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Viscosity is an important property of a fluid which governs the many phenomena that appear when work is done on them. Fluids of different viscosities behave very differently and therefore their applications can vary. For example, with lubricants, high viscosity lubricants are used in the slow moving parts reducing friction whereas liquids with low viscosity are used in fast moving parts to distribute heat. My extended essay is therefore based on studying the effect of different viscosities on the ascension of bubbles.
Why Bubbles? These strange formations of a liquid layer around air form in a variety of substances such as liquids and gases. They are even used in several practical situations including boiling, cavitations, crystal growth, chemical reactions between gas and liquid in bubble columns and stirred vessels, to mention only a few examples. Parameters such as rise velocity are very important in the scale up and design of many gas-liquid contactors, as the rise velocity of bubbles determine the amount of time the two phases are in contact for which the mixing of the fluids occur.
The research question proposed "An experimental study on the effects of viscosity on bubble drags and rise velocity in stagnant glycerol solutions" is to understand the effects of the liquids property, viscosity, on such characteristics as their rise velocity and drag coefficient, i.e. their movements through the liquid. In this investigation, I will be measuring the viscosity of five different concentration ratios of water-glycerine and the time it takes the bubble to travel between two line segments drawn on the visible screen, measured using a video camera. Comparing the viscosities and the motions of the bubbles in the fluid mixtures, I will discuss the results and establish a possible trend.
(FBD)Rise of a bubble in stagnant Newtonian fluids
The diagram below illustrates the evolution of the bubbles and all of the internal and external forces acting on the sphere as it is formed in the fluid. Figure 1.1 shows a sketch of the entire system (initially, the bubble evolves into a sphere as air is injected from the syringe). The force body diagram on the bubble as it flows upstream is the dashed cross-section that has been removed and exploded in the left portion of this figure. Note that the bubble is not actually spherical over the range of viscosities.
There are three forces acting on the bubbles during its rise to the surface, they are the buoyancy (FB), the drag (FD) and the force of gravity (FG) affected by its weight. Figure 1.0 illustrated the forces and it should be noted that the magnitudes are not to scale.
FD + FG
Fig. 1.0 Free Body Diagram of bubble travel. Fig. 1.1 Free Body Diagram of evolution.
After evolution, a bubble rapidly begins to rise to the surface with a velocity, Vb. The value of Vb is determined by the ratio between the buoyant rise force, and the drag force, which is inherently dependent on the fluids properties such as viscosity and density. The larger the buoyant force the greater the speed of ascension. As the bubble rises, a new interface is created at the upstream hemisphere whereas the old hemisphere flows down towards the bottom stream hemisphere where it eventually disappears. Naturally, when the magnitude of FB > FD is large, the rise velocity will be greater and changing, where the drag force is proportional to the change in viscosity. Hence for higher viscosities the drag coefficient will be higher.
Common controlled variables between both experiments
Among all other variables this would have to be controlled and isolated, which is why five different fluid mixtures were created with water and glycerine. Glycerine will permit changes in the viscosity of water without any significant change in the surface tension. It will have to be added to distilled water as the magnesium and calcium found in potted water could react with certain chemical components and compromise the fluids performance in the tests.
It has a large effect on fluid viscosities; the temperature affects the average speed of the molecules and the time they spend near their neighbouring molecules. Therefore, the temperature of the mixture was maintained at room temperature (~20oC) and a thermometer (-10oC to +110oC, Â±0.5oC) was used to measure the temperature of the mixture at different depths. The lab was even kept free from any source of draft.
The density (expressed as mass per unit volume) of the fluid will influence the drag force experienced by the bubble as it flows upstream. In addition, it affects the efflux rate of a liquid. The density also varies with temperature and is carefully measured using an electronic scale (Â±0.1g). Since glycerine's density is not equal (but pretty close)  to the value for the density of distilled water, some variability is expected in the values measured for the aqueous glycerine.
The total volume in each trial and experiment (viscosity and displacement) is kept the constant.
In both experiments and in every trial, the distance was fixed. During the measure of the efflux time to determine kinematic viscosity, the distance between the two points were maintained by cleaning, drying and re-using the same container. The same procedure was used for the different mixtures in the column for the displacement experiment.
Experiment (1): Fluid characterisation
The viscosity of a liquid is its resistance against shear or flow and is caused by the intermolecular friction exerted when layers of fluids attempt to slide by each other. The kinematic viscosity relies on the force of gravity and the fluid's density as providing the driving force for the movement of the fluid and is therefore measured using a simple instrument, where the time it takes the liquid to flow out as it is being sheared by the orifice is measured. The kinematic viscosity can then be derived by using a simple calibration constant, which is gained by applying a liquid of known kinematic viscosity through the apparatus (at the appropriate reference temperature) and measuring its efflux time.
