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Bubble-size distributions in foams
13
Advances in Collaid and Interface Science, 38 (19921 13-32
E~vier~ien~Publ~beraB.V.,~~r~
Bubble-size Distributions in Foams. C.Q.J. Bisperiak2, A.D. Roateltap' and A. Prim+' ' Heineken
Techniech
Beheer
bv,
Burgemeester
Smeetsweg
1,
2382
PH
Zoeterwoude, The Netherlands. a Agricultural University Wageningen, Dept. of Food Science, Bomenweg 2, 6703 HD Wageningen, The Netherlands.
Bubble-size
distributions
in foams can be used to study foam properties
physical procassas that contribute and disproportjonatian. rate of drainage,
and to distinguish
betwen
to the breakdown of the foam. These processes are drainage,
A new Foam Analyzer was developed to measure various foam characteristics
the rate of foam collapse,
the gas fraction
in the foam and the bubble-size
the
coalescence like the
distribution.
IN!FRODUCTIOlJI Soap froths, crude oil foams, bread, beer foam, shaving cream, fire fighting foams and poly-urethane insulating materials are all examples of aerated products. These aerated products are foams or have been foams during processing. These foams have a great variety of wanted and/or unwanted properties. Obviously these properties depend on the composition of the gas and liquid phase. However, the properties of a foam also depend on the distribution of the gas and liquid phase. Foams are principally unstable, meaning that foam .properties vary with time as a result of shifts in the distribution of gas and liquid in the foam. Three different processes contribute to the instability of foams i.e. drainage, coalescence and disproportionation. Drainage is the liquid flow from a foam as a result of gravity and capillary forces. As a consequence of drainage a foam becomes dryer and bubbles may become distorted. In that case foams change from spherical foams to polyeder foams.
Al-~~/92/$15.00
0 1992-ElsevierSciencePublisbersB.V. Allrigbtareserved.
14
Coalescence rupture in
is the merging
of two bubbles
of the film between
the
foam
and
Disproportionation Ostwald
is
ripening.
As
grow at the expense
the bubbles.
the
number
Larger
of
interbubble a result
as a result
gas
bubbles
bubbles
bubbles.
appear
decreases.
diffusion,
of gas diffusion
of smaller
of the
also
called
larger
Smaller
bubbles
bubbles
shrink
and finally disappear. These effect the processes may distribution of the liquid and gas phase and thus alter the foam properties In
(Ronteltap[l]).
figure
processes fresh
1
beer
sinter.
an
example
is
on the appearance foam
that
is
given
of beer
of
the
produced
by
sparging
It may contain either carbon dioxide
the initial
bubble-size
on the kind
of gas that is used to produce
the
bubble-size
bubbles
have
a
In figure
presented. result
spherical
The
foam
because
no
gas
and
the
figure
lc
a
2.5
solubility
As a result
is
nitrogen
beer
beer
foam.
evidence
of
difference
the
foam. from
old
become
have
depends
of
carbon
fact
bubbles
that
in appearance
dioxide
has
become
is low.
of a nitrogen
and carbon
with respect
dioxide
a
of
foam
can be related
distribution
in the foam. Additionally,
distribution
and bubble-size
the progress
of the three physical
In is
in the foam Coalescence
smaller
disproportionation
solubility
of carbon
As
0.20 to
smaller.
beer
the gas fraction
can be explained
foam properties
is
on the solubility
in beer
after two and a half minutes
Thus
foam
not take place in 2.5 minutes
of nitrogen
of drainage
number
all
20%
have both contributed to coarsening
and disproportionation large
and radius
has become 0.95 and the larger bubbles are distorted.
A
Initially
80% gas and
decreased
bubbles
minutes
independent
bubble
fresh
because
larger. This must be a result
did practically
the
a
the foam.
about
fraction
the rate of gas diffusion
of the
'gas through
or nitrogen
mean
old
than
liquid
have become
Disproportionation
presented.
The
these a
monodisperse
foam contains
is dryer the
0.09. Also bubbles
time because
almost
of
la presents
is practically
lb a 2.5 minutes
of drainage
coalescence
is
shape.
200 pm. The
approximately liquid.
distribution
distribution
effect
foam. Figure
of the giving
occurred.
The
dioxide
foam
by the higher
gas
to nitrogen.
to the bubble
and liquid
the shifts in the liquid
distribution
can be used to monitor
processes.
Figure
1: Photographs either
CO, or N, gas,
nitrogen minutes
of (la) a fresh beer foam containing (lb) a 2.5 minutes
beer foam and
(lc (next page))
old carbon dioxide
beer foam.
old a 2.5
Figure lc:
A 2.5 minutes old carbon dioxide beer foam.
Narsimhan Ruckenstein[2] principle to and used this investigate the enrichment of surfactant in a semibatch foam fractionater and described a model that accounts for the initial bubble-size distribution, drainage, coalescence and disproportionation. The bubble-size distribution in foams was also investigated to relate it to the rheological behaviour of a foam. Calvert and Nezhati[3][4]
presented
effect of the bubble-size the distribution on the flow properties of a foam passing through a
pipe. They described the flow with a modified Bingham plastic model and found that the yield stress of the foam depends on the bubble-size distribution. However, Xhan and Armstrong[SJ found that the yield stress, the critical strain and the stress-strain relation is independent of the bubble-size distribution. Pavel[6] described a model that relates the bubble-size distribution to the height of the foam in a steady-state foaming column. The model accounts for drainage and coalescence. The relation between the bubble-size distribution and coalescence is mentioned by Mihail and Straja(71. They presented a model describing the bubble-size distribution in
17
and explained
why a bubble-size
distribution
Hartland[8]
as a result
of coalescence.
coalescence
times in steady-foams
the
of the
height
distribution the
model
based
predicting beer
foam
in the on
caused
by
a1[12]
examined
foaming
interfacial
gas
of the
Bhandola
coalescence
this
whereas
diffusion
column
effect
of the foam height
Unfortunately
disproportionation
The
is discussed.
the variation
foam.
model
not
of beer
et
the
that within
used
size
account
foam
al[lO][ll]. in
is mainly
3 times binary
described carbon The
dioxide effect
diffusion and
coalescence
the period
of bubble
takes place. Jeelani
the creation and breakdown
Lemlich[l4]
the
initial
bubble-size
investigated
in a bubble
anionic,
column.
they concluded
From
This
bubble-size
Ranadive
Lemlich[l6]
distribution
of disproportionation. and Schechter[l7].
big
to
gas
then
differences.
Runga-Kutta
This
model
led
to
Lemlich[lO]
compared
dimensionless
initial distributions
De Vries[21][22] discussed bimodal
of gasses
experiments
it
model
the
by Monsalve
recalculated
the model
method but found
Lemlich[lS]. for
initial
on the progress
presentation
by
three
of
a
new
Cheng
and
generalized
among which are the empirical
and the theoretical
distribution
This work has led to the
with which the shifts in an initially
distribution
can
in foams
(Rieser
was
that
numerical
relating
(Lemlich[l5]).
is confirmed
and Hoelscher[23].
of an apparatus
bubble-size
diffusivity the
distribution
by Gal-or
development
the
were a result of
influence
the
distribution
nonionic
bubble-size
of a model
presented
Cheng and Lemlich[l8]
gas
Jashani
did not take place
diffusion
This observation
on
and
observed
distribution
has a major
results using a Ith-order
Boltzmannlike
cationic the
led to the development
distribution
and
bubble-size
no
distribution and coworkers.
that coalescence
but that shifts in the bubble-size gas diffusion. the
et a1[13]
solutions. of
distribution
that
of foams from supersaturated
in foams was studied by Lemlich
surfactants
et
steady-state
rise the mean bubble size increased by a factor of 2 meaning about
in for
Jeelani
a
to
bubbles,
and bubble
distributions
and concluded
and
bubble-size
et a1[9]
of
does
the collapse Ronteltap
bubble-size
bimodal
drainage
and related these processes
column.
