**4.1 TPC line enlargement during the bubble adhesion onto the solid surface in pure liquids**

Experimental studies of three-phase contact line expansion during the bubble capture on solid surface are not very often published. In pure liquids, the contact line movement is again driven by fluid dynamics, where surface, inertial, and viscous forces influence the expansion of the TPC line. Phan [30] confirmed that the combined molecular-hydrodynamic model is suitable for describing the bubble dewetting process in deionized water. However, compared to drops, the surface of the bubbles in pure liquids is much more deformable. The spreading process is dominated by the fluid viscous dissipation, and the bulk viscous friction is usually the main resistance force for the TPC line contact motion [28]. The resultant of surface, inertial, and viscous forces influences the curvature of the liquid-gas interface and therefore affects the shape of the bubble. Thus, we have to consider also additional forces resulting from quite violent bubble shape pulsations occurring during the TPC line expansion. These pulsations were confirmed both experimentally [35] and numerically [36]. A typical example is illustrated in **Figure 2**, where the images of a bubble having the diameter 0.7 mm are given. The TPC line expansion continues together with significant bubble shape deformation, where the bubble vertical diameter is firstly extended and then compressed. The bubble shape deformation during expansion could be described as a form of bouncing while keeping the three-phase contact line (liquid-gas interface pulsates). The elongation of the bubble shape results from interplay between detachment and attachment forces [37]. Due to the TPC formation, the capillary force is too strong and prevents bubble to detach from the solid surface. Consequently, the bubble is pushed back, which is the source of additional pressing force (additional pressure) and facilitating (speeding up) the rate of expansion of the TPC line (local maximum at *UTPC* vs. time curves in **Figure 3**). **Figure 3** shows the time dependence of the TPC line diameter and the expansion rate *UTPC* defined by Eq. 2.

The rupture of a liquid film is not symmetrical with respect to the vertical axis of the bubble symmetry both for pure water and surfactant solutions. This finding is in accordance with the conclusion of Chan [38], who proved that the liquid film becomes the thinnest close to the apparent contact line. In pure water, the asymmetry of the TPC line formation leads to bubble surface oscillations and asymmetry in dynamic contact angles. Similar linear oscillations and irrotational flow during the bubble contact with the solid surface were described by Vejrazka [39].

## **4.2 Influence of surfactants on the three-phase contact line enlargement**

In pure liquids, the stable perimeter of the TPC line is formed within a few milliseconds. The presence of surface-active agents significantly affects the kinetics

#### **Figure 2.**

*A series of photos illustrating the adhesion of the bubble (bubble diameter 0.705 mm) onto the solid surface (silanized glass, θequilibrium = 102°) in pure water. The time interval between individual shots is 0.0625 ms. The images illustrate the bubble adhesion process during the first 2 ms.*

**35**

**Figure 4.**

*2* **×** *10<sup>−</sup><sup>2</sup>*

*formation (time 0 ms).*

**Figure 3.**

*diameter.*

of this process. The TPC line dynamics is influenced by the surfactant adhesion on solid-liquid, solid-gas, and liquid-gas interphases and also by the Marangoni flow along the bubble surface due to the changing surfactant concentration [23, 24, 37, 40, 41]. The motion dynamics of surfactant molecules toward the bubble surface [42] should be considered as well. It can be summarized that the presence of surfactants usually slows down the entire expansion of the TPC line [43, 44]. A typical example is illustrated in **Figure 4**, where the images of a bubble having the diameter of 0.86 mm are given. Bubble adhesion is captured in three differently concentrated solutions of

*A series of photos illustrating the adhesion of the bubble (bubble diameter 0.86 mm) onto the solid surface* 

 *mol/l (C). The time in milliseconds indicates the time since the liquid film rupture and TPC line* 

 *mol/l (A), 3.7* **×** *10<sup>−</sup><sup>3</sup>*

 *mol/l (B) and* 

*(silanized glass) in aqueous solutions of SDS with concentration 5* **×** *10<sup>−</sup><sup>5</sup>*

