Chapter 1 The Fundamentals of Bubble Formation in Water …

 

 

Chapter 1

The Fundamentals of Bubble Formation in Water Treatment

Paolo Scardina and Marc Edwards1

Keywords: bubble, air binding, filters, nucleation, equilibrium, water treatment,

headloss, filtration, gas transfer

Abstract: Water utilities can experience problems from bubble formation during
conventional treatment, including impaired particle settling, filter air binding, and
measurement as false turbidity in filter effluent. Coagulation processes can cause
supersaturation and bubble formation by converting bicarbonate alkalinity to carbon
dioxide by acidification. A model was developed to predict the extent of bubble
formation during coagulation which proved accurate, using an apparatus designed to
physically measure the actual volume of bubble formation. Alum acted similar to
hydrochloric acid for initializing bubble formation, and higher initial alkalinity, lower
final solution pH, and increased mixing rate tended to increase bubble formation. Lastly,
the protocol outlined in Standard Methods for predicting the degree of supersaturation
was examined, and when compared to this work, the Standard Methods approach
produces an error up to 16% for conditions found in water treatment.

Introduction:

Gas bubble formation is of established importance to divers and fish (i.e., the

bends), carbonated beverages, solid liquid separation in mining, cavitation in pumps, gas

transfer, stripping, and dissolved air flotation processes. Moreover, it is common

knowledge that formation of gas bubbles in conventional sedimentation and filtration

facilities is a significant nuisance at many utilities, because bubbles are believed to hinder

sedimentation, cause headloss in filters through a phenomenon referred to as “air

binding,” and measure as turbidity in effluents without posing a microbial hazard.

Utilities have come to accept these problems, and to the knowledge of these authors there

is currently no rigorous basis for predicting when such problems will occur or correcting

them when they do.

1 Paolo Scardina is a graduate student at Virginia Tech, Marc Edwards is an associate professor of

environmental engineering at Virginia Tech, 418 NEB, Blacksburg, VA 24061.

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In the past, many utilities having problems with bubble formation from waters

supersaturated with dissolved gas have traced the source of the problem to air

entrainment at water intakes. However, with the increasing popularity of “enhanced

coagulation” at lower pHs, utilities may increasingly see problems arising from carbon

dioxide driven bubble formation upon acidification of waters under some circumstances.

Even if a source water is initially at equilibrium with the atmosphere and has no potential

to form bubbles, the water can become supersaturated with carbon dioxide upon

coagulant addition by conversion of bicarbonate to carbon dioxide:

[HCO3
[H2CO3] fi

-] + [H+] fi

[H2CO3]

[CO2] + [H2O].

Since treatment plants operate as closed systems with respect to gas transfer (Letterman

et al. 1996), supersaturation from the newly formed carbon dioxide can lead to bubble

formation through various mechanisms.

The goal of this paper is to describe the fundamental chemistry of bubble

formation, with a particular emphasis on carbonate supersaturation in water treatment

plants. Equations are developed to predict the volume of bubbles that potentially form

during treatment processes, and a new device to physically measure the gas formation

potential of a water is introduced. The merits and drawbacks of other approaches to

predict bubble formation are also discussed.

Fundamentals of Bubble Formation:

Bubble Nucleation

Following supersaturation of a dissolved gas, a nucleation step is necessary before

bubbles can form in solution. Homogenous or de novo nucleation describes spontaneous

bubble formation within the bulk water. This typically occurs only if the difference

between the ambient and dissolved gas pressure is greater than 100 atm. (Harvey 1975);

consequently, homogenous nucleation is not expected to be observed in water treatment.

Bubbles can also form within pre-existing gas pockets located in surface cracks

and imperfections of solids in a process known as heterogeneous nucleation (Figure 1).

Supersaturated gas diffuses into the gas pockets, causing bubble growth and eventual

detachment from the solid support. Unlike homogeneous nucleation, significantly less

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dissolved gas supersaturation

is required for heterogeneous bubble formation.

Heterogeneous bubble nucleation can occur whenever a water is supersaturated (Hey et

al. 1994) and is expected to prevail in most environmental systems.

