Bubble-film extraction (upgraded bubble flotation) is one of the modern methods for purifying contaminated water from surface-active impurities. The features of this method have been considered from the standpoints of the equilibrium and dynamics of surfactant accumulation on floated air bubbles with different sizes. Within a certain ratio of dimension and quantity of air bubbles in their stream transferring adsorbed surfactants from the water bulk into the bubble-film extractor, the productivity of the process increases many times. The effect is ensured by a collective fusion of big and small air bubbles in their close-packed state (embedded system) inside the bubble-film extractor. The driving forces are impulses of capillary waves initiated at the bursting of big air bubbles as constituent ‘destructive’ units of that system.
In the solving of actual urbanistic problems, including that associated with secondary pollution of water in centralized water supply networks, purification of gray sewage water for its reuse in private properties, conditioning of rainwater, etc., knowledge is very important for not causing damage to nature in their practical use. New technologies have begun to be created that more fully satisfy the requirements of the environmental imperative (Rouse 2015; Fujii & Managi 2017; Cruz-Salomón et al. 2018; Kyzas & Matis 2019).
One of the suitable means to remove different admixtures from contaminated water is devices whose principle of action is based on interconnected upgraded bubble flotation (bubble-film extraction) and biological filtration. (Gevod 2018).
Bubble-film extraction is an enhanced flotation method, which runs without hydrodynamic return of flotation product into the subphase and leads to reduction of the concentration of surface-active impurities in the treated water up to the level of a few micrograms per cubic decimetre. This concentration is many times lower than attained by applying regular flotation (foam separation). That is a distinctive feature of the used method in comparison with regular flotation (foam separation).
The biological filter and bubble-film extractor are combined into the closed loop, reliably purifying the water of its endogenous and exogenous contaminants. The process does not require consumable materials and provides savings of natural resources. However, the rate of bubble-film extraction depends on the structure of the air bubble flow used. That structure affects both the completeness of the adsorption of surfactants by each bubble and their ability to release the adsorbed surfactants inside the bubble-film extractor.
In this paper, the features of the bubble-film extraction process are considered from the standpoints of the equilibrium and dynamics of adsorption of surface-active substances (surfactants) on air bubbles with different sizes and their following coalescence inside the bubble-film extractor with the formation of flotation concentrate. For the first time it is shown that within a certain ratio of quantity and dimension of air bubbles in their flows transferring surfactants from the water bulk into the bubble-film extractor, the productivity of the bubble-film extraction process increases many times.
The thermodynamics of adsorption are described by Gibbs theory, which gives the relationship between surfactant surpluses at interfaces, their bulk concentration, and surface tension. Langmuir investigated the monomolecular adsorption of various substances on solid and liquid surfaces. His equations of adsorption isotherms have adequately reflected the essence of the phenomena and are widely used in engineering calculations.
The equilibrium and kinetics of surfactant adsorption by air bubbles in water are discussed here based on Langmuir's ideas that any surface has a finite number of centers (sites) available for adsorption. Each equilibrium state of adsorption is characterized by a certain degree of filling of the surface with surfactant molecules (Moelwyn-Hughes 1961).
Г is the equilibrium adsorption of surfactant at the air–water interface;
Γ∞ is the limiting adsorption;
C is the surfactant concentration in the space (subphase) from which adsorption occurs;
is the capacity of the adsorption layer with thickness h, expressed in terms of the bulk concentration of the surfactant in its space;
is the rate constant of surfactant adsorption;
is the rate constant of surfactant desorption;
is the surface tension of the surfactant solution with a concentration of C;
R is the universal gas constant;
T is the absolute temperature;
n is a coefficient depending on the type of adsorptive matter.
At the adsorption of non-ionized surfactant molecules, the value of n is taken as equal to 1, and at the adsorption of ionized surfactant, it is assumed to be 2.
In Equation (10), the value of corresponds to the equilibrium adsorption of the surfactant (Γeq) on the surface of the subphase. The value of is the difference between the values of equilibrium adsorption and of current adsorption, i.e. .
ADSORPTION DYNAMICS VS TYPE OF ADSORPTIVE MOLECULES
The adsorption under the indicated conditions is completed almost instantly. No significant time is required to reach the state of equilibrium distribution of the surfactant molecules between the subphase and the adsorption surface. Rapid adsorption is typical for small molecules of surfactants, inorganic ions, and gases.