*The TPC expansion velocity and diameter of the TPC line expansion in pure water for a bubble of 0.705 mm in* 

*Effect of Surfactants on Bubble-Particle Interactions DOI: http://dx.doi.org/10.5772/intechopen.85436*

#### **Figure 3.**

*Surfactants and Detergents*

**pure liquids**

**4.1 TPC line enlargement during the bubble adhesion onto the solid surface in** 

Experimental studies of three-phase contact line expansion during the bubble capture on solid surface are not very often published. In pure liquids, the contact line movement is again driven by fluid dynamics, where surface, inertial, and viscous forces influence the expansion of the TPC line. Phan [30] confirmed that the combined molecular-hydrodynamic model is suitable for describing the bubble dewetting process in deionized water. However, compared to drops, the surface of the bubbles in pure liquids is much more deformable. The spreading process is dominated by the fluid viscous dissipation, and the bulk viscous friction is usually the main resistance force for the TPC line contact motion [28]. The resultant of surface, inertial, and viscous forces influences the curvature of the liquid-gas interface and therefore affects the shape of the bubble. Thus, we have to consider also additional forces resulting from quite violent bubble shape pulsations occurring during the TPC line expansion. These pulsations were confirmed both experimentally [35] and numerically [36]. A typical example is illustrated in **Figure 2**, where the images of a bubble having the diameter 0.7 mm are given. The TPC line expansion continues together with significant bubble shape deformation, where the bubble vertical diameter is firstly extended and then compressed. The bubble shape deformation during expansion could be described as a form of bouncing while keeping the three-phase contact line (liquid-gas interface pulsates). The elongation of the bubble shape results from interplay between detachment and attachment forces [37]. Due to the TPC formation, the capillary force is too strong and prevents bubble to detach from the solid surface. Consequently, the bubble is pushed back, which is the source of additional pressing force (additional pressure) and facilitating (speeding up) the rate of expansion of the TPC line (local maximum at *UTPC* vs. time curves in **Figure 3**). **Figure 3** shows the time dependence of the TPC line

The rupture of a liquid film is not symmetrical with respect to the vertical axis of the bubble symmetry both for pure water and surfactant solutions. This finding is in accordance with the conclusion of Chan [38], who proved that the liquid film becomes the thinnest close to the apparent contact line. In pure water, the asymmetry of the TPC line formation leads to bubble surface oscillations and asymmetry in dynamic contact angles. Similar linear oscillations and irrotational flow during the

bubble contact with the solid surface were described by Vejrazka [39].

*A series of photos illustrating the adhesion of the bubble (bubble diameter 0.705 mm) onto the* 

*0.0625 ms. The images illustrate the bubble adhesion process during the first 2 ms.*

*solid surface (silanized glass, θequilibrium = 102°) in pure water. The time interval between individual shots is* 

**4.2 Influence of surfactants on the three-phase contact line enlargement**

In pure liquids, the stable perimeter of the TPC line is formed within a few milliseconds. The presence of surface-active agents significantly affects the kinetics

diameter and the expansion rate *UTPC* defined by Eq. 2.

**34**

**Figure 2.**

*The TPC expansion velocity and diameter of the TPC line expansion in pure water for a bubble of 0.705 mm in diameter.*

#### **Figure 4.**

*A series of photos illustrating the adhesion of the bubble (bubble diameter 0.86 mm) onto the solid surface (silanized glass) in aqueous solutions of SDS with concentration 5* **×** *10<sup>−</sup><sup>5</sup> mol/l (A), 3.7* **×** *10<sup>−</sup><sup>3</sup> mol/l (B) and 2* **×** *10<sup>−</sup><sup>2</sup> mol/l (C). The time in milliseconds indicates the time since the liquid film rupture and TPC line formation (time 0 ms).*

of this process. The TPC line dynamics is influenced by the surfactant adhesion on solid-liquid, solid-gas, and liquid-gas interphases and also by the Marangoni flow along the bubble surface due to the changing surfactant concentration [23, 24, 37, 40, 41]. The motion dynamics of surfactant molecules toward the bubble surface [42] should be considered as well. It can be summarized that the presence of surfactants usually slows down the entire expansion of the TPC line [43, 44]. A typical example is illustrated in **Figure 4**, where the images of a bubble having the diameter of 0.86 mm are given. Bubble adhesion is captured in three differently concentrated solutions of