Boss Clamp, Clamp Stand
2x 100 ml Measuring Cylinders (Â±0.5ml)
5x 400ml Beakers
1x 300ml Plastic Beaker
Electronic Stop Watch (Â±0.05s)
Thermometer (-10oC to +110oC, Â±0.5oC)
Electronic Scale (Â±0.05g)
Independent Variable: Concentration percentage.
Dependent Variable: Time.
Using the 100 ml measuring cylinders prepare five 250ml mixtures from water/glycerine and place them in separate 400ml beakers, in the concentration percentages of:
Table 1: displaying the concentrations of the separate mixtures of water and glycerine.
During the preparation of the mixtures, tiny bubbles may form due to the intake of air while pouring the liquids. In any such case the mixture will need to be stirred until the bubbles are removed and left to settle. The temperature of the mixture will need to be measured to avoid any discrepancies between other mixtures after the agitation of the liquids.
After letting the mixture settle, place it on the electronic measuring scale (Â±0.05g) and measure its mass and then, consequently its density. The variability of the density can be expressed as an uncertainty error in the values of the kinematic viscosity.
Take the plastic beaker and drill a hole of diameter 0.5cm (similar to the diameter of the air injection pipe used in creating bubbles) and attach it to the clamp stand using the boss clamp.
Using the pen marker, sketch two arbitrarily placed lines on the plastic beaker (reasonable distance between them).
Using either a stopper or your own finger, plug the hole at the bottom of the plastic beaker while pouring the mixture into it.
Place the now emptied beaker under the plastic beaker. Remove the plug and measure the amount of time it takes for the liquid to drain between the two lines.
Repeat the measurements at least three times and take an average of the results.
Experiment (2): Measuring the ascension of bubbles
The experiment was filmed using a Cannon video camera with a 25 fps recording speed.
Plastic Drain Pipe (12.00cm x 12.00cm x 30.00cm)
Metre ruler (Â±0.05cm)
Steel Wire, higher resistance the better
1x 1000ml Measuring Cylinder (Â±0.5ml)
2x 1000ml Beakers
Additional Controlled Variables
Volumetric Flow Rate: The rate of air flow affects the rise velocity as the speed at which air is pumped into the liquid governs the initial velocity gained by the bubble as the air molecules inside are rushed. A known volume of atmospheric air is injected into the liquid through a syringe (20.0ml Â±0.5ml) with an approximate flow rate, Gair â‰ˆ 0.87ml3s-1.
Kinematic Viscosity: The viscosity of a liquid as under the force of gravity and is the ratio of viscosity to density. (Measurements explicated in procedure)
Displacement and Time (Measurements explicated in procedure)
Firstly, the column to hold the liquid was built using a plastic drain pipe cut longitudinally (A steel wire was connected to the terminals of an A.C generator, running a voltage across and heating it up in order to slice the pipe with ease) with the approximate measurements for the length, breadth and height being 12.00cm, 6.00cm and 30.00cm respectively.
A hole of diameter 0.5cm (Â±0.05cm) was drilled into the back of the pipe. A tube of length 7.4cm and diameter 0.46cm (Â±0.05cm), from where the gas will be injected into the liquid, was attached.
A Perspex glass of approximate height, 30cm, and length, 12cm, was attached to the open side of the pipe (with glue) enabling the observer to view the ascension. The pipe was then attached to a wooden block to keep it levelled on all surfaces as well as acting as the base.
A number of preliminary tests should be run with the column to ensure that there are no sources of leaks. If found, the source was sealed further by tape.
Distilled water and glycerol were measured using a 1000ml measuring cylinder and stored in two separate 1000ml beakers. The mixtures started with a higher concentration of glycerol than distilled water and were diluted down into the appropriate concentrations for each experiment (hence, conserving the amount of glycerol). The amount of the original mixture required to add distilled water to, was measured using the formula:
M1V1 = M2V2, where M1 is the initial concentration of glycerol and V1 is the volume of the original solution required for dilution. M2 is the final concentration expected after the dilution and V2 is the total volume of the solution. For example, Let us take the second experiment where the concentration percentage of glycerol to distilled water is 70: 30.
Initial Concentration, M1 =,
Number of Moles =, 
Mass = VGlycerol (90% of 2000ml) x (Acquired)
= 1800ml x 1.83gml-1 = 3294g.