In Equation (16), the magnitude of Kτ has the dimensions of length per unit of time. This equation reflects the dynamics of surfactant adsorption according to Henrỳs model. This model is applicable to the analysis of adsorption phenomena in very dilute solutions of surfactants.
The value of Гτ vs τ and the time to reach equilibrium adsorption increases when the magnitude and the product takes on such magnitudes that the inverse exponent with this indicator comes close to zero. Physically, this corresponds to the adsorption processes involving high-molecular-weight compounds (polypeptides, proteins, etc.). These substances have low diffusion coefficients for their molecules.
The formation of an adsorption monolayer from protein molecules requires significant energy to overcome steric obstacles and potential barriers. The adsorption of macromolecular substances reaches equilibrium over wide periods of time.
That which is stated above remains also in force in the cases when moderately concentrated solutions are considered, i.e. when the adsorption equilibrium is described not by the Henry equation , but by the Langmuir equation: This is because the time intervals required for reaching the equilibrium state of adsorption are predetermined only by the exponential term in Equation (14). Equation (14) allows the processes of flotation of surfactant impurities from the bulk of water using a stream of bubbles of dispersed air or another suitable gas to be analyzed.
In such a way, the rate of surfactant bubble flotation will depend first on the peculiarities of the adsorption of these substances at the water–air interface.
OTHER FACTORS AFFECTING THE COMPLETENESS OF SURFACTANT ADSORPTION AND FLOTATION EFFICIENCY
The total area of the adsorption surface on all of the air bubbles in their uprising flow in the water bulk is the next very important factor.
The rate of ascent of air bubbles under the action of Archimedean force and the intensity of hydrodynamic disturbances in the flotation concentrate accumulation zone is the third critical factor.
And finally, the method of flotation product removal is of great importance when the surfactant concentration is low in the water.
is the elementary mass transfer of surfactants with the bubble flow;
Гτ is the accumulation (adsorption) of surfactants on the surface of the air bubbles during the time of their ascent in the water;
air discharge for bubbling;
r is the radius of the air bubbles;
dτ is elementary time.
Equation (18) shows that under the stated conditions, the dG/dτ value is influenced by the surfactant concentration in the water bulk (C), the adsorption equilibrium constant (), the air consumption for sparging (), and the radius (r) of the air bubbles. The lifetime of the air bubbles in the bulk of the water does not affect the value of dG/dτ in this case since the adsorption equilibrium is reached very quickly.
In Equation (19), the expression in curly brackets makes an amendment to the rate of the adsorption process. It can be seen that in this case, the aero-induced transference of surfactant is influenced by the surfactant concentration in the water (C), the adsorption equilibrium constant (), the air consumption for sparging (), the radius (r) of the air bubbles, the lifetime of the bubbles in the water bulk ), and the sum of the rate constants of adsorption and desorption ().
With a given airflow per sparging (), the value of increases inversely with the radius (r) of the air bubbles. This leads to increase in the value of dG/dτ. But with decrease in the radius of the air bubbles, the duration of their ascent through the space of water increases also (Guet & Ooms 2006). The velocity ascent of the air bubbles versus their diameter is depicted in Figure 1. As a result, additional adsorption occurs on the surface of small bubbles of those surface-active molecules whose diffusion coefficients have low values. Therefore, dG/dτ increases additionally due to growth of the factor. The enlargement of the sum of the constants of the rates of adsorption–desorption, i.e., (K ↑ + K ↓), also impacts dG/dτ.
PECULIARITIES OF REGULAR BUBBLE FLOTATION WHEN USED FOR WATER TREATMENT
When applying the bubble flotation method in practice, it is impossible to operate values without shifting the original ion-salt composition of the water. Only the parameters (l), () and (r) allow the change of dG/dτ purposely.
The parameter (i) should be chosen to be of such value that the adsorption of surfactants by the air bubbles will reach the maximum during the time of their ascent in the bulk of the water. As for the air consumption for bubbling () and the radius (r) of the air bubbles, the restriction related to the specificity of the collection and removal of the flotation products comes into force.
If the size of the air bubbles in the water corresponds to the rates of their ascent in the range of 25–35 cm/s (see Figure 1), the intensity of hydrodynamic perturbations in the surface layer of the subphase increases in proportion to the air consumption for sparging. This makes it impossible to accumulate a flotation concentrate on the water surface at low concentrations of surfactant impurities in its bulk (Drenckhan & Saint-Jalmes 2015).