Factors Impacting Nucleation

The size and number of bubbles nucleated depends on the history of the water

body and type of suspended particles (Keller 1972). The number of nucleation sites

generally increases in the presence of surface active agents (Jackson 1994). Rough

hydrophobic surfaces nucleate bubbles easily even at low supersaturations, while

hydrophilic or even smooth hydrophobic surfaces nucleate bubbles only at exceptionally

large supersaturations (Ryan and Hemmingsen 1998; Ryan and Hemmingsen 1993). The

gaseous nucleation site can persist indefinitely on surfaces (Libermann 1957; Tikuisis

1984). Surfactants such as soap reduce bubble nucleation at low micelle concentrations;

whereas, above the critical micelle concentration they can increase nucleation (Hilton et

al. 1993).

Supersaturated
Dissolved Gas
Molecule

Bubble
Detachment

(Diffusion)

Bubble

Growth

Pre-Existing Gas Pocket
on a Solid Support

Figure 1 – Heterogeneous Nucleation

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The crevice surface geometry dictates the curvature and internal pressure of the

pre-existing gas pockets. This can be estimated using various approaches for use in

modeling and predicting bubble formation. Unfortunately, no reliable analytical

techniques can currently validate the predictions experimentally for the ideal geometries

(Hey et al. 1994), although successful data can be obtained with arbitrary, irregular

surfaces (Ryan and Hemmingsen 1998).

Other system factors affect bubble formation. Increasing gas supersaturation

activates previously dormant nucleation sites and generates more bubbles from these sites

(Hilton et al. 1993; Hikita and Konishi 1984), as will increased mixing intensity (Jackson

1994; Hikita and Konishi 1984). Finally, the tendency for bubble formation increases

with temperature due to reduced Henry’s equilibrium constants and more rapid diffusion

kinetics (Hikita and Konishi 1984).

Model Conceptualization

The preceding section described how supersaturated waters could form bubbles.

Although models exist for other gas stripping processes, no model has been proposed for

bubble formation in water treatment (Boulder, 1994; Hess et al. 1996). A simple

conceptualization was developed to predict the volume of bubbles formed from this

phenomenon (Figure 2). Consider an alkaline water initially at equilibrium with the

atmosphere with no bubble forming potential. Upon acid addition, the bicarbonate is

converted to carbon dioxide and the system will become supersaturated. If nucleation
occurs, a new equilibrium can be approached by forming a volume of gas (D Vgas). In this

conceptualization, the supersaturated carbon dioxide drives the bubble formation, but the

volume of gases includes nitrogen, oxygen, and carbon dioxide.

Using conventional equations for all equilibria, partial pressures, and mass
balance equations for nitrogen, oxygen, and carbon dioxide, D Vgas can be computed

(Appendix I). The model also considers the presence of water vapor, and for simplicity

the percentage of remaining trace gases, like argon, are included with nitrogen through

the convention known as “atmospheric nitrogen” (Harvey 1975). The carbon dioxide

mass balance includes terms that considers the conversion of bicarbonate to carbon

dioxide depending on the final pH. For simplicity in calculation of bubble volumes, the

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ideal gas law was used since use of the real gas law only alters predictions by less than

0.4% under conditions typical of water treatment.

Illustrative Calculations

With the initial alkalinity, final pH (or moles of acid addition), and the ambient

temperature and pressure as starting inputs, a computer program was used to solve the

system of equations for various circumstances. For example, consider a closed system

containing 1 L water with 300 mg/L as CaCO3 alkalinity initially at pH of 8.7 and at

equilibrium with the atmosphere (Figure 3). Following acidification to pH 6.3, the

system will shift to a new equilibrium with 1.62 mL of gas predicted to form. Although

nitrogen and oxygen were not supersaturated with respect to the atmosphere before

acidification, they constitute approximately 90% of the nucleated bubble volume with the

remainder attributed to carbon dioxide (7.7%) and water vapor (2.3%). At equilibrium in

this closed system, the final carbon dioxide concentration remains supersaturated 100

times relative to the external atmosphere.

Intuitively, higher initial alkalinity or lower pH after acidification would be

expected to lead to more bubble formation. The model confirms this expectation with a

direct relationship between the initial alkalinity and bubble volume for a given final pH

(Figure 4). For a water at a given initial alkalinity, predicted bubble volume increases

roughly linearly as pH decreases from about pH 7.5 down to 5.5.