foam
may become
described
concluded
be
that
used
to
measure
and Lemlich[24]). gas
diffusion
the From
can
be
18
enhanced by convection in the liquid foam films. Markworth[25] discussed foam stability and Ostwald ripening taking into account the effect of bubble size. Bubble-size distributions were also used to determine the film thickness in the foam, but the results were subject to errors as described by De Vries[21]. The relation between the bubble-size distribution and the rate of drainage is described by Rand and Kraynik[26] for foams of drilling fluid. The enhanced stability of foams with smaller bubbles was explained by a decrease of drainage. Sita Ram Sarma and Khilar[27] found that a more uniform bubble-size distribution and high initial gas volume fraction gave more stable foams. This was explained by reduced gas diffusion as discussed by the authors. As stated before, knowledge about the bubble-size distribution in a foam is essential for a better understanding of foam properties and the stability of those properties. Shifts in bubble-size distributions can be used to distinguish between the physical processes that contribute to the changes of foam properties. Therefore it is no surprise that bubble-size distributions have been subject to intensive study. A great variety of experimental techniques has been developed. Bubble-size distribution can be measured by photographing the foam through a glass wall and analyzing the obtained images De Vries[22], Sasaki et a1[28]. Cheng and Lemlich[29] described the errors that can be made when bubble-size distributions are measured this way. At the surface of a glass wall a relative higher number of larger bubbles is observed. In addition larger distorted at the bubbles will be glass wall and disproportionation and coalescence rates may be effected by the presence of a glass wall, leading to a locally different bubble-size distribution. Bubble-size distribution can also be measured by freezing the foam and examination of a cross section Savitskaya[30], Chang et al [31]. It is argued that the freezing process does not influence the bubble-size distribution, but this may be disputed for different foams and freezing methods. Additionally, the actual bubble radii in a foam are not equal to the observed circle radii in a cross section because a cross section is in
19
general not made through the middle of the bubbles. Therefore, a proper statistical method must be used to calculate the bubble-size distribution from the observed two dimensional
circle
radii e.g. Goldsmith[32] or De Vries[22]. Bubble-size distributions were also measured at the surface of foams Segel et al[33]. This may lead to very serious errors if the distribution in the top layer of the foam does not correspond to the distribution inside the foam. Drainage, gas diffusion processes and coalescence may proceed differently at the surface of a foam. In addition bigger bubbles tend to rise to the foam surface. Bubble-size distributions can be obtained with a microscope Richardson and Nandra[34] or electron microscope Jackson et al[35] but the above mentioned possible errors in measurement are also applicable to these methods. More recently a new method to measure the bubble-size distribution in foams was described by Selecki and Wasiak[36] and Besio et a1[37]. To this end the foam is led through a capillary that has a smaller diameter than the smallest bubbles in the foam. The distances between liquid films in the capillary are measured and used to calculate the bubble-size distribution. Rieser and Lemlich[24] used this method to measure the shift in bubble-size distribution as a result of interbubble gas diffusion in an initially bimodal distribution. A disadvantage of the method is that it can only be used to measure relatively stable foams because the method can easily effect the bubble-size distribution. Bubble-size distributions in bubble columns were measured with a conductivity probe (Lewis et a1[38]). With the method bubble velocities were measured in addition to bubble sizes. A similar probe was used by Frijlink[39][40]. However, this probe was not based on conductivity but on an optical phenomenon using a glass-fibre. None of the above mentioned experimental techniques distinguishes between drainage, coalescence and disproportionation. The properties of the foam are not satisfactory characterized, because the liquid and gas distribution in the foam is not or only partly measured. For this purpose a new Foam Analyzer was developed to measure various foam
20
properties
like the collapse
gas fraction method
analyzer through
in the foam, and the bubble-size
is based
by Frijlink.
of foam, the rate of drainage,
on the optical
The difference
is based
bubbles
of a single
in a foam whereas
is based on the use of a stationary which the velocity
distribution.
technique
between both methods
on the use
immobile
glass-fibre
The
described
is that the Foam
probe
that
is moved
the Frijlink
multi glass-fibre
and the size of passing
the
bubbles
method
probe with
is measured.
EXPERIMENTAL
The Foam Analyzer of the apparatus
is displayed
in figure 2. Two different
can be distinguished.
continuous light source
2: A schematic
presentation
to move the glass fibre downwards and
an
opto-electronic
glass-fibre
part
unit of the Foam Analyzer.
through a foam at known speed
that
consists
of
an
optical
probe and electronic equipment for signal conversion,
data-acquisition
and data processing.
The glass fibre has a diameter is melted
part is used
photo-electric cell
Opto-electronic Figure
A mechanical
parts
of 200 pm. The end of the probe
in a oxygen-propane/butane
the tip has a diameter melted hemispherical
of
flame and elongated
about 20 pm. The
end
(see figure 3). Frijlink[40]
of the
until tip is
foundthatthe
21
LIGHT
UGHT
REFLECTED LIGHT
REFLECTED LIGH
3b
Figure
3: A schematic
presentation
reflection
of the fibre tip with the
of light when
it is in the gas phase
and
in the liquid phase.
highest
efficiency
hemispherical-shaped send
into
the
in
a
fibre
end. From the opto-electronic
fibre.
emitted. However,
obtained
is
At
the
end
of
the
fibre
on the refractive
light
and returned
unit. The amount of reflected
index of the medium surrounding
index of the medium
is approximately
index of the glass,
almost no light is reflected.
if the refractive
hand,
the light
is reflected.
the same as the
is converted sampled
index of the medium
is much part of
Thus, more
light is reflected
Packard
at a frequency
Vectra
known
calculated.
the
of 1 Mhz with
80386
Because
distance
Thus,
cm s‘I the signal
analogue
corporation)
QS/20
80387 co-processor. is
to a light sensitive
into an electronic
(DAS-50 by MetraByte
On
index of glass, a considerable
when
tip is in gas than when the tip is in liquid. The reflected goes via an y-splitter
to
the tip. If the
refractive
lower than the refractive
is
light depends
refractive
the other
a
unit light is most
part of the light is reflected
the opto-electronic
with
light
cell where the light
signal.
This signal
a data-acquisition
that
the
is placed
is
board
in a Hewlett-
computer
(20 Mhz)
the probe
speed and the sample rate
between
two
sample
equipped
points
with
can
a
be
if the probe is moved with a speed of about 10 is sampled
every 0.1 pm.
22
pathof
analoguesignal _____________._.
+I!
liquid level
digitized signal I
I
---P
dry level
I
I
gas
liquid k
Distance 4: A schematic
Figure
representation
when the probe
of events which
is moved through
the path of the probe and chord middle
and at the bottom
digitized
If the
probe
Figure
lengths.
through
a foam
an alternating
gas and liquid is obtained
that
the
signal
is high
when
by liquid and low when the probe tip is by gas. signal is digitized
in Asyst
positive
and negative
is considered
3.1.
The
analogue
tip
is
by means of a computer program
program
distinguishes
between
slopes of the signal. The analogue
to be a 'wet' signal
to
the bubbles.
the probe
surrounded
The analogue
and
corresponding
through
surrounded
written
In the
resp. the analogue
lengths that the probe travelled
4 shows
a foam. At the top
signal
is put
signal representing the chord
perform
the
signal
(i.e. the probe is surrounded
from the point where the slope of the analogue
by liquid) becomes
to the point where
positive
signal is considered
The analogue
the probe tip is surrounded
the slope becomes
to be a 'dry' signal
signal
negative. (i.e. when
by gas) in between the 'wet' signals.
that are part of a 'wet' signal
are assigned
The sample
points
the number
'1' and the sample points that are part of a 'dry' are
assigned
the number
obtained
of which
'0'. This way an apparent
counting
length
that of
distances calculation example.
the the
number
probe
these
of
iS
chord
the
chord
I and
III
are
><-III-><-
sample
travelled
of
points
through
lengths lengths
chord
a
can
is
of
a
single
certain
be
lengths
that
phase.
From this example
chords
I, II and III are respectively with a probe
chord
phase
the
calculated.
illustrated
by
The
the
correspond
liquid phase and II is a chord length that corresponds
calculated
signal
a part may look like this:
. . .00011111100000000000111111100... -><-->< II I By
digital
next
to
the
to the gas
it can be seen that the lengths
of the
0.6 pm, 1.1 pm and 0.7 Pm
speed of 10 cm S-I and a sample
rate of
1 Mhz. The chord lengths the probe travelled calculated point
by a procedure
of the digitized
through the gas phase are
in the computer
program.
signal has an index number
to an array number. The array has a dimension of computer
memory).
stores
index
the
The computer
numbers
'wet' chord
higher
than
fraction is
lengths
'dry' chord
the
sum
the
corresponding index number
less computer
of
first sample
case.
the
'wet'
The
memory
point
of
the
chord
than
storage
of
'dry' chord
lengths
is
chord
lengths
than the liquid distance
to the gas phase 'dry'
(2 Mb
the array and
points
of
chord
and
of the subsequent
distribution
the
gas
which length
by using
*wet' chord
index
'wet' chord
of 'dry' signals
the
chord
can be calculated
length
if
fraction,
each
of the last sample point of the
the
a chord-length
analyzes
sample
The sum of the
in the foam is higher
usually
preceding
takes
lengths.
