Chemistry and Physics of Wet Foam Stability for Porous Ceramics: A Review

Abstract

The unique structural properties of porous ceramics, such as low thermal conductivity, high surface area, controlled permeability, and low density, make this material valuable for a wide range of applications. Its uses include insulation, catalyst carriers, filters, bio-scaffolds for tissue engineering, and composite manufacturing. However, existing processing methods for porous ceramics, namely replica techniques and sacrificial templates, are complex, release harmful gases, have limited microstructure control, and are expensive. In contrast, the direct foaming method offers a simple and cost-effective approach. By modifying the surface chemistry of ceramic particles in a colloidal suspension, the hydrophilic particles are transformed into hydrophobic ones using surfactants. This method produces porous ceramics with interconnected pores, creating a hierarchical structure that is suitable for applications like nano-filters. This review emphasizes the importance of interconnected porosity in developing advanced ceramic materials with tailored properties for various applications. Interconnected pores play a vital role in facilitating mass transport, improving mechanical properties, and enabling fluid or gas infiltration. This level of porosity control allows for the customization of ceramic materials for specific purposes, including filtration, catalysis, energy storage, and biomaterials.

1. Introduction

Colloidal scientists and engineers have faced a new challenge in recent years with the increasing interest in the use of porous ceramics for many different applications, such as molten metal filtration [1,2], catalysis support [3,4], refractory insulation [5,6], hot gas filtration [7,8], and implantable bone scaffold [9,10]. Porous ceramics have all the benefits of regular ceramics plus additional desirable features due to their unique structure. These unique features can be exploited to create vacuum chucks to mount electronic parts, chemical filters, and heat and radiation shields [11,12]. Porous ceramics, known for their ceramic material benefits and cellular structure, are used in tissue engineering, catalyst support, filtering membranes, and energy storage. They are categorized by pore size into macroporous, mesoporous, and microporous materials, but practical applications redefine them as large (d > 100 µm), medium (1 µm < d < 100 µm), and small pores (d < 1 µm). Depending on the need, open porous ceramics allow mass and nutrient transport, while closed porous ceramics enhance insulation [11,12,13,14,15,16]. Porous ceramics are known for their high thermal stability, chemical resistance, and mechanical strength, making them ideal for applications like filtration and catalysis. In contrast, porous metals excel in thermal and electrical conductivity and are more ductile, suitable for aerospace and battery technology. Porous polymers offer flexibility and lightweight properties, making them useful in medical devices and insulation, though they are more sensitive to chemicals and heat. Each material’s characteristics make it suitable for different applications based on specific requirements [16,17,18,19,20]. In the field of advanced ceramics, nano- and micro-powders are utilized as primary feedstocks to fabricate porous ceramics that exhibit improved mechanical, biocompatible, thermal, and exceptional electrical properties [11,12]. Different novel processing methods for porous materials have been discussed in the literature, including the burning out of fugitive pore formers, a process that includes replica techniques [13,14], the sacrificial template method [15,16], and direct foaming [17,18,19,20,21,22,23,24,25].

In the direct foaming method, air bubbles are incorporated into a colloidal suspension or liquid medium to produce a porous ceramic with long anisotropic pores and channels. During this process, when the suspension is mixed, the introduced bubbles are kept stable, until dried in the wet foam body. In most cases, the solidified foams are then sintered at a high temperature to obtain porous ceramics [17,18,19,20,21,22,23,24,25,26,27]. In this case, the total porosity and microstructural shape of the direct formed ceramics are proportional to the amount of air bubbles contained in the suspension or liquid medium during the foaming process. The pore size, shape, and distribution are determined by the stability of the wet foam prior to setting [28,29].

In many instances, polymers (surfactants) are used to modify the properties of nanoparticles, or to aid in the processing of nanoparticles within colloidal suspensions. This is related to the thickness of the adsorbing layer that these surfactants form around the particle surface (adlayer), which markedly increases the effective radius of particle, and, therefore, decreases the suspension’s solid loading [30,31]. Hence, stabilization mechanisms are required that would enable a reduction of the effective radius of particles (and the adlayer thickness), while keeping the nano-sized particles dispersed in the liquid medium. Since classical DLVO theory has not been successful in describing the actual forces that take place at the near proximity (of (0–5) nm) of particle surfaces, a better understanding of the stabilization mechanisms that might take place within this short-range distance is needed [32,33].