Number of Moles = =35.8mol,
Initial Concentration, M1 =molml-3.
Final Concentration, M2 =,
Number of Moles =,
Mass = Expected VGlycerol x (Acquired) =
Number of Moles = = 27.8,
Final Concentration, M2 =.
The final concentration must always be lower than the initial concentration. Therefore, volume of original solution needed,
V1 == 1553.1ml
And, Volume of Distilled water = 2000.0 - 1553.1 = 446.9ml
All Calculations were done in a similar manner.
Table 2: displaying the volume of the mixture added to distilled water from the above calculation method.
âˆ†[concentration]% of glycerol
Volume of original solution(Â±0.5ml) /ml
Volume of distilled water (Â±0.5ml) /ml
90% - 70%
70% - 50%
50% - 30%
30% - 10%
Having prepared the mixtures and column, the outer tubing leading to the hand-held syringe was constricted initially to prevent an outflow of the liquid. The mixture was poured in and left to settle for 2 - 3 minutes.
The atmospheric air was injected with an approximate flow rate and the bubbles movements were recorded using a video camera, which was kept in line with the face of the column. The captured film was then digitised onto the computer and analysed through appropriate software (explained in method of analysis).
The bubbles were formed in succession of each other over different trials.
Illustration of procedure:
Gas injector (D: 0.5cm)
Able to hold 2.5 litres
Care should be taken in aligning the video camera perpendicular to the plane of the face of the column. The glass used was flat to prevent as much distortion as possible from refraction.
Experimental (1) Results (Raw):
The rheological properties for different concentration of the glycerol solutions tested are summarized in table 3.0.
Table 3.0: Experiment (1) results: The time taken for a specific volume of the liquid to drain during each successive trial.
Water: Glycerol mixture
(Percentage ratio %)
Efflux Time /s (Â±0.05s)
Efflux Time /s
Efflux Time /s
90 : 10
70 : 30
50 : 50
30 : 70
10 : 90
Experimental Results (Numerical Data analysis):
The kinematic viscosity () is proportional to the efflux time (T) of the liquid flowing through the points.
Re-arranging the equation gives the means to calculate the calibration constant (c). A liquid of known kinematic viscosity (648 cSt, Reference temperature =20.3oC) was run through the experimental setup and the average efflux time was found to be 48s.
Therefore using equation (1) the kinematic viscosity can be determined.
Table 4.0: Experiment (1) analysis: The properties of the mixtures have been measured using the above approach and are displayed below in tabular form. The kinematic viscosities uncertainty is represented as a percentage of the sum of the uncertainties in the efflux time and density.
Water: Glycerol mixture (percentage ratio %)
Average Efflux Time (Â±0.05s) (T) /s
Kinematic viscosity (Â±3.30%) () /cSt
90 : 10
70 : 30
50 : 50
30 : 70
10 : 90
Average Density: 1.83gml-1
Experiment (2) Method of analysis:
A method of Video Analysis was used to collect data on the bubbles. Firstly, the experiments were recorded on a digital video camera. The two points marked on the column (separated 30cm) acted as a known measurement to scale the distance. The difficulty being the angle of the camera, which had to be levelled and kept perfectly perpendicular to the face of the column to have as little distortion as possible. For the same reason, I had to produce the bubbles as close to the face of the column so that the scale on the plane of the bubble was as close to the scale on the plane that holds the face of the column as well.
After the experimenting phase was done, and they have been properly recorded, the footage was digitised onto the computer. The long footage was trimmed down into shorter clips for the ascension of the bubbles in each experiment; ending up with six different movie clips and were converted from .mpeg-II to .mov with a decreased frame rate of 6 fps. The clips were then imported in to Logger pro 3.8 demo (graphical analysis software with video analysis capabilities). In Logger pro I located the bubble in each frame. The clips were on average about 8 seconds long for the entire experiment, each experiment contained three trials, on average 2 seconds at 5 fps that is 10 frames per trial, and at 25 frames per second are 50 frames per trial. Although, not quite as accurate, does save a lot of time and the loss of accuracy is not significant. The clip is then scaled using the separation between the two points on the front and running a marking along the side on the column. Logger pro then proceeded to collect the time and position coordinates and from there on position and velocity (among many other) graphs can be extracted.
The graphs of the two second most extreme concentrations of glycerol are displayed below, i.e., 30% glycerol and 70% glycerol, to demonstrate the various trends in the graphs of displacement and velocity, when the concentration for glycerol is increased. All of the data sets start at the beginning of the line segment until their ascension to the top  .
