Foam Stabilization by Surfactant/SiO 2 Composite Nanoﬂuids

: This paper deals with the potential of aggregates of surfactant and SiO 2 nanoparticles as foam stabilizers for practical applications. The effects of different chain lengths and concentrations of the cationic surfactant C n TAB on the performance of C n TAB–SiO 2 nanoﬂuids are examined to gain a comprehensive understanding of their ability to stabilize foam. The results indicate enhanced foam stability in the presence of SiO 2 nanoparticles. These ﬁndings help to better understand foam stabilization and its potential in various industrial applications such as enhanced oil recovery and foam-based separation processes.


Introduction
Currently, there is growing interest in composite materials that can effectively modify the practical properties of numerous types of liquid dispersal systems, which are widely used in many industries.These included foams with different quality and stability.The stability of foams can be provided by compositions of surfactants with natural and synthetic high-molecular-weight substances [1] and particles [2].Particle-stabilized foams can be used in various industrial and technological fields, such as chemical-enhanced oil recovery, mineral flotation, and in the food industry [3][4][5][6].
Enhanced oil recovery from reservoirs is a real challenge in the global oil industry due to the decreased oil production from many reservoirs.Therefore, various efficient enhanced oil recovery (EOR) methods have been applied, including gas flooding [7][8][9][10].Here, foam is injected and increases the apparent gas viscosity, hence reducing the gas mobility in the pores.However, the practical application of foam-based EOR shows limitations in crude oil environments caused by the rapid destabilization of foam at elevated temperatures, reducing its effectiveness.
To address these limitations and to advance the field of EOR, the present study explores new approaches to improve the stability of gas foams.Specifically, the research focuses on incorporating nanoparticles as potential foam stabilizers [9][10][11][12].Nanoparticles possess intrinsic properties, such as chemical stability and low adsorption on mineral surfaces, which make them attractive candidates for producing highly stable foams.
Moreover, these particular properties extend their use in technology fields beyond enhanced oil recovery.Stable gas foams and emulsions have a broad range of applications, including subsurface remediation, carbon capture and storage, and even applications in the food and cosmetic industries.
This study seeks to provide valuable insights into the colloid-chemical properties of surfactant/nanoparticle mixtures in order to optimize foams with potential applications not only in the oil industry.The results will enable the design of efficient and environmentally friendly methods in many new technologies.
Nanoparticles, such as negatively charged silica particles, are attractive materials for stabilizing foam because they have a certain surface activity, which enables them to form a dense and uniform layer at the interface.Cationic surfactants are positively charged, which allows them to interact strongly with negatively charged surfaces, such as many types of nanoparticles.
One of the challenges in studying particle-stabilized foams is the complexity of phenomena that can influence their stability.These phenomena include the properties of the particles (such as size, shape, charge) [13][14][15][16], the properties of the liquid (such as viscosity and surface tension), and the environmental conditions under which the foam is formed and applied (such as shear rate, gas flow rate, and temperature) [17].
Overall, the theoretical background of particle-stabilized foams using silica nanoparticles and cationic surfactants is a complex and evolving field, with many open questions still and, therefore, many opportunities for further research.The main mechanism of foam stabilization by particle/cationic surfactant mixtures is the electrostatic repulsion between the adsorbed particle layers at both sides of the foam films.These stable particle layers around the gas bubbles prevent coalescence of the foam.Also, the particles can act as a physical barrier, impeding the movement of gas bubbles and reducing the drainage of liquid from the foam.Additionally, the combination of particles and surfactant can create a synergistic effect that enhances foam stability not available by use of the surfactant alone [26,[28][29][30].