the
of
program
corresponding
of 1.000.000
to the liquid phase, because storage of the
lengths corresponding
the
Every sample
number length.
is obtained.
the
length of the Thus,
24 The chord lengths are a measure for the bubble-size distribution in the foam. To calculate the bubble-size distribution in the foam a problem similar to the 'tomato salad' problem has
to be
solved. The measured
one-dimensional gas
lengths are not equal to the actual three-dimensional bubble radii, because the probe hardly ever travels through the two polar ends of a bubble. Furthermore bubbles with large diameters have a greater chance of being pierced by the optical probe than bubbles with Weibel[41] smaller diameters. and later Kawakami[42] developed a statistical method to calculate the three-dimensional size distribution from the one-dimensional chord length distribution. This method was modified and used for the calculation of the bubble-size distribution in the foam. The bubble-size distribution is given as the number of spheres per ml foam per class of sphere diameters. Bubbles were assigned to 35 classes with a width of 50 pm from 0 pm up to 1750 pm. The measurement is carried out in the following way. A fixed volume of the liquid is poured into a cylindrical glass. The glass contains a sintered glass bottom through which a gas can be sparged to produce a foam column. First the level of the liquid surface is measured with the optical probe before the foam column is produced. This level is stored in the computer and later used to calculate the gas fraction. Then a foam column is produced by dispersing gas through the glass sinter with a constant flow rate until the foam surface reaches a predetermined level. The production of foam up to this level takes about 10 seconds and the height of the foam column is then about 10 cm. This large height
is necessary to ensure that at least 200
bubbles will be detected by the probe, so that a reliable statistical calculation is possible. Then the gas supply is stopped and the first measurement is done by lowering the probe through the foam in approximately 1 second. During the measurement the computer subsequently registers the upper level of the foam (i.e. the level of the first transition of a gas signalto a liquid signal), the chord-length distribution and the level of the liquid-foam interface (i.e. the level of the last gas-liquid transition found in the signal).
25
If the
measurements
consecutive
time
are
carried
intervals
the
out
rate
in the
same
of drainage,
sample
the
at
collapse
rate of the foam, the changes
in foam volume and the gas fraction
in the foam can be determined
in addition to the evolution
bubble-size
The
distribution.
accuracy
fraction results
height
of
the
method
can
be
in the foam can be measured
from
the
measurement.
the gas fraction
where
checked
because
in two different
In one way the gas fraction
can be compared.
directly
of the
Because
with
can be calculated
the
using
the
gas
ways
and
is obtained
data
of
equation
foam
1:
ep:
gas fraction
h LI :
height of the liquid surface before a foam column
in the foam.
[n?mJ]
is produced. h,:
height
of the upper
h,:
height
of the liquid-foam
In the other way as follows
phase
divided
gas fraction
interface
from the theory,
equal to the sum of the chord
[ml [ml
level of the foam
lengths
by the foam height.Both
[ml
the gas fraction
corresponding methods
is
to the gas
to determine
the
must give the same result.
RESULTS
In figure
5 the gas fraction
chord-length fraction
distribution
in the foam
and
in the foam calculated the
independently
(eq. 1) is presented
from the
measured
as a function
gas
of time.
It is clear that these gas fractions do not differ significantly. Therefore
the
distributions
conclusion
can
be
drawn
that
in the foam can be accurately
the
bubble-size
estimated
with the
Foam Analyzer. In Figures foam
6a and
at t=O and t=2.5
6b signals
obtained
by measuring
minutes are presented.
In these
CO, beer figures,
26
gas/foam volume ratio 100
95
75 ’ 0
1
T&e
[min.] gas fraction (calculated) --A--
gas fraction (measured)
and the calculated
5: The measured
Figure
[m3mT3]versus
I 5
4
3
time
gas
fractions
[min].
Signal level
Signal level
-1
6a 7
ml
4ol
em
Ku
1
0
200
4al
6: The signals
Figure
t=O
eul
‘ml
Bm
Array index number
Array index number
obtained
by measuring
(6a) and t=2.5 minutes
CO, beer foam at
(6b).
for the sake of clarity
every 100th sample point of the total of
1.000.000
are plotted.
scale
sample points
of the
numbers
reflection
air.
and
at
the
X-axis
is an arbitrary the
array
that this
and that the resolution
index
is a rough
is low.
above the foam a constant gas signal is obtained.
level starts As
level
It must be mentioned
of the signal
Initially signal
signal
are plotted.
The Y-axis
soon
as
low because
the
probe
the probe
penetrates
travels the
foam
initially the
The in
signal
21
increases.
the height
Thus,
alternating
calculate the bubble-size at the
of the
foam
is measured.
signal of gas and liquid is obtained
liquid
the probe
the
Finely the signal remains
distribution.
level when
Then
that is used to
has passed
the
foam-liquid
interface. As can be seen signal
in figures
it takes
some time before
result of drainage
the
tip
differences probe.
upwards
between
However,
level of the
This is a result
dry as a
of the liquid after it leaves
mechanism
the
'dry'
of the fact that
the tip of the probe becomes
and evaporation
the liquid film. A possible from
6a and 6b, the
is not always reached.
probe
is the flow of liquid away
caused
by
Laplace
pressure
the very small tip and the upper part of the
the signal starts to decline
sharply
as soon as
the thin liquid film around the tip of the probe becomes thinner. When the probe penetrates period,
the signal
completely concluded
reaches
the next liquid film within this drying
increases
again to the liquid level before
it
the 'dry' level of the gas phase. This can be
from the fact that the longer the probe travels through
the gas phase after it pierced through a liquid film, the further the signal decreases
to the 'dry' level. This phenomenon
interfere
with
influence
on the above mentioned
Another
the outcome
observation
signal changes
of the experiment digitizing
that can be made
foam. This
as the probe moves downwards
the
foam
is more
can be explained
coarse
it has no
process.
is that the shape of the
the top of the foam the films are thinner Furthermore
because
does not
through
the foam. In
and the foam is dryer.
in the
upper
part
by the fact that the foam
of the
is older
in the top than in the bottom and liquid from the upper part must drain
through
forces.
the
lower
As a result,
and coalescence
part
of
have proceeded
From the differences figure 6b the following
after
measure
can be concluded.
for the collapse
as a function
by
gravity
in the top of the foam. in figure 6a and
The foam collapses
transition
From this
with
is found more to the
shift to the right
a direct
rate of the foam is obtained.
the last gas-liquid
transition
of time. This corresponds
liquid interface
caused
disproportionation
in the signals presented
2.5 minutes.
Furthermore,
foam
drainage,
further
time because the first gas-liquid right
the
the processes
and is a measure
shifts
to the
left
to the rise of the foam
for the rate of liquid drainage
Loe-cfwss(~‘) I
‘L
(1
................... .7a ...
* s
.,. _,.,,., ,.,. ._.j.,. . . .. . .,.
7b ‘.
. ‘. .._.._..._.....,.......
t. .t....(...(
Figure 7: The bubble size distributions of a CO, beer foam at t=O (7a) and tm2.5 minutes (7b) and the bubble size distributions of a W2 beer foam at t=O (7~) and t==2.5minutes (?d).
from the foam. With the change of the levels of the top of the foam and the foam-liquid interface, the change in foam height or volume are obtained. In figures 7a and 7b the bubble-size distributions in beer On the vertical axis the number foam@ made by CO, are presented. of bubbles per ml is displayed. It has to be emphasized that the ~-axis is a logarithmic scale. Therefore small variations in bar height represent: large differences in the numbsr of bubbles. On the horizontal axis the bubble size is displayed divided into classes with widths of 50 Pm. These bubble-size distributions were calculated from the signals presented in respectively figures 6a and Bb, The time intervals between the measurements is 2.5 minutes, Additionally, the bubble-size distributions of beer foam containing nitrogen at t=4 and t=2.5 minutes axe
29
presented in figure 7c and 7d respectively. As can be seen the bubble-size
distributions
presented
in
figure
7
correspond
qualitatively very well with the images of beer foam presented in figure 1. Initially the bubble-size distribution in a fresh beer foam are independent on the kind of gas that is used to produce the foam. The distributions in figure 7a and 7c are approximately equal. The gas fractions in the foams were respectively 82.6% and 83.6%. However, after 2.5 minutes the bubble-size distributions of the foams containing CO, and N, are completely different. The gas fraction in the foam has increased to respectively 95.7% and 96.2% in the CO2 and N, foams. The bubble-size distribution in a nitrogen foam shifts to the right only. The volume surface averaged bubble diameter (dJ increased from 150 km to 360 pm. Bubbles become bigger, but no smaller bubbles appear because gas diffusion does practically not take place. The solubility of carbon dioxide is 50 times higher than the solubility of nitrogen. Therefore, gas diffusion does take place in the carbon dioxide foam to a large extent within 2.5 minutes. The CO,-foam coarsens much more within the same period of time. A large number of bubbles becomes smaller as can be most clearly observed by the increase of the number of bubbles with a radius of 0 to 50 pm. The d, increased from 137 km to 190 km. Thus, using gasses of different solubility a distinction can be made between the physical processes coalescence and disproportionation on the basis of the bubble size distribution. The reproducibility of measurements with the Foam Analyzer is good. The d,, the gas fraction, the rate of drainage, the rate of foam collapse and the foam height can be measured with standard deviations of respectively 5 pm, 0.5%, 1 mm, 0.8 mm and lmm. Even the shape of the bubble size distribution is reproducible if the measurements are done in foam made from the same liquids. The apparatus is not only applicable to beer foam. In principle it can be used for different kinds of foam with the restriction that there are no hard structures in the foam that could break the very thin glass fibre. Figure 8 presents the bubble-size distributions of respectively shaving-foam and whipped cream. The measurements were done 2.5 minutes after the foam was made.