Porous ceramics are highly valued for their exceptional mechanical strength, thermal stability, and chemical resistance compared to other porous materials. Unlike porous polymers, which are typically more flexible and less heat resistant, porous ceramics can withstand extreme temperatures and harsh chemical environments without degrading. This makes them ideal for high-stress applications in industries such as aerospace and chemical processing. While porous metals also offer considerable strength, they are heavier and may corrode under chemical exposure, limiting their utility in corrosive environments. In contrast, porous ceramics maintain their integrity even in such conditions, providing long-term durability [30,32]. Porous carbons, known for their lightweight and high surface area, are excellent for filtration and adsorption applications. However, they lack the structural and thermal robustness of porous ceramics, making ceramics a better choice for structural applications requiring both thermal resistance and mechanical stability. Overall, the unique combination of durability, resistance, and stability in harsh environments makes porous ceramics stand out among other porous materials, particularly where high performance under stress is crucial [33,34].

In the case of structural porous ceramics, outstanding reliability and final mechanical properties can be achieved through a colloidal suspension processing route. Since colloidal methods allow better control of the surface forces among particles during the processing steps, agglomerates and other heterogeneities can be avoided in the final microstructure, significantly reducing the critical flaw size, and thereby minimizing the probability of the mechanical failure of ceramic components [34,35]. In addition to the accurate control of the material’s microstructure, colloidal techniques have enabled the production of complex shaped ceramic parts, without requiring intensive, time-consuming, and expensive machining steps [36]. However, liquid foams formed from colloidal suspension are thermodynamically unstable systems, due to their high gas–liquid interfacial area. Several chemical and physical processes take place in wet foam to decrease the overall system free energy, leading to foam destabilization. The main destabilization mechanisms are drainage, coalescence (film rupture), and Ostwald ripening (disproportionation) [37,38].

In this review, the surface chemistry involved in the hydrophobization of hydrophilic ceramic particles in a colloidal suspension, the physical phenomena for stabilizing the wet foam after forming and creating porous ceramics with interconnected pores, and materials with tailored properties for various applications are discussed.

2. Colloidal Suspensions

Colloids are liquid foams or suspensions that typically exhibit thermodynamic instability, owing to their high gas–liquid interfacial areas, which elevate the system’s free energy. To achieve greater stability, it is crucial to minimize the free energy. In ceramic manufacturing, the process often involves the mixing and wetting of liquid and very fine powders. Extremely small particles in the suspension may be influenced by the motion of fluid molecules, making them difficult to detect. This particle movement induced by fluid molecules is known as Brownian motion. The fluid in which this phenomenon occurs, along with the particles dispersed within it, are referred to as colloids [39]. Colloidal suspension is often used, and as time elapses, the internal particles aggregate, and become larger. As the particle size increases, the particles settle down under the influence of gravity, resulting in the loss of colloid stability. Hence, stabilized colloids are necessary to maintain dispersed particles over extended periods for subsequent processes, often utilizing additives, such as dispersants and stabilizers. Wetting is a crucial condition for ensuring proper dispersion and thorough mixing of powder particles with water or a solution, enabling the maintenance of a colloid state [40,41]. When a liquid meets a solid, the angle between the solid and the liquid is called the contact angle.

The wettability is classified according to the size of the contact angle. Figure 1 shows the contact angle and direct foaming. To disperse the solid particles in water or a solution, or to form a colloid, first, the wettability should be good. If it is not wetted, it is separated from the solution and floated on the solution depending on the specific gravity, or the powder particles are clustered together to enlarge the particles, resulting in sinking. Wetting is a phenomenon caused by the difference in the binding force between solid and liquid. Wetting generally occurs when the attraction between solid and liquid molecules is large. Even if the attractive force between the solid and the liquid is weak, when the attraction force between the liquid molecules is weak, wetting occurs; however, when the attraction force between the liquid molecules is strong, and the attraction force between the solid and the liquid molecules is weak, wetting does not occur [42,43,44].

2.1. Destabilization of Colloidal Suspension

Colloidal suspensions can be unstable due to various forces, such as Brownian motion, electrostatic repulsion, van der Waals forces, and changes in pH or ionic strength. These forces can cause particles to aggregate or floc, resulting in instability of the suspension. Liquid foams are thermodynamically unstable due to their high gas–liquid interfacial area. Several physical processes take place in wet foam to decrease the overall free energy, which leads to foam destabilization [38].

The main destabilization mechanisms are drainage (creaming and sedimentation), film rupture (coalescence and flocculation), Ostwald ripening (disproportionation), and Phase inversion [17,18,19,20,45]. Drainage is the physical separation between the gaseous and liquid phases due to gravitational force. In draining foams, light gas bubbles rise upward, forming a denser foam layer on the top, while the heavier liquid phase is concentrated on the bottom [46,47].