The goal of the present work is to examine how the combination of C n TAB-SiO 2 nanoparticles can help to stabilize foam.This understanding can lead to improved foam stability and the development of new applications for these materials.By enhancing foam stability, C n TAB-SiO 2 mixtures may have a wide range of applications in industries such as cosmetics, food, agriculture, and EOR, where foam stability is crucial for product performance and quality.
One of the notable investigations on foam stability with surfactant-nanoparticle mixtures in foam-flooding enhanced oil recovery (EOR) is the study by Rezaei et al. [9].In this study, it was found that the combination of the surfactant cocamido propyl betaine (CAPB) with silica nanoparticles and NaCl significantly improved foam stability, outperforming similar combinations with other surfactants, such as linear alkylbenzene sulphonic acid (LABSA) and cetyltrimethylammonium bromide (CTAB).Moreover, investigations on the effects of temperature demonstrated that CAPB exhibited superior foam stabilization up to 50 °C, after which CTAB surpassed CAPB and LABSA in stabilizing N 2 foams.These findings highlighted the potential of surfactant-nanoparticle mixtures for enhancing foam flooding as an effective method for EOR.In another study by Sun et al. [10], the use of partially hydrophobized SiO 2 nanoparticles in combination with the anionic surfactant sodium dodecyl sulfate (SDS) was shown to enhance foam stability for nitrogen foam flooding.The experimental results demonstrated that the SiO 2 /SDS foam exhibited better temperature tolerance and increased surface dilational viscoelasticity, leading to the maintenance of spherical or ellipsoidal foam bubbles.The SiO 2 /SDS foam also outperformed other flooding methods by effectively controlling the gas mobility, avoiding channeling, and enhancing oil recovery in micromodel and sand pack flooding experiments.
Several studies have investigated the use of cationic surfactants and silica particles to stabilize foam.For example, Wang et al. [31] investigated the interfacial rheology of nano-SiO 2 dispersions in the presence of cationic CTAB.Depending on the amount of added CTAB, the SiO 2 particles changed from hydrophilic to hydrophobic.Badri and Pallab [32] investigated the same system and found that smaller nanoparticles were more efficient as foam stabilizers.Also, Choi et al. [33] studied the same system but used specially synthesized silica particles and confirmed previous results.Most recently, Wang [34] investigated the foaming capacity of various cationic surfactants and the effects of hydrophilic and hydrophobic SiO 2 NPs on foam stability from macroscopic and microscopic perspectives.The experimental results suggested that the concentration of nanoparticles did not significantly affect the stability of the foam; however, it was higher at elevated temperatures of 50-90 • C.
Despite the many investigations, there is not sufficient knowledge available to completely understand the underlying mechanisms to stabilize foam, particularly with respect to the effect of different alkyl chain lengths of the used cationic surfactants.Therefore, the purpose of the present work is to analyze the properties of C n TAB-SiO 2 complexes (nanoparticles NP) as a foaming agent and to quantify the effects of both the alkyl chain length and the concentration of the used cationic surfactants.
Ludox AM-30 is an aqueous 30% colloidal suspension of SiO 2 and was purchased from Sigma-Aldrich Co.The silicon dioxide particles are nearly spherical, with an average particle size of 12 nm.The nanoparticles are negatively charged and pH stable (pH between 8.6 and 9.3) and have a specific surface area of 198-258 m 2 /g, as determined by BET adsorption analysis.
The 30% Ludox suspension was diluted to 3 wt% and then used to prepare mixtures with C n TAB.The required amount of C n TAB was dissolved in deionized water.The concentrations of the C n TAB solutions were in the range between 10 −5 and 10 −1 mol/L.
The prepared C n TAB solution was added drop-by-drop to the 3 wt% silicon dioxide particle suspension, and the mixture was stirred by a magnetic stirrer at 400 rpm for 30 min.The purpose of this step was to allow the C n TAB to homogeneously adsorb onto the silicon dioxide particles.A 1:1 volume ratio of the C n TAB and SiO 2 stock solutions at the given concentrations was used for the preparation of the C n TAB-SiO 2 complexes.