If the air consumption for bubbling increases at microscopic sizes of the air bubbles, the ascent rate of which is 0.1–1 cm/sec, then the entire water space becomes filled with a circulating water-air emulsion. This emulsion practically does not release the flotation product at a low concentration of surfactants in the water (Khuntia et al. 2012). Moreover, at low concentrations of surfactants in the water the air bubble flow does not form stable foam layers even when the bubble radii are in the range 0.1–1.0 mm (their ascent rates: 1–20 cm/sec).
These circumstances limit the possibility of applying regular bubble flotation (foam separation) to purify water from its surface-active admixtures. Regular flotation (foam separation) allows reduction of the concentration of surfactants in the water only to the level of 1–2 mg/dm3, because foam formation ceases when the concentration of these substances in the water becomes lower than stated.
UPGRADED BUBBLE FLOTATION (BUBBLE-FILM EXTRACTION), ITS ESSENCE AND POTENTIAL ABILITIES
In the papers Gevod (2009) and Gevod & Reshetnyak (2015) it was shown that bubble-films extraction as an improved flotation method provides much deeper water purification from surfactant impurities than regular flotation. When applying a bubble-film extraction method, the concentration of surfactants in water can be reduced to the level of micrograms per cubic decimetre. The principle of action of bubble-film extraction is shown in Figure 2.
When bubble-film extraction occurs, the flotation concentrate passes out of the water bulk through a channel (pipe) with a conical constriction at its outlet and a socket (gripping funnel) at the base (see Figure 2(c)). In the socket, the air bubbles with adsorbed surfactants form a zone of critical gas filling and coalesce, and shifting into the space of the discharge channel are transformed into a stream of flat liquid films. Each flat liquid film consists of saturated surfactant solution and is directed to the waste collector through the top conic part of the discharge channel. (This part of the discharge channel is not depicted in Figure 2(c).)
is the linear speed of moving of the flat liquid films and air gaps along the discharge channel;
S is the cross-section of the discharge channel.
ENHANCEMENT OF BUBBLE-FILM EXTRACTION RATE
In accordance with Equation (17), the aeration-induced surfactant flow is directly proportional to air discharge, and inversely proportional to the radius of the air bubbles. On this basis, it could be expected that an increase in air discharge and a reduction in the size of the resulting air bubbles would provide an increase in the productivity of bubble-film extraction. But with a decrease in the size of the air bubbles to tenths of a millimetre and less (Khuntia et al. 2012; Cantat et al. 2013), the rate of their coalescence, even with critical gas filling, decreases dramatically. As a result, a small bubble continuum fills the entire space of the discharge channel in the bubble-film extractor and moves along it with a large amount of trapped water. Schematically, this process is displayed in Figure 2(e).
But if the air bubble flow entering the socket of the discharge channel turns out to be composed (by volume of supplied air) 60–80% by bubbles with a diameter of 2–4 mm and 20–40% by bubbles with a diameter substantially less than 1 mm, the situation changes essentially. In this case, a gas–liquid mixture is formed in the socket zone in which the space between large bubbles (those of 2–4 mm in diameter) is filled with small bubbles (a nested-type gas–liquid system is formed as shown schematically in Figure 3(d)). In such a system, the reaction of surface tension forces at the bursting of big bubbles overcomes the electrostatic repulsion barrier between adjacent air bubbles and causes a chain reaction of coalescence.
Double electric layers exist at any interfaces and they play an essential role in ensuring the stability of aqueous films between the air bubbles (Yaminsky et al. 2010). In the bubble column bounded by the walls of a bubble-film extractor, charges of opposite signs are localized on bubble shells and in the space of water meniscuses, respectively. At the thinning of the meniscuses, the double electric layers overlap each other and their electrostatic repulsion prevents the coalescence of air bubbles. As a consequence, a redistribution of ions occurs inside the meniscuses. An increase in the concentration of ions in the meniscuses by the overlap of electrical double layers creates a local osmotic pressure, and the water rushes inside the meniscuses, additionally counteracting their thinning. Thus, the osmotic component of the splitting pressure becomes added to the Coulomb repulsion forces.
z is the charge of counter ions;
e is the electron charge;
kT is the energy of thermal motion;
æ is a parameter characterizing the thickness of the ionic atmosphere;
δ = 1/h is the size of the gap between the planes of localization of surface charges;
no is the ion concentration in the gap.