Spheredmmtef
8: The bubble
Figure
size distributions
and whipped
the
whipped
sprayer.
cream
cream
and
the
The gas fractions
of shaving
231
j&m and
98 pm
shaving were
foam
95.3%
were
in the
whipped
It can be seen that the shaving even 2.5 minutes
from cream
bubbles
contains
(8a)
out
and
of
cream
a
and
diameters
averaged
cream
small bubbles
to the shaving
made
in the whipped
respectively.
made
foam
(8b).
97.6% in the shaving foam. The volume-surface were
(m*iCfs)
shaving
foam
foam contains
very
after the foam was made. The foam
bubbles
that are much
larger
compared
foam. Even in the class with the largest diameter
are found. This indicates
the coarsening
of the foam.
CONCLUSIONS
The physical the
properties
distribution
of foams depend
of the
gas
and
liquid
phase.
physical
processes
that
drainage,
coalescence
and disproportionation.
Foam Analyzer of bubbles
the bubble
size distribution
way and in a relatively
the rate of drainage, height
simultaneously distribution.
and in
The
in foams
gas to
With these parameters
of foams can be analyzed.
fraction
the
Especially
are
changes
consisting
to the traditional
the rate of foam collapse, in
main
in a reproducible
time intervals
are done at consecutive
addition
on
With the developed
short time compared
changes
three
distribution
this
larger than 20 pm can be measured
methods. When measurements
foam
influences
to a large extend
the changes
can in
be
in
measured
bubble
size
a great part of the behaviour the knowledge
of the bubble
31
size distribution
and gas fraction
study of coalescence, So
it has
processes
become
hard
to distinguish
between
in foams.
these
three
can be used in foams that do not consist
structures
fibre resistant
It
and drainage
in the
that
could
break
the
very
small
of and
tip of the glass fibre. On the other hand is the glass
sensitive
used
advantage
the Foam Analyzer.
The Foam Analyzer such
disproportionation
possible
by using
is a great
against temperatures
up to 700 'C , so it can be
in foams at high temperatures. can
Analyzer
be
concluded
that
measurements
can play an important
processes
done
with
the
Foam
role in the study of the physical
in foams.
ACKNOWLEDGEMENT
The
authors
gratefully
acknowledge
support that made it possible work
is part
"Sparkling
of
a much
and Foaming
Eureka
for the
financial
to develope the Foam Analyzer.
wider
Eureka-research
Beverages"
project
This
called
(Eu 267).
REFERENCES
A.D. Ronteltap, Beer Foam Physics, Ph.D. Thesis, Agricultural University, Wageningen, The Netherlands, 1989. 2. G. Narsimhan and E. Ruckenstein, Langmuir 2(1986)494. 3. J.R. Calvert and K. Nezhati, Int. J. of Heat and Fluid Flow 7(3)(1986)164. 4. J.R. Calvert and K. Nezhati, Int. J. of Heat and Fluid Flow 8(2)(1987)102. 5. S.A. Khan and R.C. Armstrong, J. of Non-Newtonian Fluid Mechanics 25(1)(1987)61. 6. H. Pavel, J. Coll. and Interf. Sci. 134(1)(1990)161. 7. R. Mihail and S. Straja, Chem. Eng. J. 33(2)(1986)71. 8. S. Hartland, in I.B. Ivanov (Ed), Surfactant Science Series, Vol 29, Thin Liquid Films, Fundamentals and Applications, 1989, p.663. 9. P.K. Bhandola, S.A.K. Jeelani and S. Hartland, Chem. Biochem. Eng. Q. 3(1-2)(1989)1. 10. A.D. Ronteltap, B.R. Dam&e, M. de Gee and A. Prins, Colloids and Surfaces 47(1990)269. 11. A.D. Ronteltap and A. Prins, Colloids and Surfaces 47(1990)285. 12. S.A.K. Jeelani, S. Ramaswami and S. Hartland, Chem. Eng. Res. Des. 68(A3)(1990)271. 1.
32
13. S.A.K. Jeelani, N. Fidi and S. Hartland, Chem. Eng. Sci. 45(4)(1990)1043. 14. 1-L. Jashani and R. Lemlich, Ind. Eng. Chem. Fundam. 14(2)(1975)131. 15. R. Lemlich, Ind. Eng. Chem. Fundam. 17(2)(1978)89. 16. A.Y. Ranadive and R. Lemlich, J. Coll. Interf. Sci. 70(2)(1979)392. 17. A. Monsalve and R.S. Schechter, J. Coll. Interf. Sci. 97(2)(1984)327. 18. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 19(1)(1980)133. 19. R. Lemlich, Chem. Eng. Commun. 16(1982)153. 20. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 24(1)(1985)44. 21. A.J. De Vries, Receuil des Traveaux Chimiques des Pays-Bas 77(1958)209 and 283. 22. A.J. De Vries, in R. Lemlich (Ed), Adsorptive Bubble Separation Techniques, Academic Press, New York, London, 1972, p.7. 23. B. Gal-or and H.E. Hoelscher, AIChE J. 12(3)(1966)499. 24. L.A. Rieser and R. Lemlich, J. Coll. Interf. Sci. 123(1)(1988)299. 25. A.J. Markworth, J. Coll. Interf. Sci. 107(2)(1985)569. 26. P.B. Rand and A.M. Kraynik, SPEJ, Dot. Pet. Eng. J. 23(1)(1983)152. 27. D.S.H. Sita Ram Sarma and K.C. Khilar, Ind. Eng. Chem. Res. 27(5)(1988)892. 28. J. Sasaki, H. Matsukawa, S. Usui and E. Matijevic, J. Coll. Interf. Sci. 113(2)(1986)500. 29. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 22(1)(1983)105. 30. E.M. Savitskaya, Kolloid Zh. 13(1951)309. 31. R.C. Chang, H.M. Schoen and C.S. Grove Jr., Ind. Eng. Chem. 48(1956)2035. 32. P.L. Goldsmith, Brit. J. Appl. Phys. 18(1967)813. 33. E. Segel, P.R. Glenister and K.G. Koeppl, MBAA Technical. Q. 4(1967)104. 34. M.O.W. Richardson and D.S. Nandra, Cellular Polymers 5(6)(1986)423. 35. C.L. Jackson, M.T. Shaw and E.T. Samuelski, 44th Annual Technical Conference - Society of Plastic Engineers, Brookfield Center, CT, USA, 1986, p-42. 36. A. Selecki and R. Wasiak, J. Coll. Interf. Sci. 102(2)(1984)557. 37. G.J. Besio, G. Oyler and R.K. Prud'homme, Rev. Sci. Instrum. 56(5,Pt.1)(1985)746. 38. D.A. Lewis, R.S. Nicol and J.W. Thompson, Chem. Eng. Res. Des. 62(1984)334. 39. J.J. Frijlink, P.A. van Halderen, J. Hofmeester and M.M.C.G. Warmoeskerken, 12-procestechnologie 3(1986)19. 40. J.J. Frijlink, Physical Aspects of Gassed Suspension Reactors, Ph.D. Thesis, Technical University Delft, The Netherlands, 1987, p.119. 41. E.R. Weibel, Stereological Methods, Vol. 2. Academic Press. N.Y. London, 1980, p. 215. 42. M. Kawakami, N. Tomimoto, Y. Kotazawa, K. Ito, Trans. Iron. Steel. Inst. Jpn. 28(4)(1988)271.
