I

Eq. 9 describes the efficiency of removal of particles or floes onto bubbles within the contact zone. The model is instructive in that it identifies important variables affecting contact zone performance. These include the particle-bubble attachment efficiency (a'pb\ the single collector efficiency (rjr), bubble size (d/,), bubble rise velocity (vb), bubble volume concentration and the contact zone detention time (tc:). Table 3 provides a summary of these variables. The variables are categorized in terms of how they are affected by pretreatment processes and by flotation tank design and operation.

Table 3

Contact zone model variables_

Variable Dependence_

_Pretreatment_

otpb Interaction forces between particles and bubbles

Comments

Coagulation chemistry including dose and pH critical in maximizing particle attachment to bubbles rjr dp2'3: Brownian Diffusion

_dp2: Interception & Settling

_Flotation tank_

dt, db in Eqn (9) and ¿4" for rjr dependence.

rjr Primarily floe size (dp2,i &

dp2) and bubble size (dh2)

Flocculation increases dp. Desire floes of 10s of microns

Smaller bubbles yield better performance. Bubble size set mainly by the pressure difference across the nozzle; influenced also by the type of nozzle.

For mean bubble size of 60 |im, high rjr achieved for floes of 10s of microns

Recycle flow and saturator pressure.

n db tcz Depth and flow rate through the contact zone.

Controlled mainly by the recycle flow or ratio. Values as high as 8000-9000 ppm insure large volumes of bubbles for collection and floating of particles Describes motion of bubble relative to the water flow in the contact zone. Lower value means bubbles reside for longer period increasing opportunity for collection of particles

Contact zone detention times need to exceed 1-2 min

3.3. Pretreatment chemistry and flocculation

Pretreatment coagulation affects the particle-bubble attachment efficiency (ctpb), and pretreatment flocculation affects the particle size (dp) of floes in the influent to the flotation tank contact zone. Both pretreatment steps have been described in earlier Chapters, 2 and 5, and both are important to DAF. Model predictions (Eq. (9)) are presented next for typical DAF tank operation followed by discussion of the fundamentals.

One approach to evaluating aPb is an empirical viewpoint. aPb can have values between 0 (no collisions lead to attachment) and 1 (all collisions result in attachment). In this empirical approach, apb depends on coagulation pretreatment chemistry (coagulant type, dosage, and pH). Fig. 4 shows the contact zone efficiency as a function of particle or floe size for two cases of Opt,: 0.5 for good coagulation and 0.01 for poor coagulation. Model predictions in Fig. 4 show that for poor coagulation the contact zone efficiency is very low (< 5%) for particles or floes <10 ¡am, and that high efficiencies are not obtained unless floes approach 100 (am. For good coagulation (favorable attachment, apb of 0.5), floe particle sizes of tens of microns result in high efficiencies (> 80%). The model predictions also show a minimum in the contact zone efficiency for particles of 0.9 |am. This minimum at ~ 1 (am is analogous to granular media filtration efficiency. This is because the physics of particle transport is the same for the two processes. Particle transport by Brownian diffusion is the controlling mechanism for particles < 1 |am while particle transport by interception controls for particle sizes > 1 (am; transport by settling is not significant for floe particles with densities of 1100 kg/m3. In summary, floe particles of tens of microns have high rjr values yielding good contact zone removal efficiencies (Fig. 4). An important model finding then is that floe particles of tens of microns should be prepared by the pretreatment flocculation process for the influent to DAF tanks.