#### **Figure 5.**

*The TPC line expansion velocity (bubble diameter 0.86 mm) in aqueous solutions of SDS with concentration 5* **×** *10<sup>−</sup><sup>5</sup> , 3.7* **×** *10<sup>−</sup><sup>3</sup> , and 2* **×** *10<sup>−</sup><sup>2</sup> mol/l. Details in [35].*

sodium dodecyl sulfate (SDS). At low concentration (detail A, c = 5 × 10<sup>−</sup><sup>5</sup> mol/l), the higher mobility and viscoelasticity of the bubble surface, which is manifested by shape oscillations, can be seen. The expansion of TPC line is quick; the equilibrium is reached in 15 ms. At highest concentration (detail C, c = 2 × 10<sup>−</sup><sup>2</sup> mol/l), the mobility and viscoelasticity of the bubble surface are low, and all oscillations are damped. The bubble does not lose its spherical shape. The expansion of TPC line is slower; the equilibrium is reached in more than 40 ms. As the surfactant concentration increases, the wetting angle decreases. Detailed sequences are published in [35].

**Figure 5** shows the time dependence of TPC line expansion velocity for SDS solutions used in **Figure 4**. Compared to bubble adhesion in water (*UTPCmax* = 0.48 m/s), adhesion of bubbles in surfactant solutions is significantly slowed down, and *UTPCmax* ranges from 0.15 m/s (low SDS concentration) to 0.03 m/s (high SDS concentration). In the case of the highest SDS concentration, the critical micellar concentration is exceeded, and the TPC expansion velocity is very slow.

The nonlinearity of expansion velocity was also observed which cannot be explained by molecular-kinetic or by hydrodynamic model. Immediately after the TPC line formation, the solid-liquid and the air-liquid interfaces merge. Merging would be delayed if a long-range repulsive surface force acted between the interfaces. Here, the charged head groups of the surfactants adsorbed at both interfaces would lead to electrostatic double-layer repulsion. This long-range repulsion would keep the interfaces apart and delay the dewetting on the receding side [30]. Thus, the resulting gradient in surface tension would slow down the drainage of the liquid film and extend the bubble adhesion time. The dependence of the dynamic wetting angle on the dynamics of the three-phase interface motion has been confirmed experimentally in other cases as well [45].

### **5. Influence of different types of surfactants and their purity on bubble stability**

The adhesion of the bubbles is significantly influenced by the type, charge, length, and purity of the surfactant, pH, or other additives such as salts. The effect

**37**

**Figure 6.**

*and the surface tension, respectively.*

*Effect of Surfactants on Bubble-Particle Interactions DOI: http://dx.doi.org/10.5772/intechopen.85436*

of nonionic, anionic, and cationic surfactants on kinetics of the TPC formation is completely dissimilar for hydrophobic and hydrophilic solid surfaces. The following surfactant types can be considered: (i) ionic surfactants on hydrophobic (nonpolar) surfaces, (ii) ionic surfactants on hydrophilic (polar) surfaces, (iii) nonionic surfactants on hydrophobic surfaces, and (iv) nonionic surfactants on hydrophilic (polar) surfaces [46]. In the case of the hydrophobic surfaces, the charge of surfactant plays a minor role [46], and the TPC line is formed and enlarged always, independently on the surfactant type [23]. On hydrophilic surfaces, the TPC line dynamics is electrostatically driven, and thus, the bubble attachment is determined by charge and/or polar interaction [46]. For example, the bubble attaches to negatively charged surface only when the natural negative electric charge at the bubble surface is reversed

to positive, which can occur only in cationic surfactant solutions [23].

influence on the velocity of TPC line expansion could be very low [44].

