**3.4. Contact angle and surface tension**

After the stabilizing effects of zeta potential and pH, contact angle and surface tension are important determinants of colloidal systems' properties. Once a suspension is stabilized, the degree of hydrophobization is the main property which affects the production of foam. Given their thermodynamic instability, foams are often kinetically stabilized through the adsorption of surface active molecules or colloidal particles at the gas-liquid interfaces [46, 47]. The adsorbed molecules and particles stabilize the system by inhibiting the coalescence and Ostwald ripening of droplets and bubbles. Adsorption at the fluid interfaces occurs when particles are not completely wetted by any of the fluids, thus exhibiting a finite equilibrium contact angle at the triple phase boundary.

The equilibrium contact angle (*θ*) is determined by the balancing of the interfacial tensions (Equation 1). A decrease in surface tension upon increasing the initial amphiphile concentra‐ tion can be observed. However, above a critical amphiphile concentration, surface tension decreased sharply. Above this critical amphiphile concentration, the particles are sufficiently hydrophobic at the air-water interface and decrease surface tension more greatly than that expected from free amphiphiles alone [48]. This significant reduction in surface tension upon particle adsorption was caused by a decrease of the total area of the highly energetic air-water interface. Similar surface tension effects have been observed in systems employing various amphiphiles [18]

Controlling particles' contact angles at the interface is important as it determines their wettability (Fig. 7). Tailoring particles' contact angles via modification of chemical composition enables the creation of foams with a variety of functionalities [19]. Contact angle depends on surface chemistry, roughness, impurities, particle size, and fluid phase composition. Theoret‐ ical and experimental work has shown that stabilization is achieved when contact angles are of an intermediate range of 20-86º for oil-in-water foams and of 94-160º for water in oil foams [49]. Contact angle can also be tailored by changing the particles' surface chemistry or adjusting the composition of the fluids. Metallic and ceramic particles can achieve any contact angle (0< *θ* < 180º) by reacting or adsorbing hydrophobic molecules on their surfaces [28, 29]. The use of short amphiphiles to tailor particles' wettability is a general and versatile approach for the surface modification of a wide range of ceramic and metallic materials [20].

**Figure 7.** The wettability of particles in immiscible phases.2

### **3.5. Wet foam stability**

favorable change in the surface charge by the removal of (OH2

**Figure 6.** Foams produced through the adsorption of colloidal particles at the gas-liquid interface.

After the stabilizing effects of zeta potential and pH, contact angle and surface tension are important determinants of colloidal systems' properties. Once a suspension is stabilized, the degree of hydrophobization is the main property which affects the production of foam. Given their thermodynamic instability, foams are often kinetically stabilized through the adsorption of surface active molecules or colloidal particles at the gas-liquid interfaces [46, 47]. The adsorbed molecules and particles stabilize the system by inhibiting the coalescence and Ostwald ripening of droplets and bubbles. Adsorption at the fluid interfaces occurs when particles are not completely wetted by any of the fluids, thus exhibiting a finite equilibrium

The equilibrium contact angle (*θ*) is determined by the balancing of the interfacial tensions (Equation 1). A decrease in surface tension upon increasing the initial amphiphile concentra‐ tion can be observed. However, above a critical amphiphile concentration, surface tension decreased sharply. Above this critical amphiphile concentration, the particles are sufficiently hydrophobic at the air-water interface and decrease surface tension more greatly than that expected from free amphiphiles alone [48]. This significant reduction in surface tension upon particle adsorption was caused by a decrease of the total area of the highly energetic air-water interface. Similar surface tension effects have been observed in systems employing various

Controlling particles' contact angles at the interface is important as it determines their wettability (Fig. 7). Tailoring particles' contact angles via modification of chemical composition

replacement with (-OH) [44, 45].

64 Advanced Ceramic Processing

**3.4. Contact angle and surface tension**

contact angle at the triple phase boundary.

amphiphiles [18]

+

), a better leaving group, and

Liquid foams are thermodynamically unstable due to their high gas-liquid interfacial area. Several physical processes can occur to decrease the overall free energy and destabilize the foam [36]. Drainage occurs through gravity; light gas bubbles rise forming a denser foam layer, while the heavier liquid phase is concentrated below. Coalescence takes place when the thin films formed after drainage is not stable enough to keep adjacent cells apart. Their collapse results in the joining of neighboring bubbles. The stability of the thin films is therefore described in terms of attractive and repulsive interactions between the bubbles. van der Waals forces drive the bubbles closer. They can be overcome by electrostatic forces, steric repulsions force, or ligand exchange reactions. Surfactant or particles adsorbed at the air-water interface can also reduce van der Walls forces [22]. Ostwald ripening or disproportionation is another destabilizing effect that is more difficult to overcome. It occurs due to differences in the Laplace pressures between bubbles of different sizes. Laplace pressure inside a gas bubble arises from the curvature of the air-water interface. The Laplace pressure (N/m2 ) is the pressure difference between the inner and the outer side of a bubble or droplet. For spherical bubble of radius *R* and gas-liquid interfacial energy *γ*, the Laplace pressure ∆P is given by 2*γ*/R. The pressure and force generated for the stabilization can be also calculated through the measurement of bubbles at the intersection. It can be calculated by the equation given below.

$$
\Delta \mathbf{P} = \gamma \left( \frac{1}{R\_1} + \frac{1}{R\_2} \right) = \frac{2\gamma}{R} \left( \text{spherical bubble} \right),
$$

The difference in the Laplace pressure between bubbles of distinct sizes (R) leads to bubble disproportionation and Ostwald ripening because of the steady diffusion of gas molecules from smaller to larger bubbles over time. This process can be slowed by using surfactants or particles adsorbed at the interface, which decrease the interfacial energy. Wet foam's stability is also related to the degree of hydrophobicity achieved from the surfactant, which replaces part of the highly energetic interface area and lowers the free energy of the system, leading to an apparent reduction in the surface tension of the suspension [49]. Stability also depends on surface charge screening, the electrical diffuse layer around a particle's surface not sufficiently thick to overcome the attractive van der Waals forces between particles. Overcoming the van der Waals attractions requires a stable hydrophobizing mechanism (examined above). Therefore, experiments were conducted as per reported theoretical explanations [18].

These actions' combined effects may collapse the foam within minutes after air incorporation. Foams' life times have been increased from several hours to days and months by the adsorption of the short chain amphiphilic molecules [50], while only a few minutes or hours' stabilization results from the use of long-chain surfactants or proteins at the air-water interface [35]. Unlike other particle-stabilized foams [2], these foams percolate throughout the whole liquid phase and exhibit no drainage over days and months [49] due to the high concentration of modified particles in the initial suspension, which allows for the stabilization of very large total air-water interfacial areas.