Sedimentation and creaming are analogous phenomena that are characterized by unidirectional, irreversible processes arising from density differences between particles and the surrounding liquid phase. When the particles possess a higher density than the liquid medium, they tend to settle down due to gravitational forces. On the other hand, when the particles have a lower density, floating behavior occurs, and they rise to the upper portion of the suspension. Creaming is the migration of the dispersed phase of an emulsion, under the influence of buoyancy. Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained and come to rest against a barrier. These are reversible processes, so a mechanical agitation (homogenization or simple shaking) will redisperse the suspension.

In colloid chemistry, flocculation refers to the process by which fine particulates are caused to clump together and is the process of clustering colloidal particles via attractive van der Waals forces. This process can be overcome or prevented by higher-energy ultra-sonification, or by generating particles with repulsive interactions. Coalescence takes place when the thin films formed after drainage are not stable enough to keep adjacent cells apart, resulting in the joining of neighboring bubbles. Van der Waals forces push the bubbles against each other, and, thus, act as the main driving force for thin film collapse. Coalescence can be prevented by providing electrostatic forces, steric repulsions force, or ligand exchange reactions, which will overcome the attractive van der Waals force. Surfactants or particles adsorbed at the air–water interface can also reduce van der Waals forces [48,49].

Ostwald ripening or disproportionation occurs due to the difference in Laplace pressure between bubbles of different sizes. The differences in Laplace pressure between bubbles of distinct size lead to bubble disproportionation and Ostwald ripening, due to the steady diffusion of gas molecules from smaller to larger bubbles over time, as shown in Figure 2. These destabilization processes may collapse the foam within a few seconds after air incorporation, or increase the size of the incorporated bubbles, resulting in larger pores. Therefore, the most critical issue in direct foaming is the approach used to stabilize the air bubbles incorporated within the suspension [50].

2.2. Inter-Particle Behavior in Colloidal Suspension

Inter-particle behavior in colloidal suspension is based on the particles’ physical and chemical properties. Understanding factors like particle size, shape, surface charge, and surface tension is crucial to achieving the stabilization of suspensions. Figure 3 illustrates various inter-particle behaviors in colloidal suspension [51]. The size of the particles strongly affects suspension stability. Smaller particles move more vigorously due to Brownian motion, leading to increased collisions and repulsion forces among particles. These help prevent aggregation and settling, and, thus, enhance overall stability. Conversely, larger particles have less Brownian motion and weaker repulsion forces, making them more prone to aggregation and sedimentation. Particle shape also plays a significant role. Non-spherical particles, like rods or ellipsoids, show distinct hydrodynamic properties, compared to spherical particles. These differences affect interparticle forces, influencing aggregation kinetics and overall stability. For example, elongated particles tend to form chains or networks due to their anisotropic interactions, tendencies that affect the suspension’s rheological properties. Surface charge is critical to particle stability and interactions. Charged particles experience electrostatic repulsion or attraction based on the sign and magnitude of their charge. Surface charges prevent or hinder particle aggregation, contributing to suspension stability. By modifying surface charge through surface treatments or adjusting the pH, colloidal stability can be precisely controlled. Furthermore, the surface tension at the particle–liquid interface affects colloidal suspension behavior [52]. Interfacial tension determines to what degree the liquid wets the particles. Higher interfacial tension promotes aggregation and settling, while lower tension improves suspension stability. Adding surfactants or surface-active agents can modify interfacial tension, enhancing suspension stability. Finally, solid particles with tailored surface chemistry, adsorbed at the air–water interface, efficiently stabilize the gas bubbles incorporated into the suspension.

Particle-stabilized foams are exceptionally stable due to a densely packed layer of particles at the gas–liquid interface, enabling their use in various applications, from foamed food products like ice cream and dairy items to non-food applications such as ceramic foams. There is potential for their application in baked goods, though no current research exists [51,52]. Optimal particle size is crucial for effective stabilization, and particles significantly smaller than the bubble size are needed. Particles with a wetting angle close to 90° enhance stability due to strong adhesion to the interface. The shape of particles, whether spherical, microrod, or fiber, affects their packing and interaction at the interface, impacting stability. Foams undergo aging reactions such as drainage, disproportionation, and coalescence, which affect the foam’s stability and quality. Further exploration into the integration of varying particles and their properties is needed to optimize foam quality and stability. Combining fast-acting emulsifiers with slower-acting particles could be effective in continuous production settings. Experimental setups use milk protein and guar gum, with or without polyglycerol ester, to investigate the effects of different particles, shear forces, and gas fractions on foam quality using various foaming machines. Understanding the interactions of particle properties at the gas–liquid interface is key to developing stable foams, crucial for expanding applications in the food industry, particularly in areas like baked goods. Continued research and methodical experimentation are essential to fully harness these properties in food-processing techniques [52].