The ionic surfactants used both in industrial applications and in scientific studies contain some admixtures of nonionic surfactants or other contaminants. The principal organic contaminants are homologous alkyl sulfates, n-alcohols, and carboxylic acids. Dodecanol is the most important contaminant and is one of the hardest to remove [48, 49]. Even at impurity levels below 0.1%, dodecanol reduces the surface tension and leads to the well-known minimum below the critical micelle concentration (CMC). Dodecanol also significantly influences the surfactant adsorption on the solid-liquid interface [50, 51], shear viscosity, and foam stability [50, 52]. Impurities (contaminants) usually act as cosurfactants or mixtures of two different types of surfactants. Mixed surfactants exhibit synergism which means that their interfacial properties are more pronounced than those of the individual components themselves. A significant reduction in surface tension is typical. Therefore, the contaminants decrease the ability of bubbles to attach to solid surfaces when compared with the mono-surfactant solution. The influence of

*Images of bubbles captured on the hydrophobic surface in water, in aqueous solutions of SDS (sodium dodecyl sulfate), and in E12O5 (pentaethylene glycol monododecyl ether). θ and γ denote the contact angle in liquid phase* 

An important factor is also the molecular structure of the surfactant. The most common nonionic surfactants are those based on ethylene oxide. They are produced by ethoxylation of a fatty chain alcohol, and the most common ones have 12 carbons in the alkyl chain. In the case of large or other complex molecules, one should expect an adsorption barrier that consists of these branched molecules captured on phase interface and that prevents the adhesion of other molecules [47]. This barrier comes into existence in dilute solutions, then rises with increasing concentration, and again changes close to the CMC concentration. The existence of such a barrier is often connected with some steric restraints on the molecule in the proximity of the interface, because the molecules should be in the correct orientation. Unsuitable orientation could cause the molecule to diffuse back into the bulk rather than adsorbing. The transport of such molecules is low, and thus, surprisingly, their

#### *Effect of Surfactants on Bubble-Particle Interactions DOI: http://dx.doi.org/10.5772/intechopen.85436*

*Surfactants and Detergents*

**Figure 5.**

*3.7* **×** *10<sup>−</sup><sup>3</sup>*

*, and 2* **×** *10<sup>−</sup><sup>2</sup>*

sodium dodecyl sulfate (SDS). At low concentration (detail A, c = 5 × 10<sup>−</sup><sup>5</sup>

in 15 ms. At highest concentration (detail C, c = 2 × 10<sup>−</sup><sup>2</sup>

 *mol/l. Details in [35].*

angle decreases. Detailed sequences are published in [35].

exceeded, and the TPC expansion velocity is very slow.

experimentally in other cases as well [45].

higher mobility and viscoelasticity of the bubble surface, which is manifested by shape oscillations, can be seen. The expansion of TPC line is quick; the equilibrium is reached

*The TPC line expansion velocity (bubble diameter 0.86 mm) in aqueous solutions of SDS with concentration 5* **×** *10<sup>−</sup><sup>5</sup>*

coelasticity of the bubble surface are low, and all oscillations are damped. The bubble does not lose its spherical shape. The expansion of TPC line is slower; the equilibrium is reached in more than 40 ms. As the surfactant concentration increases, the wetting

**Figure 5** shows the time dependence of TPC line expansion velocity for SDS solutions used in **Figure 4**. Compared to bubble adhesion in water (*UTPCmax* = 0.48 m/s), adhesion of bubbles in surfactant solutions is significantly slowed down, and *UTPCmax* ranges from 0.15 m/s (low SDS concentration) to 0.03 m/s (high SDS concentration). In the case of the highest SDS concentration, the critical micellar concentration is

The nonlinearity of expansion velocity was also observed which cannot be explained by molecular-kinetic or by hydrodynamic model. Immediately after the TPC line formation, the solid-liquid and the air-liquid interfaces merge. Merging would be delayed if a long-range repulsive surface force acted between the interfaces. Here, the charged head groups of the surfactants adsorbed at both interfaces would lead to electrostatic double-layer repulsion. This long-range repulsion would keep the interfaces apart and delay the dewetting on the receding side [30]. Thus, the resulting gradient in surface tension would slow down the drainage of the liquid film and extend the bubble adhesion time. The dependence of the dynamic wetting angle on the dynamics of the three-phase interface motion has been confirmed