Advances in Collaid and Interface Science, 38 (19921 13-32
E~vier~ien~Publ~beraB.V.,~~r~
Bubble-size Distributions in Foams. C.Q.J. Bisperiak2, A.D. Roateltap' and A. Prim+' ' Heineken
Techniech
Beheer
bv,
Burgemeester
Smeetsweg
1,
2382
PH
Zoeterwoude, The Netherlands. a Agricultural University Wageningen, Dept. of Food Science, Bomenweg 2, 6703 HD Wageningen, The Netherlands.
Bubble-size
distributions
in foams can be used to study foam properties
physical procassas that contribute and disproportjonatian. rate of drainage,
and to distinguish
betwen
to the breakdown of the foam. These processes are drainage,
A new Foam Analyzer was developed to measure various foam characteristics
the rate of foam collapse,
the gas fraction
in the foam and the bubble-size
the
coalescence like the
distribution.
IN!FRODUCTIOlJI Soap froths, crude oil foams, bread, beer foam, shaving cream, fire fighting foams and poly-urethane insulating materials are all examples of aerated products. These aerated products are foams or have been foams during processing. These foams have a great variety of wanted and/or unwanted properties. Obviously these properties depend on the composition of the gas and liquid phase. However, the properties of a foam also depend on the distribution of the gas and liquid phase. Foams are principally unstable, meaning that foam .properties vary with time as a result of shifts in the distribution of gas and liquid in the foam. Three different processes contribute to the instability of foams i.e. drainage, coalescence and disproportionation. Drainage is the liquid flow from a foam as a result of gravity and capillary forces. As a consequence of drainage a foam becomes dryer and bubbles may become distorted. In that case foams change from spherical foams to polyeder foams.
Al-~~/92/$15.00
0 1992-ElsevierSciencePublisbersB.V. Allrigbtareserved.
14
Coalescence rupture in
is the merging
of two bubbles
of the film between
the
foam
and
Disproportionation Ostwald
is
ripening.
As
grow at the expense
the bubbles.
the
number
Larger
of
interbubble a result
as a result
gas
bubbles
bubbles
bubbles.
appear
decreases.
diffusion,
of gas diffusion
of smaller
of the
also
called
larger
Smaller
bubbles
bubbles
shrink
and finally disappear. These effect the processes may distribution of the liquid and gas phase and thus alter the foam properties In
(Ronteltap[l]).
figure
processes fresh
1
beer
sinter.
an
example
is
on the appearance foam
that
is
given
of beer
of
the
produced
by
sparging
It may contain either carbon dioxide
the initial
bubble-size
on the kind
of gas that is used to produce
the
bubble-size
bubbles
have
a
In figure
presented. result
spherical
The
foam
because
no
gas
and
the
figure
lc
a
2.5
solubility
As a result
is
nitrogen
beer
beer
foam.
evidence
of
difference
the
foam. from
old
become
have
depends
of
carbon
fact
bubbles
that
in appearance
dioxide
has
become
is low.
of a nitrogen
and carbon
with respect
dioxide
a
of
foam
can be related
distribution
in the foam. Additionally,
distribution
and bubble-size
the progress
of the three physical
In is
in the foam Coalescence
smaller
disproportionation
solubility
of carbon
As
0.20 to
smaller.
beer
the gas fraction
can be explained
foam properties
is
on the solubility
in beer
after two and a half minutes
Thus
foam
not take place in 2.5 minutes
of nitrogen
of drainage
number
all
20%
have both contributed to coarsening
and disproportionation large
and radius
has become 0.95 and the larger bubbles are distorted.
A
Initially
80% gas and
decreased
bubbles
minutes
independent
bubble
fresh
because
larger. This must be a result
did practically
the
a
the foam.
about
fraction
the rate of gas diffusion
of the
'gas through
or nitrogen
mean
old
than
liquid
have become
Disproportionation
presented.
The
these a
monodisperse
foam contains
is dryer the
0.09. Also bubbles
time because
almost
of
la presents
is practically
lb a 2.5 minutes
of drainage
coalescence
is
shape.
200 pm. The
approximately liquid.
distribution
distribution
effect
foam. Figure
of the giving
occurred.
The
dioxide
foam
by the higher
gas
to nitrogen.
to the bubble
and liquid
the shifts in the liquid
distribution
can be used to monitor
processes.
Figure
1: Photographs either
CO, or N, gas,
nitrogen minutes
of (la) a fresh beer foam containing (lb) a 2.5 minutes
beer foam and
(lc (next page))
old carbon dioxide
beer foam.
old a 2.5
Figure lc:
A 2.5 minutes old carbon dioxide beer foam.
Narsimhan Ruckenstein[2] principle to and used this investigate the enrichment of surfactant in a semibatch foam fractionater and described a model that accounts for the initial bubble-size distribution, drainage, coalescence and disproportionation. The bubble-size distribution in foams was also investigated to relate it to the rheological behaviour of a foam. Calvert and Nezhati[3][4]
presented
effect of the bubble-size the distribution on the flow properties of a foam passing through a
pipe. They described the flow with a modified Bingham plastic model and found that the yield stress of the foam depends on the bubble-size distribution. However, Xhan and Armstrong[SJ found that the yield stress, the critical strain and the stress-strain relation is independent of the bubble-size distribution. Pavel[6] described a model that relates the bubble-size distribution to the height of the foam in a steady-state foaming column. The model accounts for drainage and coalescence. The relation between the bubble-size distribution and coalescence is mentioned by Mihail and Straja(71. They presented a model describing the bubble-size distribution in
17
and explained
why a bubble-size
distribution
Hartland[8]
as a result
of coalescence.
coalescence
times in steady-foams
the
of the
height
distribution the
model
based
predicting beer
foam
in the on
caused
by
a1[12]
examined
foaming
interfacial
gas
of the
Bhandola
coalescence
this
whereas
diffusion
column
effect
of the foam height
Unfortunately
disproportionation
The
is discussed.
the variation
foam.
model
not
of beer
et
the
that within
used
size
account
foam
al[lO][ll]. in
is mainly
3 times binary
described carbon The
dioxide effect
diffusion and
coalescence
the period
of bubble
takes place. Jeelani
the creation and breakdown
Lemlich[l4]
the
initial
bubble-size
investigated
in a bubble
anionic,
column.
they concluded
From
This
bubble-size
Ranadive
Lemlich[l6]
distribution
of disproportionation. and Schechter[l7].
big
to
gas
then
differences.
Runga-Kutta
This
model
led
to
Lemlich[lO]
compared
dimensionless
initial distributions
De Vries[21][22] discussed bimodal
of gasses
experiments
it
model
the
by Monsalve
recalculated
the model
method but found
Lemlich[lS]. for
initial
on the progress
presentation
by
three
of
a
new
Cheng
and
generalized
among which are the empirical
and the theoretical
distribution
This work has led to the
with which the shifts in an initially
distribution
can
in foams
(Rieser
was
that
numerical
relating
(Lemlich[l5]).
is confirmed
and Hoelscher[23].
of an apparatus
bubble-size
diffusivity the
distribution
by Gal-or
development
the
were a result of
influence
the
distribution
nonionic
bubble-size
of a model
presented
Cheng and Lemlich[l8]
gas
Jashani
did not take place
diffusion
This observation
on
and
observed
distribution
has a major
results using a Ith-order
Boltzmannlike
cationic the
led to the development
distribution
and
bubble-size
no
distribution and coworkers.
that coalescence
but that shifts in the bubble-size gas diffusion. the
et a1[13]
solutions. of
distribution
that
of foams from supersaturated
in foams was studied by Lemlich
surfactants
et
steady-state
rise the mean bubble size increased by a factor of 2 meaning about
in for
Jeelani
a
to
bubbles,
and bubble
distributions
and concluded
and
bubble-size
et a1[9]
of
does
the collapse Ronteltap
bubble-size
bimodal
drainage
and related these processes
column.