Foam Generation and Stability
Foamability and foam stability measurements were carried out using the air sparging method.Gas was passed through a porous membrane at the bottom of a glass cylinder (d = 20 mm).A total of 2 mL of the sample suspension was placed in the glass cylinder, and air was injected for 15 s at a constant gas flow rate of 1.5 mL/s to generate the foam.The maximum foam height and the liquid height in the cylinder were measured immediately after terminating the foam formation.
To evaluate the foam stability, the bulk foam height was measured at different time intervals.The foam stability was determined by plotting the normalized foam height as a function of time.The normalized foam height was computed using Equation (1) as described by Yekeen et al. [35].
Images of the foam were taken using a micro-camera, which was attached to the foam-generating set-up.All images were stored and subsequently analyzed.

Zeta Potential Measurements
The zeta potential of the nanoparticles was measured using a Zetasizer Nano ZS (Software Version 7.13) (Malvern).Before the measurements, the instrument was tested with the Malvern zeta potential transfer standard.

Measurement of the Surface Tension
To determine the surface tension of the suspensions, a Profile Analysis Tensiometer PAT 1M (SINTERFACE Technology, Berlin, Germany) was used.A complete description of the experimental set-up has been given in [36].The method can measure the surface and interfacial tension of liquid/gas and liquid/liquid interfaces for periods of up to several hours and even days.

Image Analysis and Data Statistics
Image analysis and data statistics were performed using different software packages, such as Excel and Image J.All measurements were performed in triplicates and we calculated the mean average values and standard deviation and used error bars in the graphs.

Foam Formation and Stability by C n TAB-SiO 2 NPs
Figure 1 presents the maximum foam height as a function of the number of carbon atoms (n) for both pure C n TAB and C n TAB-SiO 2 mixtures, with the surfactant concentration fixed at 1 × 10 −3 mol/L.From the figure, it is evident that the foam height was generally higher for the composite (C n TAB-SiO 2 mixtures) compared to the pure surfactants.However, for C 16 , the foam height was not increased by the addition of silica nanoparticles.The foamability of dispersions of the C n TAB-SiO 2 mixtures was investigated in a concentration range between 1 × 10 −5 mol/L and 1 × 10 −1 mol/L (Figure 2).It is expressed as the height of the foam produced with the dispersions after 10 min.The foamability of the mixtures varies with the concentration and chain length of C n TAB.At a concentration of 1 × 10 −3 mol/L (see Figure 3b), the foams generated from C  TAB-SiO2 nanoparticles behaved similarly to pure surfactant foams, but with slightly higher stability, except for C 16 TAB, for which no significant change in the foam stability was noted.Instead, the foam remained unstable in the presence of the silica nanoparticles.In contrast, at a concentration of 1 × 10 −1 mol/L (see Figure 4b), the foams generated with C 12 TAB and C 14 TAB exhibited high stability, while the foams generated with the C 10 TAB and C 16 TAB solutions showed lower stability.At a concentration of 1 × 10 −2 mol/L, phase separation was observed for C 10 , C 12 , and C 14 , which resulted in decreased foamability.An intriguing deviation in the behavior was observed for C 14 TAB combined with SiO 2 nanoparticles, which deviated from the trends observed for C 10 TAB, C 12 TAB, and C 16 TAB.At a concentration of 1 × 10 −3 mol/L, the foamability of C 14 TAB was found to be higher compared to C 10 TAB, C 12 TAB, and C 16 TAB, where the foamability increased with increase in concentration.The study suggests that the foamability of C n TAB-SiO 2 nanoparticles can be tuned by controlling the concentration and chain length of the surfactant in order to modify the nanoparticles in an optimum way to act as a foam stabilizer.
The Figures 3a,b and 4a,b show the changes in normalized foam height (H/H 0 ) over time at various concentrations for different surfactants, C n TAB alone, and in mixtures with SiO 2 particles.
At a concentration of 1 × 10 −3 mol/L (see Figure 3b), the foams generated from C n TAB-SiO 2 nanoparticles behaved similarly to pure surfactant foams, but with slightly higher stability, except for C 16 TAB, for which no significant change in the foam stability was noted.Instead, the foam remained unstable in the presence of the silica nanoparticles.
In contrast, at a concentration of 1 × 10 −1 mol/L (see Figure 4b), the foams generated with C 12 TAB and C 14 TAB exhibited high stability, while the foams generated with the C 10 TAB and C 16 TAB solutions showed lower stability.
These results suggest that the addition of SiO 2 NPs to C n TAB solutions can improve foam stability, particularly for C 12 TAB and C 14 TAB.
These results suggest that the addition of SiO2 NPs to C  TAB solutions can im foam stability, particularly for C 12 TAB and C 14 TAB.The foam images were taken by a microscope camera.Figure 5a shows the phology for pure surfactants at a concentration of 1 × 10 −3 mol/L, taken 10 min formation.It was observed that, with increasing surfactant chain length, the b The foam images were taken by a microscope camera.Figure 5a shows the foam morphology for pure surfactants at a concentration of 1 × 10 −3 mol/L, taken 10 min after foam formation.It was observed that, with increasing surfactant chain length, the bubble size decreased, and the shape of the bubbles became more spherical.On the other hand, for all C n TAB-SiO 2 mixtures (Figure 5b), the bubbles broadly appeared to be more spherical, more uniform and smaller, leading to an efficient packing density without many bubble deformations.Overall, the images provide visual evidence of the improved foam stability for C n TAB-SiO 2 nanoparticle dispersions compared to pure surfactant solutions.
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Zeta Potential of SiO2 NPs in Aqueous Dispersions
To follow the adsorption of C  TAB molecules onto the SiO2 particle surfaces in the dispersion, the zeta potential of the formed particles was measured at different surfactant concentrations and using a fixed amount of 3 wt% SiO2.
The measured zeta potentials presented in Figure 6 show how the silicon dioxide particles were step-by-step covered by the surfactants, leading to progressive surface charge compensation and further to charge inversion.Before the addition of surfactant, the silicon dioxide NPs had a zeta potential of around −38 mV, indicating a high degree of surface hydrophilicity.With increasing C  TAB concentration, the zeta potential gradually became less negative, indicating a reduction in the surface hydrophilicity due to the adsorption of positively charged C  TAB molecules onto the negatively charged SiO2 particle surfaces.At a surfactant concentration above 1 × 10 −2 mol/L, the zeta potential started to become positive, while the exact concentration for the charge inversion depended on the chain length.The point of zero charge indicates that the SiO2 particles were fully covered with surfactant molecules and the surface charge had been neutralized.For C 14 TAB and C 16 TAB, charge neutralization began at lower surfactant concentrations, i.e., at around 10 −2 mol/L, while for C 12 TAB, it occurred at higher concentrations, and, for C 10 TAB, the particle charge neutralization happened at the highest concentration of almost 10 −1 mol/L.These differences can be attributed to the shorter alkyl chains of C 10 TAB, resulting in a lower tendency to adsorb at the particle surface.In turn, due to the higher surfactant concentration required for a complete charge neutralization, a less efficient formation of the second corona around the particle resulted.
Additionally, as the amount of surfactant adsorbed onto the particle surface in-