**5. Influence of different types of surfactants and their purity on bubble** 

The adhesion of the bubbles is significantly influenced by the type, charge, length, and purity of the surfactant, pH, or other additives such as salts. The effect

mol/l), the

*,* 

mol/l), the mobility and vis-

**36**

**stability**

of nonionic, anionic, and cationic surfactants on kinetics of the TPC formation is completely dissimilar for hydrophobic and hydrophilic solid surfaces. The following surfactant types can be considered: (i) ionic surfactants on hydrophobic (nonpolar) surfaces, (ii) ionic surfactants on hydrophilic (polar) surfaces, (iii) nonionic surfactants on hydrophobic surfaces, and (iv) nonionic surfactants on hydrophilic (polar) surfaces [46]. In the case of the hydrophobic surfaces, the charge of surfactant plays a minor role [46], and the TPC line is formed and enlarged always, independently on the surfactant type [23]. On hydrophilic surfaces, the TPC line dynamics is electrostatically driven, and thus, the bubble attachment is determined by charge and/or polar interaction [46]. For example, the bubble attaches to negatively charged surface only when the natural negative electric charge at the bubble surface is reversed to positive, which can occur only in cationic surfactant solutions [23].

An important factor is also the molecular structure of the surfactant. The most common nonionic surfactants are those based on ethylene oxide. They are produced by ethoxylation of a fatty chain alcohol, and the most common ones have 12 carbons in the alkyl chain. In the case of large or other complex molecules, one should expect an adsorption barrier that consists of these branched molecules captured on phase interface and that prevents the adhesion of other molecules [47]. This barrier comes into existence in dilute solutions, then rises with increasing concentration, and again changes close to the CMC concentration. The existence of such a barrier is often connected with some steric restraints on the molecule in the proximity of the interface, because the molecules should be in the correct orientation. Unsuitable orientation could cause the molecule to diffuse back into the bulk rather than adsorbing. The transport of such molecules is low, and thus, surprisingly, their influence on the velocity of TPC line expansion could be very low [44].

The ionic surfactants used both in industrial applications and in scientific studies contain some admixtures of nonionic surfactants or other contaminants. The principal organic contaminants are homologous alkyl sulfates, n-alcohols, and carboxylic acids. Dodecanol is the most important contaminant and is one of the hardest to remove [48, 49]. Even at impurity levels below 0.1%, dodecanol reduces the surface tension and leads to the well-known minimum below the critical micelle concentration (CMC). Dodecanol also significantly influences the surfactant adsorption on the solid-liquid interface [50, 51], shear viscosity, and foam stability [50, 52]. Impurities (contaminants) usually act as cosurfactants or mixtures of two different types of surfactants. Mixed surfactants exhibit synergism which means that their interfacial properties are more pronounced than those of the individual components themselves. A significant reduction in surface tension is typical. Therefore, the contaminants decrease the ability of bubbles to attach to solid surfaces when compared with the mono-surfactant solution. The influence of

#### **Figure 6.**

*Images of bubbles captured on the hydrophobic surface in water, in aqueous solutions of SDS (sodium dodecyl sulfate), and in E12O5 (pentaethylene glycol monododecyl ether). θ and γ denote the contact angle in liquid phase and the surface tension, respectively.*

contaminants is crucial below the critical micelle concentration of the main surfactant, and it may even happen that the capture of bubbles is avoided [43]. Typical example, images of bubbles in five different solutions, is illustrated in **Figure 6**. The bubble is most stable attached in clean water. In solutions of common surfactants, e.g., in SDS, the wetting angle and thus the bubble stability decrease with the decreasing surface tension of the solution. For molecules with complex structure or, in the case of contaminants or additives, this simple rule may not apply.