Fig.1.0 represents the graph of the displacement against time for the bubble travelling in 30% glycerine measured every frame, which was gathered from analysing the footage.
Fig.2.0 represents the graph of the displacement against time for the bubble travelling in 70% glycerine measured every frame, which was gathered from analysing the footage.
Through point-by-point video analysis I was able to extrapolate position data sets for the bubbles. The bubbles approach what seems to be a linear trend very shortly after starting their ascension. There were three trials for every concentration of glycerol and in all three, the graphs for each concentration arrives at a linear trend, and when fitted with a line of best fit has a correlation of at least 0.980  . This linear trend in the position means a constant velocity, which then means no acceleration. This section of constant velocity is said to be the bubble's terminal velocity. Zero acceleration also means that the net Force is zero (F=ma). The terminal velocity as represented by the graph has also been calculated, which will be later used to understand it as a function of the Reynolds number.
Fig. 3.0 illustrates the position versus time with the velocity measurements done by logger pro superimposed on the graph as well.
However, though the velocity has been established to be constant, the graph does not show up constant. This is caused by the method of data collection. Point by point video analysis basically collects a series of times and coordinates, which makes it perfect for collecting position data. However, it does not calculate velocity that well due to limited frame rate as it takes the âˆ†y and âˆ†t values between each frame and possible distortions makes this process less accurate and further from the desired instantaneous value of dy and dt.
Reynolds number calculation:
The Reynolds number is dimensionless number that is compared to the terminal velocity as it is a better representation of the forces acting on the bubble as it flows through the liquid, in terms of a ratio of the viscous to inertial forces and is computed by :
tRe ....... (2), where ........ (3),
Where, ut = terminal velocity (acquired, cms-2), v = kinematic viscosity (acquired, cm2s-1), Pliquid = density of the liquid (acquired, gcm-3), Âµ = dynamic viscosity.
Bubble Diameter Measurement
A bubble equivalent diameter (deq) was measured from the still frames obtained from the video recording. The still images were then processed using Pixcavator IA 3.2 demo and the bubble height (dh) and bubble width (dw) were measured in pixels. The pixel measurements were converted to millimetres by calibrating it from the video camera's resolution and the measurements are only considered to be relative to each other. The bubble equivalent diameter, Deq was determined  as
Deq = ...... (4)
Where dw is the horizontal length and dh is the vertical length of the bubble. For this measurement it was assumed that the bubble was symmetric with respect to its vertical axis  . The average equivalent diameter (deq) using equation (4) was found to be,
deq â‰ˆ 2.54mm (Â±0.05mm).
Rise velocity results/analysis:
Fig. 4.0 the rise velocity on a sphere as a function of the Reynolds number measured using equation (2) & (3) Tempref â‰ˆ 20oC.
The bubble velocity was measured at a height of 30cm above the point of air injection and the results obtained for the different kinematic viscosities is illustrated above in figure 4.0. It can be seen from figure 4.0 that the bubbles flowing in the solutions of higher Reynolds number have a large terminal velocity. It can be seen from figure 4.0 that bubbles flowing in solutions of lower Reynolds number are greatly dominated by viscous forces and changes in viscosity have larger impacts on their terminal rise velocity. When the concentration of glycerol is lower (10% to 50%) compared to distilled water, higher Reynolds number, the values are very close together, suggesting that the viscous force seems less dominant. Therefore, increase in viscosity from 115 to 133 Cst has little effect on the terminal velocity.
Drag coefficient calculation/analysis:
The drag force, similar to friction, slows the upward movement of the bubble and the coefficient of drag is used as a relationship to determine the resistance of an object in the fluid, which is an important property to understand and in the assumed case of non spherical bubbles the drag coefficient is calculated according to the given formula :
Cd = â€¦â€¦â€¦.. (5)
Where deq is the equivalent sphere diameter and dw is the diameter of the horizontal length or long axis length of the bubble and âˆ†Ï is the density difference between the liquid and the atmospheric air.
Having calculated the average density of the liquid in table 4.0, the density for the atmospheric air can be calculated by using an extension of the gas law in terms of density:
, where Ïair = density of the air, P = pressure, 1atm = 101325 Nm-2, R = gas constant (dry air) = 286.9 J K-1 mol-1, T = temperature, at 20oC = 293.16 K (Â±0.5K),
Therefore, the density of air is, Ï = 1.205 kgm-3 (Â±0.17%)
And, using those values measured in experiment (2), I can calculate the drag coefficient using equation (5).
