Molecular Dynamics Investigation of Mass Transport During Evaporation for the Binary System of n-Dodecane and Nitrogen

TL;DR

Addressing interfacial mass transport during evaporation in a Type-III binary mixture, the paper uses non-equilibrium molecular dynamics to resolve diffusion-dominated vapor–liquid interfaces at near-critical conditions. It introduces two complementary flux evaluations—the fixed boundary method and the two-boundary method—and applies Gaussian Process Regression to quantify uncertainty in QoIs, enabling a data-driven, uncertainty-aware evaporation coefficient model $\alpha_{\text{evap}}(T_r)$. Key findings show that both evaporation and reflected fluxes rise with increasing reduced temperature $T_r$, while $\alpha_{\text{evap}}$ decreases roughly linearly with $T_r$, described by $\alpha(T_r) \approx -0.2848\,T_r + 1.1740$. The work provides a framework for kinetic boundary conditions applicable to hydrocarbon–nitrogen mixtures, laying groundwork for coupling MD insights with CFD boundary closures in high-$T$ and high-$P$ applications.

Abstract

The study of interfacial fluxes under evaporative or condensation processes are ubiquitous in thermal systems, propulsion devices, and many other engineering applications. Most continuum scale models fail to capture the true nature of thermodynamic property variation across the interface, particularly under high-temperature and high-pressure conditions. An improvement over the sharp interface assumption of such continuum scale models is the consideration of a diffused interface and using Kinetic Boundary Conditions (KBCs) to model the mass-transport across the liquid vapor interface. Prior studies on KBCs mainly address monoatomic fluids. Two of the main ingredients required to form KBCs are: density and mass flux. Here, we study a Type-III binary mixture of n-dodecane and nitrogen using non-equilibrium molecular dynamics at near-critical temperatures. Interfacial properties such as thickness, density gradient, and surface tension were analyzed. A key result is the temporal evolution of the evaporation and reflected mass fluxes across the vapor-liquid interface. We observe that both the evaporation and reflection fluxes increase with increasing temperature, indicating enhanced molecular activity and mass transport across the interface at higher Tr. In contrast, the evaporation coefficient alpha_evap decreases from about alpha approximately 0.978 at Tr equals 0.70 to alpha approximately 0.905 at Tr equals 0.95 because the reflected-out flux increases along with the evaporation flux, which reduces the net efficiency of molecular evaporation across the interface. To the authors' knowledge, this is one of the very few studies estimating mass transport coefficients for Type-III binary systems, laying the foundation for KBCs in hydrocarbon and nitrogen mixtures.

Figures (25)

• Figure 1: Schematic representation of the vapor--liquid interfacial structure, showing the interfacial layer, the Knudsen layer, and the corresponding kinetic boundaries. Kinetic boundary I marks the transition from the interfacial region to the Knudsen layer, where molecular-level mass transport is dominant, while kinetic boundary II denotes the interface with the vapor bulk region.
• Figure 2: Atomistic configuration and schematic of the simulation domain used for the NEMD calculations. The liquid phase consists of n-dodecane molecules modeled with the SKS united-atom potential, while nitrogen is represented using the 2CLJ potential. A liquid slab is placed at the center of the domain with nitrogen gas on both sides. The simulation box has lateral dimensions of $L_x = L_y = 8~\mathrm{nm}$ and periodic boundary conditions are applied in all directions. The gas regions are thermally regulated to drive evaporation from the liquid surface under controlled non-equilibrium conditions.
• Figure 3: Schematic of the computational domain for the fixed boundary method. The fixed box enclosing the initial liquid slab is used to track the number of molecules over time, allowing evaluation of the net evaporation flux.
• Figure 4: Schematic of the left vapor--liquid interface region used in the two-boundary method. Two reference planes are defined: one near the vapor side and the other near the liquid core, with the separation corresponding to the interface thickness determined by the 90--10 rule.
• Figure 5: Temporal evolution of the vapor–liquid interfaces for n-dodecane/N$_2$ at $T_r=0.70$ (Case 1) and $T_r=0.95$ (Case 5). Interfaces are identified using the 90–10 rule. The interfacial region broadens over time, and in Case 5 the interface disappears once the liquid n-dodecane becomes depleted.