Zeta Potential of SiO 2 NPs in Aqueous Dispersions
To follow the adsorption of C n TAB molecules onto the SiO 2 particle surfaces in the dispersion, the zeta potential of the formed particles was measured at different surfactant concentrations and using a fixed amount of 3 wt% SiO 2 .
The measured zeta potentials presented in Figure 6 show how the silicon dioxide particles were step-by-step covered by the surfactants, leading to progressive surface charge compensation and further to charge inversion.Before the addition of surfactant, the silicon dioxide NPs had a zeta potential of around −38 mV, indicating a high degree of surface hydrophilicity.With increasing C n TAB concentration, the zeta potential gradually became less negative, indicating a reduction in the surface hydrophilicity due to the adsorption of positively charged C n TAB molecules onto the negatively charged SiO 2 particle surfaces.At a surfactant concentration above 1 × 10 −2 mol/L, the zeta potential started to become positive, while the exact concentration for the charge inversion depended on the chain length.The point of zero charge indicates that the SiO 2 particles were fully covered with surfactant molecules and the surface charge had been neutralized.For C 14 TAB and C 16 TAB, charge neutralization began at lower surfactant concentrations, i.e., at around 10 −2 mol/L, while for C 12 TAB, it occurred at higher concentrations, and, for C 10 TAB, the particle charge neutralization happened at the highest concentration of almost 10 −1 mol/L.These differences can be attributed to the shorter alkyl chains of C 10 TAB, resulting in a lower tendency to adsorb at the particle surface.In turn, due to the higher surfactant concentration required for a complete charge neutralization, a less efficient formation of the second corona around the particle resulted.

Dynamic and Equilibrium Surface Tension of Pure 𝐶 𝑛 TAB and Mixed 𝐶 𝑛 TAB-SiO2 Solutions
The surface tension isotherms of pure C  TAB solutions (C 10 , C 12 , C 14 , C 16 ) in Figure 7 were taken from Mucic et al. [37].The resulting curves show a clear dependence on the chain length of the surfactant molecules, with longer chains exhibiting higher surface activity, as expected from the Traube rule.The colored experimental points are data obtained in this work, which agree rather well with the literature data in [38].In Figure 8, the dynamic interfacial tensions of the   TAB and   TAB-SiO2 NP mixtures at a fixed surfactant concentration of 1 × 10 −3 mol/L are shown.The results demonstrate a reduction in the surface tension for the mixture compared to the pure surfactant solutions.All solutions of the pure C  TABs showed an almost constant surface tension from the beginning, which means that, even after only a few seconds, the adsorption of the surfactant molecules had reached equilibrium.Due to the large differences in surface Additionally, as the amount of surfactant adsorbed onto the particle surface increased, the magnitude of the zeta potential also increased, becoming more and more positive until it reached values between 10 mV and 25 mV.This further confirmed the adsorption of C n TAB onto the silicon dioxide particle surface and the formation of a bilayer structure around the SiO 2 particles.