2.3. Hydrophobization of Colloidal Particles

In this process, the attachment of colloidal ceramic particles at the air–water interface is promoted by changing the hydrophobicity of the particle upon the adsorption of short-chain amphiphiles on the surface. This process enables the preparation of a high volume of wet foams by stabilizing the particles with different chain amphiphilic molecules containing more than eight carbon atoms in the hydrophobic tail, as shown in Figure 4. The anchoring group of the molecules attaches to the particle surface and promotes the surface hydrophobization of colloidal particles [53]. The amphiphiles used here adsorb onto the particle surface through electrostatic interactions between the positively charged surfaces and negatively ionized amphiphilic molecules. Surface modification of particles using these amphiphiles was carried out at pH close to the pKa values of the molecules. At this condition, approximately half of the amphiphilic molecules are present in ionized form, and, thus, are easily adsorbed on the oppositely charged particle surface [54]. The hydrophobicity imparted by the first layer of deprotonated amphiphiles adsorbed onto the surface leads to an energetically unfavorable exposure of hydrophobic species to the aqueous phase. This favors the adsorption of additional molecules from the aqueous phase onto the particles’ surfaces to decrease the system’s free energy, which determines the stability of a suspension or wet foam. Particles attached to the gas–liquid interfaces of foams and mists lower the overall free energy by replacing part of the interfacial area, rather than reducing the interfacial tension, as in the case of the surfactants shown in Figure 4 [55].

3. The Chemistry and Physics of Wet Foam

The breakdown structure of foam refers to the mechanisms that lead to the collapse of the wet foam. This can occur due to a range of factors, including drainage of the liquid film between the bubbles, the coalescence of adjacent bubbles, and the rupture of bubble walls. These processes are influenced by the physical and chemical properties of the liquid or solid matrix, as well as external factors, such as temperature, pressure, and shear forces. Understanding the chemistry and physics of wet foam is essential for developing new materials and applications that rely on the stability, wet foam, and microstructure, as shown in Figure 5 [18,20,21,22,23,56].

3.1. Chemistry of Wet Foam from Colloidal Suspension

In general, while in aqueous solution, ceramic powders are well dispersed and mixed uniformly, in water-based solutions, some non-oxide ceramic powders are poorly dispersed and also mixed. Both hydrophilic and hydrophobic classes of particles can have a significant impact on the performance of air bubbles, with the particle stabilized in the colloidal suspension to obtain porous ceramics by direct foaming [18,20,21,22,23,26,57]. Hydrophobic particles are defined by the geometry of water on a flat surface; specifically, the angle between a droplet’s edge, and the surface underneath it. If the droplet spreads, causing the wettability of a large area of the surface, then the contact angle is less than 90 degrees, and that surface is considered hydrophilic, or water-loving. But if the droplet forms a sphere that barely touches the surface, like drops of water on a hot griddle, the contact angle is more than 90 degrees, and the surface is hydrophobic, or water-fearing.

Surfactant molecules in a solution combine to produce micelles (or foam/bubbles). As the micelle forms, the surfactant heads position themselves so that they are exposed to water, while the tails are grouped in the center of the structure protected from water, as shown in Figure 6. In the synthesis of the wet foam, the long-chain amphiphilic molecules and biomolecules can be used as surface-active agents to stabilize wet aqueous foams, and these molecules slow down the coalescence and disproportionation of bubbles by adsorbing at the air bubble surface and reducing the air–water interfacial energy. However, due to the low adsorption energy of surfactants at the gas–liquid interface, long-chain surfactants and biomolecules cannot prevent the long-term destabilization of foam, because, as demonstrated, after a few steps of the creation of the wet foam with long-chain surfactants, the foam has collapsed and exhibited the disproportionation of the bubble [58]. The choice of amphiphile head group highly depends on the surface chemistry of the particle involved. The use of short amphiphiles to tailor particle wettability provides a general and versatile approach for the surface modification of a wide range of ceramic and metallic materials. Surface hydrophobization can be accomplished by choosing amphiphiles (surfactants) with functional groups that react with surface hydroxyl groups [6,18,19,20,21,22,23,24,59,60].