foam
may become
described
concluded
be
that
used
to
measure
and Lemlich[24]). gas
diffusion
the From
can
be
18
enhanced by convection in the liquid foam films. Markworth[25] discussed foam stability and Ostwald ripening taking into account the effect of bubble size. Bubble-size distributions were also used to determine the film thickness in the foam, but the results were subject to errors as described by De Vries[21]. The relation between the bubble-size distribution and the rate of drainage is described by Rand and Kraynik[26] for foams of drilling fluid. The enhanced stability of foams with smaller bubbles was explained by a decrease of drainage. Sita Ram Sarma and Khilar[27] found that a more uniform bubble-size distribution and high initial gas volume fraction gave more stable foams. This was explained by reduced gas diffusion as discussed by the authors. As stated before, knowledge about the bubble-size distribution in a foam is essential for a better understanding of foam properties and the stability of those properties. Shifts in bubble-size distributions can be used to distinguish between the physical processes that contribute to the changes of foam properties. Therefore it is no surprise that bubble-size distributions have been subject to intensive study. A great variety of experimental techniques has been developed. Bubble-size distribution can be measured by photographing the foam through a glass wall and analyzing the obtained images De Vries[22], Sasaki et a1[28]. Cheng and Lemlich[29] described the errors that can be made when bubble-size distributions are measured this way. At the surface of a glass wall a relative higher number of larger bubbles is observed. In addition larger distorted at the bubbles will be glass wall and disproportionation and coalescence rates may be effected by the presence of a glass wall, leading to a locally different bubble-size distribution. Bubble-size distribution can also be measured by freezing the foam and examination of a cross section Savitskaya[30], Chang et al [31]. It is argued that the freezing process does not influence the bubble-size distribution, but this may be disputed for different foams and freezing methods. Additionally, the actual bubble radii in a foam are not equal to the observed circle radii in a cross section because a cross section is in
19
general not made through the middle of the bubbles. Therefore, a proper statistical method must be used to calculate the bubble-size distribution from the observed two dimensional
circle
radii e.g. Goldsmith[32] or De Vries[22]. Bubble-size distributions were also measured at the surface of foams Segel et al[33]. This may lead to very serious errors if the distribution in the top layer of the foam does not correspond to the distribution inside the foam. Drainage, gas diffusion processes and coalescence may proceed differently at the surface of a foam. In addition bigger bubbles tend to rise to the foam surface. Bubble-size distributions can be obtained with a microscope Richardson and Nandra[34] or electron microscope Jackson et al[35] but the above mentioned possible errors in measurement are also applicable to these methods. More recently a new method to measure the bubble-size distribution in foams was described by Selecki and Wasiak[36] and Besio et a1[37]. To this end the foam is led through a capillary that has a smaller diameter than the smallest bubbles in the foam. The distances between liquid films in the capillary are measured and used to calculate the bubble-size distribution. Rieser and Lemlich[24] used this method to measure the shift in bubble-size distribution as a result of interbubble gas diffusion in an initially bimodal distribution. A disadvantage of the method is that it can only be used to measure relatively stable foams because the method can easily effect the bubble-size distribution. Bubble-size distributions in bubble columns were measured with a conductivity probe (Lewis et a1[38]). With the method bubble velocities were measured in addition to bubble sizes. A similar probe was used by Frijlink[39][40]. However, this probe was not based on conductivity but on an optical phenomenon using a glass-fibre. None of the above mentioned experimental techniques distinguishes between drainage, coalescence and disproportionation. The properties of the foam are not satisfactory characterized, because the liquid and gas distribution in the foam is not or only partly measured. For this purpose a new Foam Analyzer was developed to measure various foam
20
properties
like the collapse
gas fraction method
analyzer through
in the foam, and the bubble-size
is based
by Frijlink.
of foam, the rate of drainage,
on the optical
The difference
is based
bubbles
of a single
in a foam whereas
is based on the use of a stationary which the velocity
distribution.
technique
between both methods
on the use
immobile
glass-fibre
The
described
is that the Foam
probe
that
is moved
the Frijlink
multi glass-fibre
and the size of passing
the
bubbles
method
probe with
is measured.
EXPERIMENTAL
The Foam Analyzer of the apparatus
is displayed
in figure 2. Two different
can be distinguished.
continuous light source
2: A schematic
presentation
to move the glass fibre downwards and
an
opto-electronic
glass-fibre
part
unit of the Foam Analyzer.
through a foam at known speed
that
consists
of
an
optical
probe and electronic equipment for signal conversion,
data-acquisition
and data processing.
The glass fibre has a diameter is melted
part is used
photo-electric cell
Opto-electronic Figure
A mechanical
parts
of 200 pm. The end of the probe
in a oxygen-propane/butane
the tip has a diameter melted hemispherical
of
flame and elongated
about 20 pm. The
end
(see figure 3). Frijlink[40]
of the
until tip is
foundthatthe
21
LIGHT
UGHT
REFLECTED LIGHT
REFLECTED LIGH
3b
Figure
3: A schematic
presentation
reflection
of the fibre tip with the
of light when
it is in the gas phase
and
in the liquid phase.
highest
efficiency
hemispherical-shaped send
into
the
in
a
fibre
end. From the opto-electronic
fibre.
emitted. However,
obtained
is
At
the
end
of
the
fibre
on the refractive
light
and returned
unit. The amount of reflected
index of the medium surrounding
index of the medium
is approximately
index of the glass,
almost no light is reflected.
if the refractive
hand,
the light
is reflected.
the same as the
is converted sampled
index of the medium
is much part of
Thus, more
light is reflected
Packard
at a frequency
Vectra
known
calculated.
the
of 1 Mhz with
80386
Because
distance
Thus,
cm s‘I the signal
analogue
corporation)
QS/20
80387 co-processor. is
to a light sensitive
into an electronic
(DAS-50 by MetraByte
On
index of glass, a considerable
when
tip is in gas than when the tip is in liquid. The reflected goes via an y-splitter
to
the tip. If the
refractive
lower than the refractive
is
light depends
refractive
the other
a
unit light is most
part of the light is reflected
the opto-electronic
with
light
cell where the light
signal.
This signal
a data-acquisition
that
the
is placed
is
board
in a Hewlett-
computer
(20 Mhz)
the probe
speed and the sample rate
between
two
sample
equipped
points
with
can
a
be
if the probe is moved with a speed of about 10 is sampled
every 0.1 pm.
22
pathof
analoguesignal _____________._.
+I!
liquid level
digitized signal I
I
---P
dry level
I
I
gas
liquid k
Distance 4: A schematic
Figure
representation
when the probe
of events which
is moved through
the path of the probe and chord middle
and at the bottom
digitized
If the
probe
Figure
lengths.
through
a foam
an alternating
gas and liquid is obtained
that
the
signal
is high
when
by liquid and low when the probe tip is by gas. signal is digitized
in Asyst
positive
and negative
is considered
3.1.
The
analogue
tip
is
by means of a computer program
program
distinguishes
between
slopes of the signal. The analogue
to be a 'wet' signal
to
the bubbles.
the probe
surrounded
The analogue
and
corresponding
through
surrounded
written
In the
resp. the analogue
lengths that the probe travelled
4 shows
a foam. At the top
signal
is put
signal representing the chord
perform
the
signal
(i.e. the probe is surrounded
from the point where the slope of the analogue
by liquid) becomes
to the point where
positive
signal is considered
The analogue
the probe tip is surrounded
the slope becomes
to be a 'dry' signal
signal
negative. (i.e. when
by gas) in between the 'wet' signals.
that are part of a 'wet' signal
are assigned
The sample
points
the number
'1' and the sample points that are part of a 'dry' are
assigned
the number
obtained
of which
'0'. This way an apparent
counting
length
that of
distances calculation example.
the the
number
probe
these
of
iS
chord
the
chord
I and
III
are
><-III-><-
sample
travelled
of
points
through
lengths lengths
chord
a
can
is
of
a
single
certain
be
lengths
that
phase.
From this example
chords
I, II and III are respectively with a probe
chord
phase
the
calculated.
illustrated
by
The
the
correspond
liquid phase and II is a chord length that corresponds
calculated
signal
a part may look like this:
. . .00011111100000000000111111100... -><-->< II I By
digital
next
to
the
to the gas
it can be seen that the lengths
of the
0.6 pm, 1.1 pm and 0.7 Pm
speed of 10 cm S-I and a sample
rate of
1 Mhz. The chord lengths the probe travelled calculated point
by a procedure
of the digitized
through the gas phase are
in the computer
program.
signal has an index number
to an array number. The array has a dimension of computer
memory).
stores
index
the
The computer
numbers
'wet' chord
higher
than
fraction is
lengths
'dry' chord
the
sum
the
corresponding index number
less computer
of
first sample
case.
the
'wet'
The
memory
point
of
the
chord
than
storage
of
'dry' chord
lengths
is
chord
lengths
than the liquid distance
to the gas phase 'dry'
(2 Mb
the array and
points
of
chord
and
of the subsequent
distribution
the
gas
which length
by using
*wet' chord
index
'wet' chord
of 'dry' signals
the
chord
can be calculated
length
if
fraction,
each
of the last sample point of the
the
a chord-length
analyzes
sample
The sum of the
in the foam is higher
usually
preceding
takes
lengths.