Particle Diameter (jim)

Fig. 4. Contact zone efficiency as a function of particle or floe size for good (dp/, = 0.5) and poor (a^, = 0.01) coagulation for conditions of t„ = 3 min, p„ = 1100 kg m"3, T = 293 °K, db = 60 (am, and <J>4 = 8000 ppm (Source: Adapted from Haarhoff and Edzwald [1])

Particle Diameter (jim)

Fig. 4. Contact zone efficiency as a function of particle or floe size for good (dp/, = 0.5) and poor (a^, = 0.01) coagulation for conditions of t„ = 3 min, p„ = 1100 kg m"3, T = 293 °K, db = 60 (am, and <J>4 = 8000 ppm (Source: Adapted from Haarhoff and Edzwald [1])

The empirical approach to the evaluation of aPb has had some success. Haarhoff and Edzwald [1] reported on empirically determined apb values between 0.5 and 1 for optimum alum coagulation characterized by pH around 6 and dosing yielding floes of zero or no charge. Shawwa and Smith [13] found aPb values of 0.35-0.55 for good coagulation conditions, and Schers and Van Dijk [14] found apb values of 0.2-1 from data for six DAF plants in The Netherlands.

As particles are transported from the bulk solution to close distances at the bubble surface, forces between the bubble and particle affect attachment, as depicted in Fig. 5. Detjaguin et al. [7] have described this bubble-particle interaction for small particles according to classical colloidal particle interactions. These forces occur at separation distances of tens of nanometres. These forces include electrostatic forces from overlapping of electrical double layers (charge repulsion), London-van der Waals forces, and a hydrophobic force. Another force affecting bubble-particle attachment is hydrodynamic retardation. Excluding the hydrophobic force, Han [15] and Leppinen [16] have considered the above forces to model collisions and attachment of particles to bubbles. Next, some discussion is presented of these fundamental factors affecting the particle-bubble attachment efficiency, Otpb-

Fig. 5. Attachment affected by particle-bubble interaction forces and hydrodynamic retardation

Air bubbles carry a negative charge, even in distilled water or distilled water containing simple non-hydrolyzing salts. Negative zeta potentials have been reported in the range of-15 to -25 mV [7, 17, 18]. Dockko and Han [18] reported zeta potentials of about - 25 mV at pH 6 to 8 for bubbles of about 30 (im. They found the isoelectric point at about pH 2.5. Unlike inorganic and organic particles in waters, air bubbles do not contain surface functional groups that ionize or complex metals leading to charged surface groups; however, they can obtain a charge by three mechanisms. First for the case of bubbles in clean water, their charge is attributed to a higher concentration of small anions close to the bubble surface compared to the larger hydrated cations. Second, water supplies may contain negatively charged surfactants that accumulate at the bubble surface causing a negative charge. Third, the addition of positively charged polymers or metal coagulants that precipitate positively charged particles can accumulate at the bubble interface reducing its charge or even reversing its charge.

Particle

Particle-bubble interaction forces and hydrodynamic retardation

London-van der Waals forces between dissimilar particles - i.e., solid particle and air bubble - may be attractive or repulsive. Lu [19] in considering the London dispersion force for a non-polar bubble and a particle in water makes a case for a repulsive interaction. Others, however, indicate that the net DLVO force (double layer repulsion and London-van der Waals) may be attractive or repulsive [7, 17] with the double layer repulsion due to interaction of negatively charged particles and bubbles playing a key role preventing particle attachment to air bubbles.

Ducker et al, [17] made force measurements and found that the hydrophobic force is strong at distances exceeding those associated with double layer interactions, and it is the primary force explaining attachment of hydrophobic particles to air bubbles.

Another force that can hinder collisions, and thus attachment, is hydrodynamic retardation. This is the force that causes a deviation in the particle trajectory as the particle approaches the bubble surface due to resistance to motion from thinning of the viscous water between the particle and bubble. The single collector collision efficiency equations presented above, for interception and settling (Eqs. (6) and (7)), do not account for hydrodynamic retardation, and show a basic dependence of 77/ and ijs according to dp, although the interception dependence is a little more complicated than that. The exponent on dp should be less than 2 if hydrodynamic retardation affects 77. Collins and Jameson [20] found dependence according to dp5 indicating an effect from hydrodynamic retardation. Their experiments were undertaken using polystyrene particles of 4-20 pm collected by bubbles of about 50 pm, a system where 77/ (interception) dominates. On the other hand when settling (rjs) was the main transport mechanism, Reay and Ratcliff [12] found dependence according to dp'05.