3.2. Hydrophobization of Particles through Surface Modification

The surface chemistry of oxide particles in water is determined by the protonation and deprotonation reactions of surface hydroxyl groups (–OH) with H₃O⁺ and OH⁻ ions from the aqueous medium. The reactivity of the hydroxyl groups is strongly influenced by the charge-to-size ratio of the underlying metal ion of the solid oxide. The in situ hydrophobization of particles with different surface chemistries was accomplished using butyric acid, propyl gallate, and hexylamine as amphiphiles, as shown in

Table 1. Amphiphiles used to surface modify particles with different surface chemistries and the conditions under which the experiments were carried out, from the stabilization of foams with inorganic colloidal particles [33].

Predominant State of Surface Hydroxyl Groups	Surfactant	Particles/IEP	Solvent/pH	Solid Content (vol.%)
	Butyric acid	Al2O3/9.4	Water/pH 4.75	35
	Propyl gallate	Al2O3/9.4	Water/pH 9.9	35
	Hexylamine	SiO2/1.5	Water/pH 10.6	35

. Colloidal particles containing predominantly –OH₂⁺, –OH, and –O⁻ groups on the surface were selected to represent the possible surface chemistries typically encountered in oxide surfaces [41,62,63].

One of the most common approaches used to promote the dispersion of colloidal suspensions is the adsorption of electrically charged (ionic) polymers [58]. In addition to such homopolymers shown in Figure 7 specially tailored molecular architectures based on block- and comb-like copolymers have been investigated to control the ratio of electrostatic/steric mechanisms contributing to particle dispersion.

Upon in situ surface modification of the dispersed particles, bubbles are stabilized when introduced to the modified suspension. Wet foams produced with the direct foaming method will enable ultra-stability against drainage, Ostwald ripening, and bubble coarsening as shown in Figure 8 [49,50].

4. Physics of Wet Foam from Colloidal Suspension

Foam, in physics, is a system of gas bubbles separated by liquid thin films, as shown in Figure 8. It is formed when a gas is dispersed in a liquid and stabilized by surfactants. Foams can be categorized, based on bubble size, into macrofoam, micro foam, or nanofoam. They exhibit unique properties, such as high surface area-to-volume ratios, and viscoelastic behavior.

To avoid foam collapse in the wet state, the air–liquid interface of the foam needs to be stabilized. Typically, the surface tension of the gas–liquid interface is reduced by surfactants to reduce the Laplace pressure, and to prolong the lifespan of the newly formed bubbles. The magnitude of the pressure ΔP at this time is given by the following Equation (1) [30]:

ΔP = 2γ/R

(1)

Equation (1), which relates the radius of a capillary (R) to the surface energy of a liquid (γ), is known as the Young–Laplace equation, where ΔP is the pressure difference between the inside and outside of the capillary. This is a phenomenon in which fine particles in colloidal suspension are strongly flocculated, agglomerated, and settled with others, due to the movement of each other.

Pressure differences between the bubble walls and vertex drive the fluid flow direction. The radius of curvature of the bubbles along the walls creates the pressure differential. The pressure difference (ΔP) across the surface of a liquid is related to the surface curvature, for the radius of curvature in directions 1 (R₁) and 2 (R₂). Hence, γ is balanced by ΔP, or the surface tension tends to compress the droplet, increasing the internal pressure, and this is described by the Young–Laplace equation [18]:

$$∆\mathrm{P}=\mathsf{\gamma }\left[{\displaystyle \frac{1}{{\mathrm{R}}_1}}+{\displaystyle \frac{1}{{\mathrm{R}}_2}}\right]$$

(2)

Since the adsorption energy of the surfactant molecules is in the range of the thermal energy (kT), the molecules are in a constant adsorption–desorption equilibrium on the gas–liquid interface, which limits the foam stability [6,18,19,20,21,22,23,24,60,65,66]. The energy of the attachment, i.e., the Gibbs free energy (G), gained by the adsorption of a particle of radius r at the interface can be calculated using simple geometrical arguments that lead to the following equation [18,19,20,21,22,23,24,67]:

$$∆\mathrm{G}={\mathrm{r}}^2{\mathsf{\gamma }}_{\mathrm{L}\mathrm{G}}(1-\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\theta })\mathrm{for}\mathsf{\theta }<{90}^{\mathrm{o}}$$

(3)

where ‘θ’ is the contact angle and ${\mathsf{\gamma }}_{\mathrm{L}\mathrm{G}}$ is the gas–liquid interfacial tension. The maximum energy gain can only be achieved at θ = 90°.

