Chapter 1: The Mechanism of Surfactant Interfacial Behavior Regulation under Ultra-High Pressure
1.1 Pressure-Induced Molecular Conformation Evolution
Under ultra-high pressure conditions (>4.8 MPa), surfactant molecules undergo significant conformational reorganization. Taking alkylbenzene sulfonate surfactants used in Daqing Oilfield as an example, the extension of the molecular chain shows a nonlinear change as pressure increases. X-ray scattering studies indicate that at 4.8 MPa, the compression rate of the molecular chain reaches 23%, leading to a reduction in the effective length of the hydrophobic tail, thereby decreasing its spreading efficiency at the oil-water interface. This conformational change directly results in an increase in the interfacial adsorption free energy, corresponding to an increase in interfacial tension from 10⁻³ mN/m to 10⁻¹ mN/m.

Further studies have shown that when the pressure exceeds 10 MPa, the molecular structure of the surfactant tends to adopt a more compact conformation, with the hydrophobic part's influence on the interface becoming more pronounced. This change directly affects the wettability of the liquid and the stability of the interface. Upon further analysis, it was found that when the pressure exceeds 15 MPa, more complex interactions occur during the interfacial adsorption process, causing the variation trend of interfacial tension to show a nonlinear characteristic, distinct from the behavior under conventional pressure conditions.

1.2 Interfacial Dynamics of Supercritical Systems
When the system enters the supercritical state (pressure > 7.38 MPa, temperature > 31.04°C), there is a sudden change in the solvent density gradient. At this point, the aggregation number of surfactant micelles becomes pressure-dependent: under 15 MPa, the average size of the micelles shrinks to 8.2 nm (compared to 12.5 nm at ambient pressure), and the critical micelle concentration (CMC) increases by about two orders of magnitude. This structural evolution leads to:

• The interfacial adsorption time constant increasing from 0.8 s to 3.5 s
• The surface coverage θ decreasing from 0.92 to 0.78
• A 40% decrease in interfacial elastic modulus

As the pressure continues to increase, the internal structure of the micelles undergoes changes. Surfactant molecules gradually transform into a more ordered aggregation state, further intensifying the aggregation strength of the micelles. Another important impact of this change is the significant alteration of the hydrophilic-hydrophobic balance of surfactants in supercritical fluids, resulting in a more complex multi-phase behavior of interfacial tension changes under high-pressure environments.

1.3 Pressure-Temperature Coupling Effects
Experimental data reveal a significant synergistic effect of pressure and temperature on interfacial tension. Under constant temperature conditions of 50°C, for every 1 MPa increase in pressure, the activation energy of the interface ΔG‡ increases by 0.28 kJ/mol. By establishing an extended Gibbs adsorption equation:

where α is the pressure correction coefficient (measured value 0.17), this model can accurately predict the trend of interfacial tension changes within 15 MPa, with a prediction error of less than 5%. This result provides a theoretical basis for the adsorption behavior of surfactants under ultra-high pressure environments and offers guidance for optimizing interfacial control under pressure-temperature coupling conditions.

Chapter 2: The Measurement Principle and Technological Evolution of Spinning Drop Method
2.1 Fluid Mechanics Basics and Instrument Architecture
The physical essence of the spinning drop method is the dynamic balance between the centrifugal force field and the interfacial tension. When the rotational angular velocity ω reaches a critical value (typically >5000 rpm), the drop aspect ratio L/D and the dimensionless number Bo = Δρω²R³/σ form a definitive relationship. Modern spinning drop tensiometers use:

• High-pressure chamber (pressure resistance up to 70 MPa)
• Dual temperature control system (±0.05°C)
• Convolutional neural network image recognition ADSA fitting
• TFOV lens technology

Through precise hardware and algorithm upgrades to the spinning drop method, it is now capable of providing real-time, high-precision measurement results under ultra-high pressure conditions, in addition to measuring interfacial tension at conventional pressures. The latest TFOV lens technology (full-field lens technology) can capture droplet shapes at higher resolutions, thus enhancing the accuracy of observing the droplet deformation process. This technology application has elevated the stability and precision of interfacial tension measurements to a new height.

Based on the control equations of the spinning drop method:

According to the governing equations of the rotating drop method:

$\frac{dθ}{ds} + \frac{\sinθ}{y} = \frac{2}{R_0} - \left( \frac{Δρω^2 y^2}{2} + Δρgy \right)\frac{1}{σ}$

These equations describe the changes in the droplet shape and its relationship with interfacial tension and rotational speed. By numerically solving these equations, one can calculate the droplet profile dimensions and the curvature radius at the apex, further deriving the relationship between interfacial tension and rotational speed.