Dynamic and Equilibrium Surface Tension of Pure C n TAB and Mixed C n TAB-SiO 2 Solutions
The surface tension isotherms of pure C n TAB solutions (C 10 , C 12 , C 14 , C 16 ) in Figure 7 were taken from Mucic et al. [37].The resulting curves show a clear dependence on the chain length of the surfactant molecules, with longer chains exhibiting higher surface activity, as expected from the Traube rule.The colored experimental points are data obtained in this work, which agree rather well with the literature data in [38].

Dynamic and Equilibrium Surface Tension of Pure 𝐶 𝑛 TAB and Mixed 𝐶 𝑛 TAB-SiO2 Solutions
The surface tension isotherms of pure C  TAB solutions (C 10 , C 12 , C 14 , C 16 ) in Figure 7 were taken from Mucic et al. [37].The resulting curves show a clear dependence on the chain length of the surfactant molecules, with longer chains exhibiting higher surface activity, as expected from the Traube rule.The colored experimental points are data obtained in this work, which agree rather well with the literature data in [38].In Figure 8, the dynamic interfacial tensions of the   TAB and   TAB-SiO2 NP mixtures at a fixed surfactant concentration of 1 × 10 −3 mol/L are shown.The results demonstrate a reduction in the surface tension for the mixture compared to the pure surfactant solutions.All solutions of the pure C  TABs showed an almost constant surface tension from the beginning, which means that, even after only a few seconds, the adsorption of the surfactant molecules had reached equilibrium.Due to the large differences in surface In Figure 8, the dynamic interfacial tensions of the C n TAB and C n TAB-SiO 2 NP mixtures at a fixed surfactant concentration of 1 × 10 −3 mol/L are shown.The results demonstrate a reduction in the surface tension for the mixture compared to the pure surfactant solutions.All solutions of the pure C n TABs showed an almost constant surface tension from the beginning, which means that, even after only a few seconds, the adsorption of the surfactant molecules had reached equilibrium.Due to the large differences in surface activity, the absolute values were lowest for C 16 and highest for C 10 TAB.In contrast, when SiO 2 particles were added to the respective surfactant solutions, the dynamic surface tension curves first decreased and then leveled off at the respective equilibrium surface tension.The much slower change in surface tension points to the fact that the surfactant molecules did not adsorb, but complex particles, i.e., the SiO 2 particles, were modified via the electrostatically bound cationic surfactants.The particles modified by the longest chains C 16 were the most hydrophobic ones, and, hence, led to the lowest surface tension values.Aidarova et al. [39], in their study, obtained a similar result for polymers decorated by surfactants with longer hydrophobic chains, which required more time to reach a final value due to the slow diffusion of the polymer/surfactant complexes.
Colloids Interfaces 2023, 7, x FOR PEER REVIEW 10 of 15 activity, the absolute values were lowest for C 16 and highest for C 10 TAB.In contrast, when SiO2 particles were added to the respective surfactant solutions, the dynamic surface tension curves first decreased and then leveled off at the respective equilibrium surface tension.The much slower change in surface tension points to the fact that the surfactant molecules did not adsorb, but complex particles, i.e., the SiO2 particles, were modified via the electrostatically bound cationic surfactants.The particles modified by the longest chains C16 were the most hydrophobic ones, and, hence, led to the lowest surface tension values.Aidarova et al. [39], in their study, obtained a similar result for polymers decorated by surfactants with longer hydrophobic chains, which required more time to reach a final value due to the slow diffusion of the polymer/surfactant complexes.

