvature, and '
P
is the pres-
sure difference across the interface. '
P
can be expressed as a linear func-
tion of the elevation
gz
'
P
'
P
'
(2)
0
where '
P
0
is the pressure difference at a reference plane, 'U is the density
difference between water and air,
g
is the gravity constant and
z
is the ver-
tical height of the bubble measured from the reference plane. The earliest
efforts in the analysis of axisymmetric interfaces (drops and bubbles) were
those of Bashforth and Adams (1883). Later many authors improved the
calculations by using computer programmes to integrate the Laplace equa-
tion. An important step ahead was the development of the Axisymmetric
Drop Shape Analysis (ADSA), which allows fitting the Laplace equation
to the shape of drops or bubbles obtained by a video camera (Neumann
and Spelt 1996). Today, due to increased quality of the video chips, the
various corrections introduced into the ADSA package became less impor-
tant so that simple calibration procedures can be applied rather than a cali-
bration with a grid covering homogenously the whole field of the screen. It
has been demonstrated that a determination of the magnification by using a
single sphere is usually sufficient to reach high accuracy of the measure-
ments, typically better than 0.1 mN m
-1
.
The oscillating bubble tensiometer, devised for marine studies, shows a
particular feature, consisting of a couple of inlet and outlet tubes (Figure
1). Such conduit allows sea water to be fed either from the sampling bottle
or directly from a continuously-flowing pumping system, submersed in the
sea. Then, the tensiometer vessel can be initially flushed with sea water for