Figure 5.0 Log - Log plot of the drag coefficients on a sphere as a function of Reynolds number, Tempref â‰ˆ 20oC.
As the particle Reynolds number increases from 106 to 106.5 (Â±6.3%) there is a large decrease in the drag coefficient (Â±7.7%), Cd, from a value of about 104.5 to a value of about 104.0. As according to documentation , this happens due to the viscous flows around the bubble creating "wakes" behind the sphere and the decrease in viscosity, higher Reynolds number, corresponds to the formation of a turbulent boundary layer in front of the sphere while accompanied by a narrower "wake" behind the sphere. This narrower "wake" that forms behind the bubble causes the drag force to decrease. Also, there is clearly an inverse relationship between the drag coefficient and Reynolds number for the liquid.
An experimental set-up was used to analyse the characteristics of the bubbles rising in different kinematic viscosities of glycerol and distilled water. The bubble rise characteristics, namely, bubble velocity and drag coefficient produced reasonable results. The bubble rise phenomena showed how the bubble velocity varies with the increase in liquid viscosity as the bubble rises through the liquid column. The velocity graph displays a trend for different concentrations of glycerol solutions that the average bubble rise velocity decreases with the increase in kinematic viscosity. For smaller concentrations of glycerol (10% and 30%) the viscous forces are less dominant and a small decrease in bubble velocity is observed for increasing solution viscosity. The graph displaying the relationship between the Cd and Re for the fluid illustrates that with decreasing kinematic viscosity, the resistance felt by the bubble decreases due to the formation of a turbulent boundary which transcends into a narrower wake and can be inferred that with lower concentrations the viscous flows are not the dominant forces. This research project could be extended to include the effects of viscosity on the bubbles trajectory as it rises to the surface, which is also an important characteristic to consider in gas-liquid contactors. Also, the possibility of extending the correlation for bubble rise characteristics to Non-Newtonian fluids for their many applications and wide availability in the world and industries.
After reviewing my experimental procedure I have noted a few limitations that might cause deviations in the resulting data and with the largest percentage error of 7.7%. The most common error in the experiment would be a parallax error and could have been made during the measurements of required glycerol and distilled water as the apparatus was held in hand during which the points were read, leading to a possible misread of the meniscus from tilting. Also, the apparatus used to hold the liquid while measuring the efflux time could have tilted as well when placed on the stand. Secondly, due to the limited frame rate of the camera, the images were distorted as the movements were too quick for it to capture, leaving it blurred, making it difficult to locate during the point by point analysis. Thirdly, the volumetric rate of atmospheric air injected into the column would have differed slightly each time due to human error. And as previously mentioned the limited frame rate caused discrepancies in the data which made the velocity not appear constant. The method of still frame analysis to determine the width and height did not take into account distortions from the video camera and the actual diameter may vary widely. Although, precaution was taken to prevent leakages, the board that was attached as the base to keep it sturdy was made from wood, which absorbed some of the solution as it is permeable. As the glycerol and distilled water were mixed, so too were air molecules trapped in the layers and the agitation experienced by each solution to remove the air bubbles would be different and this would affect the consistency of the data. Also, an assumption was made on the humidity in the air due to the weather conditions, which would affect the accuracy of the density measurements.
Possible solutions that I would suggest is a high speed video camera with a large frame rate clearly capturing the objects movement. The equipment should be placed on a stand and the observers eye sight perpendicular to the meniscus or line segment, or possibly use a ruler as a reference for a straight line. The base should be fitted with an impermeable surface such as aluminium (light-weight and strong). A video camera with a larger frame rate would also reduce the distortion in the liquid and make diameter measurements more accurate. I would have liked to compare my values with those available in literature to see the extent of the deviations and possibly arrive at a solution to optimise the experimental method further. A hygrometer would have helped establish the amount of humidity present in the room at the time of conducting the experiment.
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Kulkarni, A. A. and Joshi, J. B., Bubble Formation and Bubble Rise Velocity in Gas-Liquid Systems: A Review, Ind. Eng. Chem. Res., 44, 2005, 5873-5931.
Miyahara, T. and Takahashi, T., Drag Coefficient of a Single Bubble Rising through a Quiescent Liquid, Int. Chem. Eng., 25 (1), 1985.
Burris, A.W. factors affecting bubble size in water, Technical notes pg.54 -57
Ron Darby. "Chemical Engineering Fluid Mechanics" Marcel Dekker, Inc. 2001
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