𝐶 𝑛 TAB-SiO2 NPs Composite Foam Characteristics and Stability
Foam formation and stability are important factors in various industrial applications.The larger foamability observed in Figure 1 for the composite C  TAB-SiO2 as foaming agents compared to the corresponding pure surfactants (except for C 16 TAB) can be attributed to the surfactant-silica aggregates, which were able to improve the foam stability and lead to an increased foam height.
The foamability of the mixtures varied with the concentration and chain length of C  TAB (Figure 2).Above a concentration of 10 −2 mol/L, the foamability for all C  TAB-SiO2 dispersions sharply increased.This increase in foamability was surely caused by the sufficiently high surface activity of the formed surfactant-particle complexes due to the hydrophobization effect, as well as a sufficient electric charge after the charge inversion provided by the formed second corona.Below a concentration of 10 −2 mol/L, the complexes could possess a sufficiently high charge to stabilize the foam films and, thereby, the foam, but the corresponding surface activity was probably insufficient.The unexpected behavior of the C 14 surfactant in combination with the SiO2 nanoparticles presented a notable deviation from the trends observed for C 10 TAB, C 12 TAB, and C 16 TAB.One plausible explanation for this particular behavior involves the concept of complete charge neutralization occurring at various surfactant concentrations, depending on the carbon chain length.Notably, shorter carbon chains require higher concentrations for achieving complete charge neutralization.At a concentration of 1 × 10 −2 mol/L, it can be postulated that the particles and functional groups of C 14 TAB experienced complete charge neutralization, contributing to the observed reduction in foamability.This observation is in line with the noticeable decrease in foamability observed above.

C n TAB-SiO 2 NPs Composite Foam Characteristics and Stability
Foam formation and stability are important factors in various industrial applications.The larger foamability observed in Figure 1 for the composite C n TAB-SiO 2 as foaming agents compared to the corresponding pure surfactants (except for C 16 TAB) can be attributed to the surfactant-silica aggregates, which were able to improve the foam stability and lead to an increased foam height.
The foamability of the mixtures varied with the concentration and chain length of C n TAB (Figure 2).Above a concentration of 10 −2 mol/L, the foamability for all C n TAB-SiO 2 dispersions sharply increased.This increase in foamability was surely caused by the sufficiently high surface activity of the formed surfactant-particle complexes due to the hydrophobization effect, as well as a sufficient electric charge after the charge inversion provided by the formed second corona.Below a concentration of 10 −2 mol/L, the complexes could possess a sufficiently high charge to stabilize the foam films and, thereby, the foam, but the corresponding surface activity was probably insufficient.The unexpected behavior of the C 14 surfactant in combination with the SiO 2 nanoparticles presented a notable deviation from the trends observed for C 10 TAB, C 12 TAB, and C 16 TAB.One plausible explanation for this particular behavior involves the concept of complete charge neutralization occurring at various surfactant concentrations, depending on the carbon chain length.Notably, shorter carbon chains require higher concentrations for achieving complete charge neutralization.At a concentration of 1 × 10 −2 mol/L, it can be postulated that the particles and functional groups of C 14 TAB experienced complete charge neutralization, contributing to the observed reduction in foamability.This observation is in line with the noticeable decrease in foamability observed above.
The results of the normalized foam height in Figures 3 and 4 indicate that the addition of SiO 2 nanoparticles to C n TAB solutions can improve the foam stability compared to foams formed by pure surfactant solutions.The foams generated from the C n TAB-SiO 2 mixed solutions showed a slower rate of foam decay and higher foam stability compared to the pure surfactant foams.This increased foam stability can be attributed to the presence of SiO 2 NPs in the foam films, which increased the strength of the film and reduced the rate of drainage.This was true at both the studied concentrations, 10 −3 mol/L and 10 −1 mol/L.
It is worth noting that the results of the study also revealed that the stability of the foams generated from the C n TAB-SiO 2 mixtures was consistent even after particle charge neutralization, while the stability of the foams generated from the pure surfactants was reduced.This suggests that the presence of SiO 2 NPs in the foam film not only improves the initial stability during foam formation but also maintains its stability over time.
The images shown in Figure 5a,b provide additional information on the physical characteristics of the foam generated from solutions of pure surfactants and the C n TAB-SiO 2 mixtures.The observed decrease in bubble size with increasing surfactant chain length can be attributed to the decrease in surface tension.In contrast, the C n TAB-SiO 2 mixture foams exhibited more uniformly spherical bubbles that were densely packed.This suggests that the addition of SiO 2 NPs may act as stabilizers, helping to prevent bubble coalescence and, thereby, increasing foam stability.Additionally, the densely packed bubbles indicate that the C n TAB-SiO 2 particles may have a higher surface coverage compared to pure surfactant foams, further supporting the idea that SiO 2 NPs can increase foam stability.