In summary, coagulation is essential in water treatment to reduce repulsive charge interactions between particles or floes and bubbles. Favorable attachment (high apb values) of particles to bubbles requires reduction in the repulsive charge interaction between particles and bubbles. Floes with zero or very low zeta potentials should be produced through coagulation. Under these conditions, attractive forces can prevail (London-Van der Waals or hydrophobic) leading to attachment. Coagulant chemicals are used to obtain favorable attachment so apb depends on coagulation conditions (type, dosage, and pH). In some waters hydrophilic colloids may exist that are resistant to bubble attachment, but proper coagulation can alter the colloid surface properties so that attachment to bubbles is favored.

3.4. Bubble size, bubble concentration, and contact time

Eq. (9) shows the variables affecting contact zone performance. Important design and operating variables associated with the flotation tank and recycle system are bubble size (¿4), bubble volume concentration and the contact zone detention time (tc:) as summarized in Table. 3.

Overall, the contact zone efficiency depends on db' - see Eq. (9) and Table 3. Smaller bubbles provide for better performance. Bubble size also affects Tjj with higher single collector efficiencies for smaller bubbles. The principle that smaller bubbles are better for the contact zone agrees with observations that DAF is more efficient than dispersed air flotation. Bubble size of say 60 pm is characteristic of DAF in contrast to bubbles of about 1 mm for dispersed air flotation.

Model predictions in which the contact zone detention time is varied (iC2) are made using Eq. (9). The model assumes plug flow. Haarhoff and Edzwald [1] examined the hydraulics of the contact zone and the effects of dispersion, and found that plug flow provides reasonable predictions of contact zone efficiency. To evaluate the effect of bubble concentrations, two cases of <f>/, are examined. In one case was set at 9000 ppm, this represents high bubble concentrations (Table 2) that are achieved with recycle ratios (R) of about 10-12% and saturator pressures of 500-600 kPa. was set at a much lower value of 3000 ppm, which may result from low recycle ratios such as 4% or combinations of lower R and lower saturator pressures.

Model predictions for removing 20 |xm floes are presented in Fig. 6 showing the dependence of contact zone efficiency on the detention time for the two bubble volume concentration cases. Poor efficiency occurs for low bubble volume concentrations unless high contact zone detention times are used. Low bubble volume concentrations do not provide sufficient bubble volume for efficient collection of floes. Low bubble volume concentration of 3000 ppm means the air bubble mass (Q,) and number concentrations (tit) are also low, corresponding to values of 3.6 mg L"1 and 25xl06 bubbles L"1, respectively. Fig. 6 shows that for a bubble volume concentration of 9000 ppm, the contact zone efficiency is high and insensitive to detention times exceeding 1.5 min. Contact zone detention times used in practice are 2 to 4 min. The theoretical predictions support design practice, and show that shorter times lead to poor performance. They also show there is no benefit to increasing the detention time where is about 9000 ppm. A of 9000 ppm corresponds to Q and nb concentrations of 10.7 mg L"' and 70xl06 bubbles L"1, respectively. DAF systems are usually designed to release about 10 mg L"1 of air so a good benchmark value for is 9000 ppm.

Fig. 6. Contact zone efficiency as a function of detention time for high (4>t = 9000 ppm) and low = 3000 ppm) bubble volume concentrations for floe size of 20 |im for conditions of = 0.5, pp = 1100 kg m"3, T= 298 °K, and db = 60 ^m (Source: Adapted from Haarhoff and Edzwald [1])

Fig. 6. Contact zone efficiency as a function of detention time for high (4>t = 9000 ppm) and low = 3000 ppm) bubble volume concentrations for floe size of 20 |im for conditions of = 0.5, pp = 1100 kg m"3, T= 298 °K, and db = 60 ^m (Source: Adapted from Haarhoff and Edzwald [1])

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