The maximum capillary pressure describes how the particles residing on and between the two air–water interfaces increase the stability of the foam lamella against thinning of the water film between a single layer of particles at the air–water interface. It represents the pressure required to bring two bubbles together to coalesce, with the capillary pressure necessary to rupture the liquid film between two particles. From these calculations, the stabilization of the foam film reaches its minimum at a 90° contact angle and is best stabilized at 0°. The contact angle influences the (a) interfacial adsorption, and (b) the resistance to film thinning. However, the wet foam stability is both influenced by particle–interface interactions, and by interactions between the particles themselves. These interactions mainly include dipole–dipole (var der Waals) and electrostatic interactions, possible steric interaction, and capillary forces that cause attraction or repulsion between two particles at the air–water interface. These different particles result in a stronger particle shell around the foam bubbles. In turn, this increases the stability of the particle network in the foam lamellae, and, thus, even more strongly hinders the bubbles from shrinkage or growth, while further reducing bubble coalescence [17,18,19,20,21,22,62,68].

The air is trapped in small discrete containers that are referred to as bubbles, which are surrounded by the continuous phase, in our case, the liquid. Foaming agents are the key to avoiding the instantaneous collapse of the structure because they stabilize the interfaces between air and water. The physical properties of foam depend critically on the volume of liquid or gas within the foam, gas fraction (=gas volume/bubble volume), or bubble size distribution. The amount of gas in the foam (volume fraction) lies generally in the range 50–97%, and when the volume fraction is above 75%, bubbles will deform each other [56,69]. From micrometers to centimeters, bubbles can be extremely monodispersed, or highly polydisperse, and the gas fraction may vary throughout. Moreover, the choice of foaming method depends on both the properties of the foam obtained, and on how quickly it can be produced.

4.1. Physical Phenomena of the Bubble

In a single bubble, the two opposing forces at play are surface tension (σ) and excess pressure (∆P = P_i − P_o), with the influence of gravity being neglected. The Law of Laplace and Young for a single soap bubble, as depicted in Figure 9, describes the relationship between surface tension and excess pressure.

$$\begin{gathered} \mathsf{\Delta }PdV=2\sigma dA \\ V=4/3\pi R^3 \\ dV=4\pi R^{2}dR \\ A=4\pi R^2 \\ dA=8\pi RdR \end{gathered}$$

(4)

$$\mathsf{\Delta }\mathrm{P}\left[4\mathsf{\pi }{\mathrm{R}}^{2}dR\right]=2\sigma \left[8\pi RdR\right]$$

(5)

When a soap bubble is formed, two forces act on it, namely, surface tension and excess pressure. Surface tension is the cohesive force between the molecules in the liquid, which creates a thin film of liquid around the bubble. On the other hand, excess pressure is the difference in pressure between the inside and outside of the bubble. The relationship between surface tension and excess pressure is described by the formula ∆P = 2σ/r, where ΔP is the excess pressure, σ is the surface tension, and r is the radius of the bubble. This formula is derived by balancing the forces between the surface film and excess pressure. Surface tension tends to minimize the surface area of the bubble by pulling the liquid molecules together. However, excess pressure counteracts this force by pushing the bubble outwards. As a result, the bubble reaches an equilibrium size where the forces of surface tension and excess pressure are balanced by the following equation [56].

4.2. Stabilizing Mechanisms of Bubbles

The elasticity of the film and the surfactant-induced viscous layer provide complementary stabilizing mechanisms for bubbles in films or foams, as the elastic deformation allows the bubble to absorb stress, while the viscous layer prevents coalescence and rupture, ultimately leading to the maintenance of a stable foam structure [56]; the research focuses on enhancing the wet foam stability in colloidal suspensions through surfactant-driven foam stabilization. The stability of bubbles or foams is determined by several factors that affect surface energy, and the interactions between bubbles and adjacent bubbles can lead to the complex phenomena shown in Figure 10. Bubbles are arranged in networks of films and channels, which make the liquid–air separation process challenging to describe, due to the influence of buoyancy. In the presence of gravity, the liquid flows through the bubble, causing bubble drains. When the bubble is not in equilibrium under gravity, the liquid is expelled through the bubble, until capillary force equals gravity [69,70].