the
of
program
corresponding
of 1.000.000
to the liquid phase, because storage of the
lengths corresponding
the
Every sample
number length.
is obtained.
the
length of the Thus,
24 The chord lengths are a measure for the bubble-size distribution in the foam. To calculate the bubble-size distribution in the foam a problem similar to the 'tomato salad' problem has
to be
solved. The measured
one-dimensional gas
lengths are not equal to the actual three-dimensional bubble radii, because the probe hardly ever travels through the two polar ends of a bubble. Furthermore bubbles with large diameters have a greater chance of being pierced by the optical probe than bubbles with Weibel[41] smaller diameters. and later Kawakami[42] developed a statistical method to calculate the three-dimensional size distribution from the one-dimensional chord length distribution. This method was modified and used for the calculation of the bubble-size distribution in the foam. The bubble-size distribution is given as the number of spheres per ml foam per class of sphere diameters. Bubbles were assigned to 35 classes with a width of 50 pm from 0 pm up to 1750 pm. The measurement is carried out in the following way. A fixed volume of the liquid is poured into a cylindrical glass. The glass contains a sintered glass bottom through which a gas can be sparged to produce a foam column. First the level of the liquid surface is measured with the optical probe before the foam column is produced. This level is stored in the computer and later used to calculate the gas fraction. Then a foam column is produced by dispersing gas through the glass sinter with a constant flow rate until the foam surface reaches a predetermined level. The production of foam up to this level takes about 10 seconds and the height of the foam column is then about 10 cm. This large height
is necessary to ensure that at least 200
bubbles will be detected by the probe, so that a reliable statistical calculation is possible. Then the gas supply is stopped and the first measurement is done by lowering the probe through the foam in approximately 1 second. During the measurement the computer subsequently registers the upper level of the foam (i.e. the level of the first transition of a gas signalto a liquid signal), the chord-length distribution and the level of the liquid-foam interface (i.e. the level of the last gas-liquid transition found in the signal).
25
If the
measurements
consecutive
time
are
carried
intervals
the
out
rate
in the
same
of drainage,
sample
the
at
collapse
rate of the foam, the changes
in foam volume and the gas fraction
in the foam can be determined
in addition to the evolution
bubble-size
The
distribution.
accuracy
fraction results
height
of
the
method
can
be
in the foam can be measured
from
the
measurement.
the gas fraction
where
checked
because
in two different
In one way the gas fraction
can be compared.
directly
of the
Because
with
can be calculated
the
using
the
gas
ways
and
is obtained
data
of
equation
foam
1:
ep:
gas fraction
h LI :
height of the liquid surface before a foam column
in the foam.
[n?mJ]
is produced. h,:
height
of the upper
h,:
height
of the liquid-foam
In the other way as follows
phase
divided
gas fraction
interface
from the theory,
equal to the sum of the chord
[ml [ml
level of the foam
lengths
by the foam height.Both
[ml
the gas fraction
corresponding methods
is
to the gas
to determine
the
must give the same result.
RESULTS
In figure
5 the gas fraction
chord-length fraction
distribution
in the foam
and
in the foam calculated the
independently
(eq. 1) is presented
from the
measured
as a function
gas
of time.
It is clear that these gas fractions do not differ significantly. Therefore
the
distributions
conclusion
can
be
drawn
that
in the foam can be accurately
the
bubble-size
estimated
with the
Foam Analyzer. In Figures foam
6a and
at t=O and t=2.5
6b signals
obtained
by measuring
minutes are presented.
In these
CO, beer figures,
26
gas/foam volume ratio 100
95
75 ’ 0
1
T&e
[min.] gas fraction (calculated) --A--
gas fraction (measured)
and the calculated
5: The measured
Figure
[m3mT3]versus
I 5
4
3
time
gas
fractions
[min].
Signal level
Signal level
-1
6a 7
ml
4ol
em
Ku
1
0
200
4al
6: The signals
Figure
t=O
eul
‘ml
Bm
Array index number
Array index number
obtained
by measuring
(6a) and t=2.5 minutes
CO, beer foam at
(6b).
for the sake of clarity
every 100th sample point of the total of
1.000.000
are plotted.
scale
sample points
of the
numbers
reflection
air.
and
at
the
X-axis
is an arbitrary the
array
that this
and that the resolution
index
is a rough
is low.
above the foam a constant gas signal is obtained.
level starts As
level
It must be mentioned
of the signal
Initially signal
signal
are plotted.
The Y-axis
soon
as
low because
the
probe
the probe
penetrates
travels the
foam
initially the
The in
signal
21
increases.
the height
Thus,
alternating
calculate the bubble-size at the
of the
foam
is measured.
signal of gas and liquid is obtained
liquid
the probe
the
Finely the signal remains
distribution.
level when
Then
that is used to
has passed
the
foam-liquid
interface. As can be seen signal
in figures
it takes
some time before
result of drainage
the
tip
differences probe.
upwards
between
However,
level of the
This is a result
dry as a
of the liquid after it leaves
mechanism
the
'dry'
of the fact that
the tip of the probe becomes
and evaporation
the liquid film. A possible from
6a and 6b, the
is not always reached.
probe
is the flow of liquid away
caused
by
Laplace
pressure
the very small tip and the upper part of the
the signal starts to decline
sharply
as soon as
the thin liquid film around the tip of the probe becomes thinner. When the probe penetrates period,
the signal
completely concluded
reaches
the next liquid film within this drying
increases
again to the liquid level before
it
the 'dry' level of the gas phase. This can be
from the fact that the longer the probe travels through
the gas phase after it pierced through a liquid film, the further the signal decreases
to the 'dry' level. This phenomenon
interfere
with
influence
on the above mentioned
Another
the outcome
observation
signal changes
of the experiment digitizing
that can be made
foam. This
as the probe moves downwards
the
foam
is more
can be explained
coarse
it has no
process.
is that the shape of the
the top of the foam the films are thinner Furthermore
because
does not
through
the foam. In
and the foam is dryer.
in the
upper
part
by the fact that the foam
of the
is older
in the top than in the bottom and liquid from the upper part must drain
through
forces.
the
lower
As a result,
and coalescence
part
of
have proceeded
From the differences figure 6b the following
after
measure
can be concluded.
for the collapse
as a function
by
gravity
in the top of the foam. in figure 6a and
The foam collapses
transition
From this
with
is found more to the
shift to the right
a direct
rate of the foam is obtained.
the last gas-liquid
transition
of time. This corresponds
liquid interface
caused
disproportionation
in the signals presented
2.5 minutes.
Furthermore,
foam
drainage,
further
time because the first gas-liquid right
the
the processes
and is a measure
shifts
to the
left
to the rise of the foam
for the rate of liquid drainage
Loe-cfwss(~‘) I
‘L
(1
................... .7a ...
* s
.,. _,.,,., ,.,. ._.j.,. . . .. . .,.
7b ‘.
. ‘. .._.._..._.....,.......
t. .t....(...(
Figure 7: The bubble size distributions of a CO, beer foam at t=O (7a) and tm2.5 minutes (7b) and the bubble size distributions of a W2 beer foam at t=O (7~) and t==2.5minutes (?d).
from the foam. With the change of the levels of the top of the foam and the foam-liquid interface, the change in foam height or volume are obtained. In figures 7a and 7b the bubble-size distributions in beer On the vertical axis the number foam@ made by CO, are presented. of bubbles per ml is displayed. It has to be emphasized that the ~-axis is a logarithmic scale. Therefore small variations in bar height represent: large differences in the numbsr of bubbles. On the horizontal axis the bubble size is displayed divided into classes with widths of 50 Pm. These bubble-size distributions were calculated from the signals presented in respectively figures 6a and Bb, The time intervals between the measurements is 2.5 minutes, Additionally, the bubble-size distributions of beer foam containing nitrogen at t=4 and t=2.5 minutes axe
29
presented in figure 7c and 7d respectively. As can be seen the bubble-size
distributions
presented
in
figure
7
correspond
qualitatively very well with the images of beer foam presented in figure 1. Initially the bubble-size distribution in a fresh beer foam are independent on the kind of gas that is used to produce the foam. The distributions in figure 7a and 7c are approximately equal. The gas fractions in the foams were respectively 82.6% and 83.6%. However, after 2.5 minutes the bubble-size distributions of the foams containing CO, and N, are completely different. The gas fraction in the foam has increased to respectively 95.7% and 96.2% in the CO2 and N, foams. The bubble-size distribution in a nitrogen foam shifts to the right only. The volume surface averaged bubble diameter (dJ increased from 150 km to 360 pm. Bubbles become bigger, but no smaller bubbles appear because gas diffusion does practically not take place. The solubility of carbon dioxide is 50 times higher than the solubility of nitrogen. Therefore, gas diffusion does take place in the carbon dioxide foam to a large extent within 2.5 minutes. The CO,-foam coarsens much more within the same period of time. A large number of bubbles becomes smaller as can be most clearly observed by the increase of the number of bubbles with a radius of 0 to 50 pm. The d, increased from 137 km to 190 km. Thus, using gasses of different solubility a distinction can be made between the physical processes coalescence and disproportionation on the basis of the bubble size distribution. The reproducibility of measurements with the Foam Analyzer is good. The d,, the gas fraction, the rate of drainage, the rate of foam collapse and the foam height can be measured with standard deviations of respectively 5 pm, 0.5%, 1 mm, 0.8 mm and lmm. Even the shape of the bubble size distribution is reproducible if the measurements are done in foam made from the same liquids. The apparatus is not only applicable to beer foam. In principle it can be used for different kinds of foam with the restriction that there are no hard structures in the foam that could break the very thin glass fibre. Figure 8 presents the bubble-size distributions of respectively shaving-foam and whipped cream. The measurements were done 2.5 minutes after the foam was made.