Mechanism of Foam Stabilization by C n TAB-SiO 2 NPs
The mechanism of foam stabilization by C n TAB-SiO 2 nanoparticles can be explained based on the results obtained for the adsorption of C n TAB onto the surface of the colloidal silicon dioxide particles including electrostatic and hydrophobic interactions.
The change in the zeta potential of the SiO 2 NP is caused by a surface charge compensation by the adsorbed C n TAB molecules (Figure 6).The negatively charged particle surface attracts positively charged C n TAB molecules via electrostatic attraction.This electrostatic interaction allows the surfactant molecules to adsorb onto the silica surface, forming a primary layer.Via hydrophobic interaction, at further surfactant concentration increase, i.e., after the negative surface charges of the silica particles are compensated, the surfactant molecules adsorb at the particle surface, forming a secondary adsorption layer and causing electrostatic interparticle repulsion.
The observation that the adsorbed amounts did not differ for the studied chain lengths was not observed for C n TAB equilibrium concentrations below 10 −4 mol/L, which indicates that the first step of adsorption occurred before the critical micelle concentration (CMC) [37] for all C n TABs.This suggests that the adsorption mechanism is not solely based on micelle formation, but also involves the adsorption of individual surfactant molecules onto the silica surface.
The increase in surfactant concentration gradually reduces the negative zeta potential, indicating decreased surface hydrophilicity due to the adsorption of positively charged C n TAB molecules.Complete charge neutralization of the particles occurs at different surfactant concentrations depending on the alkyl chain length, with shorter chains requiring higher concentrations.Wu et al. (2018) [40] also observed that the affinity of silica nanoparticles to the surface can be adjusted by altering the concentration of surfactants.
The continuous increase in the zeta potential with increasing amount adsorbed of surfactants indicates that the surface of the silicon dioxide particles becomes more positively charged as more C n TAB molecules are adsorbed.This increased positive charge on the silica surface enhances the foam stability by providing electrostatic repulsion between the bubbles.
The surface tension of pure C n TAB solutions decreases with increasing C n TAB concentration due to the adsorption of C n TAB molecules at the air-water interface (Figure 7).At the same time, the maximum surface excess concentration increases with increasing chain length.The values measured here are in good agreement with the isotherms taken from the literature [37,38].
The measured dynamic surface tension curves shown in Figure 8 are more informative than the isotherms in Figure 7 because they provide insights into the adsorption behavior of the SiO 2 NP complexes at the foam bubble surface.The dynamics of adsorption for the C n TAB-SiO 2 systems is much slower than for the pure C n TAB solutions at the same surfactant concentration.The slower rate of adsorption is clearly caused by the larger size of the surfactant-particle aggregates and their lower concentration compared to the pure molar surfactant solutions.
Interestingly, in Figure 8, the C 16 TAB-SiO 2 system exhibits the lowest dynamic surface tension, suggesting efficient surfactant impact on the reduction in the surface tension at the air-water interface.However, the foam stability of the system appears to be relatively low.This observation can be attributed to the effect of silica nanoparticles on the foam behavior.Previous studies have shown that the presence of nanoparticles at the interface can even hinder the formation of a stable foam structure [41].Silica nanoparticles tend to adsorb at the interface and may limit the mobility and arrangement of surfactant molecules, affecting their ability to form a cohesive surfactant film around the gas bubbles.Additionally, the hydrophobicity of the nanoparticles can play a significant role, with highly hydrophobic nanoparticles potentially causing agglomeration at the interface and contributing to foam destabilization.
The general behavior of C n TAB-SiO 2 interaction and its impact on foam stabilization can be explained based on the cartoon provided in Figure 9.The interaction between C n TAB and SiO 2 nanoparticles plays a crucial role in foam stabilization.This figure illustrates the behavior of two SiO 2 particles in a position of interacting with each other at different stages of surfactant molecules adsorbing at their surface, shedding light on the underlying mechanisms.
In the absence of surfactants (Figure 9a), the SiO 2 particles experience repulsion due to their negative surface charge, resulting in a well-dispersed suspension.The repulsion is primarily governed by electrostatic forces between the charged particles, while the van der Waals forces, which are typically weak at this stage, play a minor role [42].However, as the surfactant concentration increases, the first layer of C n TAB molecules adsorbs onto the surface of the SiO 2 particles (Figure 9b).This adsorption process generates a hydrophobic attraction between the particles.The hydrophobic tails of the surfactant molecules interact with each other, leading to flocculation or agglomeration of the SiO 2 particles.Additionally, van der Waals forces can also contribute to the particle flocculation at this stage.At surfactant concentrations above this point of zero charge (i.e., the concentration at which the surfaces of SiO 2 particles are neutralized), bilayer adsorption occurs (Figure 9c).This process results in the generation of positive charges at the surface of the SiO 2 particles.The electrostatic repulsion between the positively charged particles counteracts the hydrophobic attraction, thereby redispersing the suspension once again.