4.3. Wet Foam Stability

In the direct foaming process, partially hydrophobic small particles are useful as stabilizing agents for foaming applications. Although they behave similarly to chemical surfactants by adsorption at the bubble interface, there are significant differences. Particles are much larger than the molecular dimensions of chemical surfactants and cannot aggregate or self-assemble. Furthermore, particles cannot solubilize in the bulk solution. Despite these limitations, particles can act as effective foam stabilizers at moderate concentrations, and when moderately hydrophobic, provide highly stable foams. However, to achieve higher degrees of foamability and foam stability, it is generally more convenient to combine the particles with other surface-active components, like polymers, dispersants, or chemical surfactants [18,20,21,22,64,71,72].

Film elasticity is a self-healing mechanism in thin air–water–air films stabilized by surfactants. The surfactants arrange themselves at the interfaces based on their affinity for water, and when a force or stress creates a thin spot on the bubble surface, the concentration of surfactants at the interface decreases, creating gradients that initiate the transfer of surfactants toward the thinned spot to restore them. The concentration of solute affects film elasticity; at low concentrations, the solute may not stabilize the foam, due to a marginal increase in film elasticity. Conversely, extremely high concentrations can eliminate stabilizing mechanisms, making it necessary to adsorb additional molecules from the aqueous phase onto particle surfaces to decrease the system’s free energy, and ensure stability. Particles attached to gas–liquid interfaces in foam and mist lower the overall free energy by replacing interfacial area [71]. The Gibbs free energy gained by adsorbing particles can be calculated using Equation (2), which predicts the energy of particle attachment G and surface free energy as a function of the contact angle for three different particle sizes [18,20].

The stability of wet foam depends on the degree of hydrophobicity achieved by the surfactant, which lowers the free energy of the system by replacing part of the highly energetic interface area, leading to a reduction in the suspension’s surface tension. Surface charge screening also plays a role, as the electrical diffuse layer around a particle surface may not be thick enough to overcome the attractive van der Waals forces between particles. To overcome these attractions, a stable hydrophobizing mechanism is required [72,73,74,75,76,77,78].

Short-chain amphiphilic molecules have been shown to increase foam lifetimes from hours to days or months, while long-chain surfactants or proteins at the air–water interface only provide stabilization for a few minutes or hours. These foams percolate throughout the whole liquid phase and exhibit no drainage over long periods, 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 [58,61,71,74,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97].

Table 2. Physical characteristics of colloidal suspensions that exhibit wet foam stability of over 80% achieved through the surfactant [18].

Sample	Surfactant	θ (°)	γ (mN/m)	$∆\mathbf{G}$ (J)	$∆\mathbf{P}$ (mPa)	Wet Foam Stability (%)
Al2O3	Propyl gallate	86.94	22.67	1.0 × 10−12	0.56	50−65
Al2O3–SiO2	Propyl gallate	63.90–86.91	23.77–70.32	1.3 × 10−12–6.9 × 10−13	0.52–1.31	>89
	Propionic acid	56.46–74.58	28.44–34.85	3.6 × 10−13–8.1 × 10−13	0.63–0.86	>89
	Butyric acid	56.29–68.80	20.94–27.45	2.0 × 10−13–5.3 × 10−13	0.60–0.76	>85
	Valeric acid	61.63–70.13	20.30–22.27	3.2 × 10−13–4.4 × 10−13	1.37–1.64	>90
Al2O3–TiO2	Propyl gallate	47.45–69.03	7.76–136.06	1.5 × 10−13–1.6 × 10−12	0.11–2.80	>94
Al2O3–SiO2–TiO2	Propyl gallate Hexylamine	45.99–55.23	23.56–56.13	2.2 × 10−13–2.7 × 10−12	1.30–2.23	>92
Al2O3–TiO2–ZrO2	Propyl gallate Hexylamine	45.75–74.08	38.50–56.02	2.6 × 10−13–1.0 × 10−12	1.37–2.23	>87
Al2O3–TiO2–ZrO2–SiO2	Propyl gallate	45.85–74.94	27.50–56.15	$2.6$ × ${10}^8$–7.6 × 108	1.45–3.46	>85
ZrO2–TiO2	Propyl gallate	54.92–65.82	68.4–79.49	9.3 × 10−12–1.7 × 10−11	1.06–2.05	>84
SiO2	Hexylamine	38.96–70.88	13.23–46.94	2.3 × 10−14–$6$.6 × 10−13	0.30–0.99	>83
SiC	Hexylamine	31.52–57.33	10.28–33.17	4.2 × 10−16–1.4 × 10−14	0.25–0.59	>88
SiC–SiO2	Hexylamine	49.01–70.98	48.19–81.90	8.1 × 10−13–2.8 × 10−12	1.06–1.87	>82

shows the wet foam stability of various ceramic systems in terms of surfactants.