Spheredmmtef
8: The bubble
Figure
size distributions
and whipped
the
whipped
sprayer.
cream
cream
and
the
The gas fractions
of shaving
231
j&m and
98 pm
shaving were
foam
95.3%
were
in the
whipped
It can be seen that the shaving even 2.5 minutes
from cream
bubbles
contains
(8a)
out
and
of
cream
a
and
diameters
averaged
cream
small bubbles
to the shaving
made
in the whipped
respectively.
made
foam
(8b).
97.6% in the shaving foam. The volume-surface were
(m*iCfs)
shaving
foam
foam contains
very
after the foam was made. The foam
bubbles
that are much
larger
compared
foam. Even in the class with the largest diameter
are found. This indicates
the coarsening
of the foam.
CONCLUSIONS
The physical the
properties
distribution
of foams depend
of the
gas
and
liquid
phase.
physical
processes
that
drainage,
coalescence
and disproportionation.
Foam Analyzer of bubbles
the bubble
size distribution
way and in a relatively
the rate of drainage, height
simultaneously distribution.
and in
The
in foams
gas to
With these parameters
of foams can be analyzed.
fraction
the
Especially
are
changes
consisting
to the traditional
the rate of foam collapse, in
main
in a reproducible
time intervals
are done at consecutive
addition
on
With the developed
short time compared
changes
three
distribution
this
larger than 20 pm can be measured
methods. When measurements
foam
influences
to a large extend
the changes
can in
be
in
measured
bubble
size
a great part of the behaviour the knowledge
of the bubble
31
size distribution
and gas fraction
study of coalescence, So
it has
processes
become
hard
to distinguish
between
in foams.
these
three
can be used in foams that do not consist
structures
fibre resistant
It
and drainage
in the
that
could
break
the
very
small
of and
tip of the glass fibre. On the other hand is the glass
sensitive
used
advantage
the Foam Analyzer.
The Foam Analyzer such
disproportionation
possible
by using
is a great
against temperatures
up to 700 'C , so it can be
in foams at high temperatures. can
Analyzer
be
concluded
that
measurements
can play an important
processes
done
with
the
Foam
role in the study of the physical
in foams.
ACKNOWLEDGEMENT
The
authors
gratefully
acknowledge
support that made it possible work
is part
"Sparkling
of
a much
and Foaming
Eureka
for the
financial
to develope the Foam Analyzer.
wider
Eureka-research
Beverages"
project
This
called
(Eu 267).
REFERENCES
A.D. Ronteltap, Beer Foam Physics, Ph.D. Thesis, Agricultural University, Wageningen, The Netherlands, 1989. 2. G. Narsimhan and E. Ruckenstein, Langmuir 2(1986)494. 3. J.R. Calvert and K. Nezhati, Int. J. of Heat and Fluid Flow 7(3)(1986)164. 4. J.R. Calvert and K. Nezhati, Int. J. of Heat and Fluid Flow 8(2)(1987)102. 5. S.A. Khan and R.C. Armstrong, J. of Non-Newtonian Fluid Mechanics 25(1)(1987)61. 6. H. Pavel, J. Coll. and Interf. Sci. 134(1)(1990)161. 7. R. Mihail and S. Straja, Chem. Eng. J. 33(2)(1986)71. 8. S. Hartland, in I.B. Ivanov (Ed), Surfactant Science Series, Vol 29, Thin Liquid Films, Fundamentals and Applications, 1989, p.663. 9. P.K. Bhandola, S.A.K. Jeelani and S. Hartland, Chem. Biochem. Eng. Q. 3(1-2)(1989)1. 10. A.D. Ronteltap, B.R. Dam&e, M. de Gee and A. Prins, Colloids and Surfaces 47(1990)269. 11. A.D. Ronteltap and A. Prins, Colloids and Surfaces 47(1990)285. 12. S.A.K. Jeelani, S. Ramaswami and S. Hartland, Chem. Eng. Res. Des. 68(A3)(1990)271. 1.
32
13. S.A.K. Jeelani, N. Fidi and S. Hartland, Chem. Eng. Sci. 45(4)(1990)1043. 14. 1-L. Jashani and R. Lemlich, Ind. Eng. Chem. Fundam. 14(2)(1975)131. 15. R. Lemlich, Ind. Eng. Chem. Fundam. 17(2)(1978)89. 16. A.Y. Ranadive and R. Lemlich, J. Coll. Interf. Sci. 70(2)(1979)392. 17. A. Monsalve and R.S. Schechter, J. Coll. Interf. Sci. 97(2)(1984)327. 18. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 19(1)(1980)133. 19. R. Lemlich, Chem. Eng. Commun. 16(1982)153. 20. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 24(1)(1985)44. 21. A.J. De Vries, Receuil des Traveaux Chimiques des Pays-Bas 77(1958)209 and 283. 22. A.J. De Vries, in R. Lemlich (Ed), Adsorptive Bubble Separation Techniques, Academic Press, New York, London, 1972, p.7. 23. B. Gal-or and H.E. Hoelscher, AIChE J. 12(3)(1966)499. 24. L.A. Rieser and R. Lemlich, J. Coll. Interf. Sci. 123(1)(1988)299. 25. A.J. Markworth, J. Coll. Interf. Sci. 107(2)(1985)569. 26. P.B. Rand and A.M. Kraynik, SPEJ, Dot. Pet. Eng. J. 23(1)(1983)152. 27. D.S.H. Sita Ram Sarma and K.C. Khilar, Ind. Eng. Chem. Res. 27(5)(1988)892. 28. J. Sasaki, H. Matsukawa, S. Usui and E. Matijevic, J. Coll. Interf. Sci. 113(2)(1986)500. 29. H.C. Cheng and R. Lemlich, Ind. Eng. Chem. Fundam. 22(1)(1983)105. 30. E.M. Savitskaya, Kolloid Zh. 13(1951)309. 31. R.C. Chang, H.M. Schoen and C.S. Grove Jr., Ind. Eng. Chem. 48(1956)2035. 32. P.L. Goldsmith, Brit. J. Appl. Phys. 18(1967)813. 33. E. Segel, P.R. Glenister and K.G. Koeppl, MBAA Technical. Q. 4(1967)104. 34. M.O.W. Richardson and D.S. Nandra, Cellular Polymers 5(6)(1986)423. 35. C.L. Jackson, M.T. Shaw and E.T. Samuelski, 44th Annual Technical Conference - Society of Plastic Engineers, Brookfield Center, CT, USA, 1986, p-42. 36. A. Selecki and R. Wasiak, J. Coll. Interf. Sci. 102(2)(1984)557. 37. G.J. Besio, G. Oyler and R.K. Prud'homme, Rev. Sci. Instrum. 56(5,Pt.1)(1985)746. 38. D.A. Lewis, R.S. Nicol and J.W. Thompson, Chem. Eng. Res. Des. 62(1984)334. 39. J.J. Frijlink, P.A. van Halderen, J. Hofmeester and M.M.C.G. Warmoeskerken, 12-procestechnologie 3(1986)19. 40. J.J. Frijlink, Physical Aspects of Gassed Suspension Reactors, Ph.D. Thesis, Technical University Delft, The Netherlands, 1987, p.119. 41. E.R. Weibel, Stereological Methods, Vol. 2. Academic Press. N.Y. London, 1980, p. 215. 42. M. Kawakami, N. Tomimoto, Y. Kotazawa, K. Ito, Trans. Iron. Steel. Inst. Jpn. 28(4)(1988)271.