Initially
at
Equilibrium

P = atmosphere

Acid

to Final

pH

HCO3

-+H+ H2O+CO2

Figure 2 – Model Conceptualization

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D Vgas

P = 1 atm.
Temp. = 20 oC

V=1.62mL/L

[N2]aq=5.37 x 10-4 M

[O2]aq=2.84 x 10-4 M

[CO2]aq=1.34 x 10-5 M
Alkalinity = 300
mg/L as CaCO3

pH = 8.7

Initial Conditions

[N2]aq=4.90 x 10-4 M

[O2]aq=2.71 x 10-4 M

[CO2]aq=3.01 x 10-3 M

pH
lowered
to 6.3

[HCO3

-]=0.003 M

Final Closed System
Equilibrium

N2(g)=4.7 x 10-5 moles
O2(g)=1.3 x 10-5 moles
CO2(g)=5.0 x 10-6 moles
pN2=70.51%
pO2=19.54%
pCO2=7.65%
water vapor =2.30%

Figure 3 – Model Illustrative Example

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

)

/

L
L
m

(

e
m
u

l
o
V

e
l
b
b
u
B

0

5

40 mg/L as CaCO3
100 mg/L as CaCO3
160 mg/L as CaCO3

Temp. = 15oC
Press. = 1 atm.

6

6

7

Final pH

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Figure 4 – Bubble Formation Potential as a Function of Initial Alkalinity and pH

The model also predicts increased gas volume production at higher temperatures

(Figure 5). For example, a water with 250 mg/l as CaCO3 alkalinity initially at
equilibrium with the atmosphere would form about 50% more bubbles at 25 (cid:176) C than for

the corresponding conditions at 5 (cid:176) C. The enhanced bubble formation at higher

temperatures is due to the changing Henry’s constant with temperature. The carbon

dioxide from acidification in the water at 25 °C exerts a partial pressure of 0.15 atm.

when pH is depressed to below 5 (1.15 atm. initial total pressure) compared to 0.08 atm.

(1.08 atm. total pressure) at 5 °C. This effect overwhelms the decreased volume of initial

dissolved gas in solution at the higher temperature. Of course, all equilibrium constants

should be corrected to the actual system temperature or significant errors will result.

Like temperature, the ambient pressure or the depth of the solution can impact

bubble formation. The model assumes atmospheric pressure for the pre-existing gas

pockets and the final internal pressure of nucleated bubbles. Hydrostatic forces increase

pressures, and the net result is that at a depth of 1.5 meters the bubble formation potential

is greatly reduced (Figure 6).

Model Confirmation:

Development of Bubble Apparatus

In order to validate the model predictions and provide a tool for use in practical

situations, an apparatus was developed to physically measure the total volume of gas

released from solution. The apparatus (Figure 7) follows the idealized conceptualization

(Figure 2), with gas release occupying some volume within the closed system as

indicated by a water level drop within the measuring pipette. Volume measurements are

taken after the pressure within the pipette is normalized with respect to the atmosphere by

moving the pipette upwards until the water levels (and pressure) in the pipette and

holding container are equal.

Gases formed in the apparatus can either be located as bubbles in the original
liquid volume (a), producing a rise in the flask’s water level D WL, or transferred to the

headspace of the container (b). In either case, the total volume of gas formed appears as
D Vg (Figure 7), and D WL directly measures bubbles remaining in solution.

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5 oC
15 oC
25 oC

Press. = 1 atm.
Final pH = 5

)

/

L
L
m

(

e
m
u
l
o
V

e
l
b
b
u
B

4.5

3.5

2.5

1.5

4

3

2

1

0

0.5

)

/

L
L
m

(

e
m
u
l
o
V

e
l
b
b
u
B

3.5

2.5

1.5

3

2

1

0

0.5

0

50

100

150

200

250

300

350

Alkalinity (mg/L as CaCO3)

Figure 5 – Bubble Formation Potential as a Function of Temperature

40 mg/L as CaCO3
160 mg/L as CaCO3
320 mg/L as CaCO3

Temp. = 15oC
Final pH = 5

1

1.05

Pressure Head (atm.)
Hydrostatic Pressure Depth (m)

1.1

1.0

1.15

1.5

0.5

1.2

2.0

Figure 6 – Bubble Formation Potential as a Function of Pressure

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