Conclusions
In this study, we investigated the stabilization of aqueous foam by C  TAB-SiO2 complexes.The results provide insights into the interfacial properties and interactions within the nanofluid system that are essential for explaining the mechanisms governing the for- These microcosmic interactions between the C n TAB and SiO 2 nanoparticles highlight the complex interplay between electrostatic and hydrophobic forces, resulting in the stabilization or destabilization of the foam.The flocculation and subsequent dispersion of the SiO 2 particles can have direct implications for foam stabilization, as the interaction behavior of the particles affects foam structure, drainage, and stability.

Conclusions
In this study, we investigated the stabilization of aqueous foam byC n TAB-SiO 2 complexes.The results provide insights into the interfacial properties and interactions within the nanofluid system that are essential for explaining the mechanisms governing the formation and stabilization of foam.
The tests performed confirm the higher foam stability caused by the presence of C n TAB-SiO 2 complexes compared to the effects provided by pure surfactants.The foam height, drainage rate, and bubble size distribution measurements consistently support the improved foam stability in the presence of the modified SiO 2 nanoparticles.
The dynamic surface tension measurements undertaken reveal a significant reduction in surface tension for the C n TAB-SiO 2 nanofluid systems compared to the pure surfactant solutions, indicating an interaction between the surfactant and SiO 2 nanoparticles, leading to sufficiently high surface activity required for high foamability and foam stability.
First and foremost, the improved foam stability achieved via the C n TAB-SiO 2 complexes has profound implications for enhanced oil recovery strategies.These stabilized foams can potentially enhance oil displacement and recovery rates, thereby contributing to the optimization of oil production processes.Furthermore, the enhanced foam stability has broader applications in foam-based separation processes and mineral flotation, where stable foams play an essential role in achieving the efficient separation and concentration of valuable materials.Additionally, the novel insights into the interfacial behavior of C n TAB-SiO 2 nanofluids provided have implications for designing advanced materials and formulations for various industries, including subsurface remediation and CO 2 capture and storage.

Figure 3 .Figure 3 .Figure 4 .
Figure 3. Normalized foam height (H/H0) as a function of time for (a) pure C  TAB aqueou and (b) C  TAB-SiO2 nanoparticle dispersions at a fixed surfactant concentration of 10 −3 mol

Figure 4 .
Figure 4. Normalized foam height (H/H 0 ) as a function of time for (a) pure C n TAB aqueous foams and (b) C n TAB-SiO 2 dispersions at a fixed surfactant concentration of 10 −1 mol/L.

Figure 5 .
Figure 5. Morphology of foams generated with (a) pure C  TAB and (b) C  TAB-SiO2 mixed solutions.

Figure 5 .
Figure 5. Morphology of foams generated with (a) pure C n TAB and (b) C n TAB-SiO 2 mixed solutions.

Figure 6 .
Figure 6.Zeta potential as a function of C  TAB concentration for 3 wt% SiO2 NP dispersions

Figure 6 .
Figure 6.Zeta potential as a function of C n TAB concentration for 3 wt% SiO 2 NP dispersions.

Colloids 15 Figure 6 .
Figure 6.Zeta potential as a function of C  TAB concentration for 3 wt% SiO2 NP dispersions

Figure 8 .
Figure 8. Dynamic surface tension γ(t) for pure C  TAB and C  TAB-SiO2 mixed solutions

Figure 8 .
Figure 8. Dynamic surface tension γ(t) for pure C n TAB and C n TAB-SiO 2 mixed solutions.