2.2 Numerical Solutions and Integration with the Young-Laplace Equation
For the control equations of the spinning drop method:

$$\frac{dθ}{ds} + \frac{\sinθ}{y} = \frac{2}{R_0} - \left( \frac{Δρω^2 y^2}{2} + Δρgy \right)\frac{1}{σ}$$

The spectral method is employed for spatial discretization, transforming the partial differential equations into a system of nonlinear algebraic equations. By introducing dimensionless parameters:

The equations are simplified to:

2.3 Evolution of the Algorithm System
The evolution of the measurement algorithm can be divided into three stages:

The latest algorithm optimizes accuracy by training the ResNet-50 network for feature extraction of droplet profiles. Under 15 MPa conditions, the measurement error is controlled within 0.1 mN/m. This optimization significantly improves the measurement accuracy under ultra-high pressure and enables finer analysis of complex flow and phase transition processes.

Chapter 3: Ultra-High Pressure Interfacial Tension Response Characteristics and Phase Transition Analysis
3.1 Full Pressure Gradient Experimental Data
The complete pressure response dataset for the ternary composite system at 50°C constant temperature is shown below:

Figure 1: Interfacial tension evolution curve under full pressure domain (semi-logarithmic scale)

	
	

		γ(mN/m)
0.2 |               ▲(4.8,0.171)
    |              / \
0.1 |             /   ◆(10.2,0.113)
    |            /      \
    |           /        ◆(14.56,0.078)
0.01|----------/---------------◆(19.93,0.074)
    |         /                  \
    |        /                    ◆(25.03,0.054)
0.001|------◆(0,0.0083)               ▲(30.4,0.074)
    +---------------------------------------
     0       10       20       30     Pressure (MPa)  
	

Based on experimental data, a four-stage evolution model is established:

Figure 2: Comparison of Experimental Data and Theoretical Model

	
	

		
	

	

		
		

			
			

				
			

		

	

	

		Experimental Values: ◆
Model Prediction: ——           
0.2 |               ▲
    |              / \
0.1 |             /———◆
    |            /———◆ 
    |           /———◆  
0.01|----------/—————◆———
    |         /———————◆————▲
0.001|◆——————/————————————▲
    +--------------------------------
     0       10      20      30  Pressure (MPa)  
	

The increase in tension after 25 MPa is attributed to:

• Entropy-Enthalpy competitive effect: When pressure > 25 MPa, the loss of solvation entropy exceeds the gain from intermolecular potential energy.
• Nanocluster phase separation: Molecular dynamics simulations show that the size of nanoclusters reaches a critical value of 6.8 nm at 25 MPa.
• Interface reconstruction energy barrier: The pressure-induced adsorption energy barrier ΔG‡ increases sharply from 42 kJ/mol to 58 kJ/mol.

Figure 3: Molecular dynamics simulation results (25 MPa phase transition point)

	
	

		
		

			
			

				
			

		

	

	

		Nanocluster Size (nm)
7 |        ◆------------▲
6 |       /              \
5 |      /                \
4 |-----/                  \
   +-------------------------
   20      25      30     Pressure (MPa)  
	

Chapter 4: In-Depth Analysis of Ultra-High Pressure Experimental Data
4.1 Nonlinear Pressure Gradient Response
The experimental data from Daqing Oilfield indicate that the relationship between interfacial tension γ and pressure P can be described by a piecewise function:

For P ≤ 5 MPa:
γ = 0.0083 + 0.152 P¹⁷

For P > 5 MPa:
γ = 0.0735 e^−0.12(P−5)

This nonlinearity arises from two competitive mechanisms:

• Pressure promotes surfactant desorption (dominates in low-pressure regions).
• Pressure enhances intermolecular hydrophobic interactions (dominates in high-pressure regions).

4.2 Multi-Scale Simulation Validation
Molecular dynamics (MD) and computational fluid dynamics (CFD) coupling simulations at 15 MPa yielded:

• Interface thickness: 2.8 nm (experimental value: 3.1 nm)
• Diffusion coefficient: 1.2×10⁻¹⁰ m²/s (experimental value: 0.9×10⁻¹⁰ m²/s)
• Adsorption energy barrier: 42 kJ/mol (experimental value: 38 kJ/mol)

The simulation results show an over 85% correlation with experimental data, confirming the role of pressure in reconstructing the interfacial structure.

Chapter 5: Technological Development Outlook
5.1 New Surfactant Design
Pressure-responsive surfactants based on machine learning:

• Incorporating fluorocarbon segments (3× higher pressure sensitivity)
• Constructing star-shaped topological structures (CMC reduction by 40%)
• Adding nanoparticle synergists (60% increase in interfacial elasticity modulus)

5.2 Smart Measurement System Development
Next-generation rotating drop technology will integrate:

• Terahertz wave in-situ detection
• Digital twin real-time simulation
• Adaptive pressure compensation algorithms

By 2025, the precision of ultra-high pressure interfacial tension measurement is expected to reach 10⁻⁴ mN/m, providing crucial technological support for unconventional oil and gas development.

Conclusion
This paper systematically reveals the molecular mechanisms of surfactant interfacial behavior under ultra-high pressure, establishes a rotating drop measurement system based on an improved Young-Laplace equation, and proposes technological solutions for high-pressure environments. The results are of significant guiding value for deep oil and gas extraction and supercritical CO₂ enhanced oil recovery.

Appendix
Appendix A: Experimental Equipment Technical Specifications