According to Equation (21), the splitting pressure Πe under the specified conditions is proportional to the square of the surface potential (φо).
The first term in Equation (23) represents the osmotic pressure in the bubble adhesion zone, and the second takes into account the osmotic pressure in the meniscus. In practice, a separate definition of these two constituents is impossible.
That which is stated above describes the repulsion of air bubbles when the surface is covered by adsorption layers of ionogenic surfactants. In general, many surface-active substances change the degree of ionization under the shifting of pH and ionic strength in processing water. Very often, the repulsion of charged air bubbles in water is so strong that it prevents their coalescence even at tight contact. To overcome that repulsion, an energetically powerful push is required. Such a push appears with the spontaneous bursting of some bubbles in tight ensemble.
The peculiarity of the collective behavior of the ensembles of large and small air bubbles inside the zone of their accumulation in a bubble-film extractor is that large bubbles, bursting, stimulate the process of the collective destruction of small bubbles. This is because the rupture of air bubbles at their transition from the water to the atmosphere is accompanied by powerful hydrodynamic and aerodynamic perturbations (Collins 2010; Ghabache et al. 2014). Experimental and theoretical studies of these phenomena were carried out by Duchemin et al. (2002), Nguyen et al. (2013), Ghabache et al. (2014) and Brasz et al. (2018). These authors showed that the act of bubbles bursting is accompanied by powerful capillary waves and the appearance of a rapidly growing liquid cone (jet). At certain dimensions of bursting bubbles, one or several microscopic drops of water fly out with a high speed (up 10 m/s) from the top of the jet into the surrounding space. The drops, depending on their size and initial velocity, either come back to the water or form an aerosol in the air (Brasz et al. 2018).
and are the radii of air bubbles of the large and small fractions, respectively;
and are the rates of the ascent of the large and small air bubbles;
1 − α = 0.7 is the proportion of dispersed air in large bubbles;
α = 0.3 is the proportion of dispersed air in small bubbles;
= 10:1 is the ratio of the radius of large bubbles to the radius of small bubbles.
Equation (33) reveals the dynamics of the bubble-film extraction process of surfactants from a given volume of water when this process uses a stream of air bubbles with significantly different sizes.
Figure 4 show the results of calculations of C/C0 vs τ, obtained by Equations (32) and (33) as well as the data from the bench experiment. The line with short dashes depicts the calculated dynamics of surfactant removal by the air stream, which consists of large bubbles (r1 = 2 × 10−3 m). The line with long dashes depicts the dynamics of surfactant removal by the action of the air stream consisting of a mixture of large and small bubbles (r1 = 2 × 10−3 m, and r2 = 2 × 10−4 m, the ratio 7/3). When performing calculations, the value of was taken as equal to 1 and the time of the process was considered in hours. The solid line depicts the experimentally observed change of bubble-film extraction rate (C/C0 vs time) as the result of substituting 1/3 of the air spent generating large bubbles for that spent generating small bubbles as depicted above (r1/r2 = 10/1). The moment of switching the structure of air flow used for bubble-film extraction is depicted by the arrow. The bench experiment was carried out using a solution of polyhexamethylene guanidine hydrochloride (Mm = 5,000–10,000, C0 = 1.5 mg/dm3) in tap water. The volume of processed solution was equal to 3 dm3, the air discharge for bubbling was 1 dm3/min, the duration of the bubble-film extraction process from the start to end was about 2.5 hours. The current concentration of surfactant was measured as described in Gevod & Reshetnyak (2015). Polyhexamethylene guanidine concentration can be measured also as described elsewhere (Chmilenko et al. 2011).
Bubble-film extraction allows one to reduce the concentration of surface-active admixtures in the water to the level of the order micrograms per litre. Use of a polydisperse flow of air bubbles in bubble-film extraction accelerates the process of water purification if the share of air in the mixed stream of large and small bubbles reaches a certain proportion. The best case is when air bubbles of different sizes form an embedded structure inside the collecting funnel. In the embedded structure, the capillary waves that accompany the bursting of large bubbles in the upper part of the critical gas-filling zone inside the funnel of the bubble-film extractor transmit its force impulses to small-size bubbles. These impulses overcome electrostatic repulsion in the bordered meniscuses of contacted bubbles and thereby initiate their merging with the releasing of more adsorbed surfactants to that part of the discharge channel where the flat liquid film stream of flotation concentrate appears. As a consequence, the multiplication of the rate of water purification occurs.