5. Microstructure

In the direct foaming method, the bubbles gradually distort from the sphere to minimize surface energy. Drainage of liquid and distortion of the bubble induce the motion of bubble, changing its position between the air compartments. The purpose of this reduction is to promote less compact particle packing at the air–water interface, thereby limiting coalescence. Furthermore, the introduction of hydrophilic particles into the foam walls could cause particle jamming, which can impede complete coalescence, and potentially induce the formation of interconnected pores. After foaming, the sample is typically sintered at high temperature to densify the material and promote bonding between the particles. Sintering involves heating the material to induce particle bonding and densification. During this stage, the particles within the foam undergo diffusion-driven processes, such as neck growth and particle rearrangement, which lead to enhanced interparticle contact and consolidation. The high temperature utilized during sintering promotes the diffusion of atoms, enabling the particles to bond together, and form a solid ceramic structure. This densification process reduces the overall porosity of the material, while enhancing its mechanical strength and structural integrity. The sintering stage is crucial for achieving the desired properties in the final porous ceramic material; it allows for the elimination of remaining voids, ensures the fusion of particles, and enables the formation of strong interparticle bonds.

The specific sintering conditions, such as temperature, time, and atmosphere, are carefully controlled to achieve the desired microstructure and properties. Optimizing these parameters is essential to tailor the material’s characteristics, including the pore size, distribution, and connectivity. Overall, the combination of foaming and sintering processes plays a vital role in the fabrication of porous ceramics. Foaming helps create the initial porous structure, while sintering promotes densification, particle bonding, and the development of interconnected pores, shown in Figure 11. These steps are essential for producing porous ceramics with tailored properties that are suitable for various applications.

Interconnected pores are vital in bone substitutes for multiple reasons. They enhance biological integration by allowing blood vessels and cells to infiltrate the material, promoting tissue healing and integration. Interconnected pores also contribute to structural integrity, evenly distributing mechanical forces, and preventing material failure [98,99,100]. They facilitate cell attachment and migration, enabling the formation of new bone tissue [101,102,103,104]. Additionally, interconnected pores can be used to control drug delivery and for efficient fluid transport, improving healing potential and waste removal. In summary, interconnected pore architectures are crucial for the development of effective and functional bone substitute materials [105,106,107,108,109].

6. Conclusions

The use of porous ceramics has attracted significant interest in various applications, presenting new challenges for colloidal scientists and engineers. The fabrication of porous ceramics with improved properties, such as mechanical strength, biocompatibility, and thermal and electrical characteristics, is achieved by utilizing nano- and micro-powders as the primary feedstocks. Different processing methods, including direct foaming, have been explored for creating porous materials. Direct foaming involves incorporating air bubbles into a colloidal suspension or liquid medium, which is then stabilized, until the wet foam is dried. Subsequently, sintering at high temperature yields the desired porous ceramics. The porosity, microstructural shape, and pore characteristics of the ceramics depend on the initial amount and stability of air bubbles within the suspension. Surfactants or polymers are often employed to modify nanoparticle properties, or to aid in their dispersion within colloidal suspensions. The adsorbing layer formed by these surfactants (adlayer) influences the effective particle radius and solid loading of the suspension. Therefore, understanding the stabilization mechanisms operating at short-range distances is crucial. Colloidal suspension processing offers advantages in the fabrication of structural porous ceramics, enabling the control of surface forces, and minimizing heterogeneities, agglomerates, and critical flaws. This processing results in improved mechanical reliability and a reduced probability of failure. Additionally, colloidal techniques allow for the production of complex-shaped ceramic components, without extensive and costly machining steps.

However, wet foams formed from colloidal suspensions are thermodynamically unstable systems, due to their high gas–liquid interfacial area. Destabilization mechanisms, such as drainage, coalescence, and Ostwald ripening, lead to foam destabilization, and pose challenges to maintaining stable porous structures. This review emphasizes the importance of surface chemistry in the hydrophobization of hydrophilic ceramic particles, as well as the physical phenomena involved in stabilizing wet foams and creating porous ceramics with interconnected pores. These advances enable the tailoring of ceramic materials with specific properties for diverse applications. Further research and understanding of stabilization mechanisms within colloidal systems at short-range distances are crucial to advance the field of porous ceramics. By addressing these challenges, scientists and engineers can continue to develop innovative porous ceramic materials for a wide range of applications.