| dc.description.abstract | The study of bubble formation in liquids is of
great importance because of its application in the design
of many industrial bubble contactors like distillation
columns, bubble cap columns, absorption towers, reactors,
extraction apparatus, etc.
The main object of the present investigation is
to make an attempt to develop a mechanism which can explain
the bubble formation phenomenon. A theoretical equation has
been developed on the basis of the mechanism and it is found
to be applicable to a considerable extent. The proposed
mechanism is for bubble formation in viscous liquids under
constant flow conditions.
In order to collect the necessary data for
testing the validity of the proposed theoretical equation,
an apparatus has been designed. It consists of a constant
pressure arrangement to give an air stream under constant
pressure. This is achieved by allowing water to flow into
an aspirator bottle from a constant level tank. By the
flow of water into the aspirator bottle the air gets
compressed. Arrangements are provided to dry this air and
then saturate it with the particular liquid in which the
bubbles are formed. The air supply is let into an eductor
tube by means of a needle valve. The capillaries or
orifices used are fixed at the bottom of the eductor tube in
which the liquid is filled.
The bubbles formed at the capillaries or orifices
are allowed to pass through a soap-film flow meter using
which the bubble volume measurements are made.
Six capillaries of diameters ranging from 0.0692 cm
to 0.312 cm have been employed during the present investigation,
and bubble frequencies up to about 200 bubbles/minute
have been studied for liquids of viscosities varying from
100 to 908 centipoises.
In the experiments with the air–water system with
capillaries, the bubble volume decreased with increasing
flow rates at the very beginning, then started increasing
with flow rate. But when the same capillary was filled
with glass powder and the experiments were conducted, it
was seen that the bubble volume never decreased with
increasing flow rate but showed an increasing trend right
from 0 cm³/sec flow rate. This difference in trends in
these two cases may be explained as follows:
In the former case, the operation was not carried
out under conditions of constant flow, whereas a constant
flow condition could be ensured in the other case.
From the experiments conducted with viscous
liquids the following observations are made:
The gas flow rate affects the bubble volume to
different extents for liquids of different viscosities.
The diameter of the capillary comes into play
at the initial stages of formation by providing increased
circumference for the surface tension force to act on,
and also during the detachment stage by providing a higher
area for gas flow.
The effect of surface tension of the liquid on
the bubble formation exists only during the inflation of the
bubble at the tip of the capillary and not during the
motion and detachment of the bubble.
The liquid viscosity affects the bubble
formation phenomenon in a complex manner. The bubble
volume increases with liquid viscosity and also the rate
of increase is high for high viscous liquids. Further,
with the increase in capillary diameter the influence of
viscosity becomes predominant.
The various models available in the literature
have been analysed, and the equations given by different
investigators have been employed for calculating the bubble
volume using the data collected during the present investigation.
Since most of the equations are empirical in
nature, the comparison is not very satisfactory. Therefore
in the beginning a semi?theoretical equation has been
developed in the following lines.
According to this Model I, the bubble is
considered to be formed in two stages, i.e., the stage of
initial bubble formation and secondly the stage of detachment.
During the first stage the following equation is
assumed to be applicable.
For the second stage the Stokes’ equation is
considered to be applicable and on these grounds a
final expression for the bubble volume VbV_bVb? is derived:
Vb=4.270D?0.068v?1.247or0.052gv5/5S(2)V_b = 4.270D - 0.068\sqrt{v} - 1.247
\quad\text{or}\quad
0.052g\frac{v^{5/5}}{S}
\tag{2}Vb?=4.270D?0.068v??1.247or0.052gSv5/5?(2)
The bubble volumes have been calculated using
the above equation and compared with the experimental
values. The maximum deviation is about 10% and most of
the calculated values fall within 5% of the experimental
ones.
Model II is also based on a two?step
mechanism.
In the first stage the bubble grows at the tip
of the capillary and does not move as a free bubble.
Throughout this stage the sum of the downward forces is
larger than the upward buoyancy force, though the difference
between the two goes on getting reduced as the bubble
expansion continues. The first stage is considered to be
complete when the buoyancy force equals the total downward
force.
After completion of the first stage, the
upward forces become higher and the bubble starts moving
upwards. The bubble does not move with a constant velocity
but actually accelerates. This upward ascent continues
until the bubble breaks off. Until this stage, the bubble
continues to obtain the supply of gas from the
main stream.
Thus the final bubble volume VbV_bVb? is given by the
equation:
Vb=Vgi+Qt(5)V_b = V_{gi} + Qt
\tag{5}Vb?=Vgi?+Qt(5)
where VgiV_{gi}Vgi? is the force?balance bubble volume obtained
from:
Vgi?(?l??g)?g=2?r(34?)1/3(4)V_{gi} \, ( \rho_l - \rho_g ) \, g =
\frac{2\sigma}{r} \left( \frac{3}{4\pi} \right)^{1/3}
\tag{4}Vgi?(?l???g?)g=r2??(4?3?)1/3(4)
To determine the QtQtQt value, the value of ttt has to be
evaluated.
Two criteria have been proposed to get the
value of ttt.
Using the first criterion,
tc=C(NM)t_c = C \left(\frac{N}{M}\right)tc?=C(MN?)
According to the second criterion,
t=Vl(5)t = \sqrt{V_l}
\tag{5}t=Vl??(5)
During the present studies it was found that
the first criterion of detachment is applicable to glass
capillaries and the second criterion of detachment is
applicable to stainless?steel orifices.
Using these equations the bubble volumes have
been calculated and compared with the observed ones,
and the agreement has been found to be good.
The effect of orifice geometry on bubble formation
in viscous liquids has also been studied during the course
of the present study.
The different geometries of the orifices which
were used are triangle, square, pentagon and hexagon.
Experiments have been conducted in viscous liquids of three
different viscosities.
Before attempting to correlate the results, the
equivalent?dimension concept based on the following was
tried:
Diameter basis
Perimeter basis
Area basis
None of the above three could satisfactorily
take into account the variation in bubble size for
geometrical orifices.
Two new parameters were defined as below:
P?=Area of the non?circular orificeArea of the inscribed circular orificeP' = \frac{\text{Area of the non?circular orifice}}{\text{Area of the inscribed circular orifice}}P?=Area of the inscribed circular orificeArea of the non?circular orifice?
?=Bubble volume from the non?circular orificeBubble volume from the inscribed circular orifice(7)\alpha = \frac{\text{Bubble volume from the non?circular orifice}}{\text{Bubble volume from the inscribed circular orifice}}
\tag{7}?=Bubble volume from the inscribed circular orificeBubble volume from the non?circular orifice?(7)
Using these two parameters it was
possible to evaluate an equation using which we could get
the bubble volume from the non?circular orifice once we
knew the inscribed circular orifice diameter and the
experimental condition.
The final relationship is:
Vd=Vc×?V_d = V_c \times \alphaVd?=Vc?×?
To obtain the bubble volume from the circular
orifice the equation (3) can be used. | |
