Session D14: Nanoscale Flows: Basics and Modeling

Atomistic Modeling of the Fluid-Solid Interface in Simple Fluids

Fluids can exhibit pronounced structuring effects near a solid boundary, typically manifested in a layered structure that has been extensively shown to directly affect transport across the interface. We present and discuss several results from molecular-mechanical modeling and molecular-dynamics (MD) simulations aimed at characterizing the structure of the first fluid layer directly adjacent to the solid. We identify a new dimensionless group -- termed the Wall number -- which characterizes the degree of fluid layering, by comparing the competing effects of wall-fluid interaction and thermal energy. We find that in the layering regime, several key features of the first layer layer -- including its distance from the solid, its width, and its areal density -- can be described using mean-field-energy arguments, as well as asymptotic analysis of the Nernst-Planck equation. For dense fluids, the areal density and the width of the first layer can be related to the bulk fluid density using a simple scaling relation. MD simulations show that these results are broadly applicable and robust to the presence of a second confining solid boundary, different choices of wall structure and thermalization, strengths of fluid-solid interaction, and wall geometries.   

Layering at the Fluid-Solid Interface and Anomalous Diffusion in Nanoconfined Fluids

Molecular self-diffusion in a fluid under nanoconfinement can differ considerably from its counterpart in the bulk; this ``anomalous" diffusion can have profound implications for applications involving transport in nanoconfined systems. In this talk we study the contribution of fluid layering at the solid-liquid interface to anomalous diffusion, using molecular-mechanical modeling and molecular-dynamics (MD) simulations of simple fluids confined within a graphene nano-slit. We find that fluid layering near the fluid-solid interface strongly affects molecular diffusion; the former can be characterized by a non-dimensional group -- referred to as the Wall number -- which compares the competing effects of wall-fluid interaction and thermal energy. We specifically demonstrate that the dependence of the {\it overall} diffusion coefficient on the confinement lengthscale can be modeled by superposing the contributions of the bulk and near-wall regions. The anomalous diffusive behavior in the near-wall region is due to a ``dimensional restriction" of the near-wall fluid. MD simulation results suggest that the difference between the bulk and near-wall diffusivity can be modeled using the excess entropy of the fluid in each region.   

Confinement effects on liquid oxygen flows in carbon nanotubes: A MD simulation study

Molecular dynamics simulations are performed to investigate the liquid flow mechanism of diatomic molecules in armchair carbon nanotubes (CNTs). Oxygen molecules are considered as the fluid inside armchair (n,n) (n=6-20) CNTs at a temperature of 133[K] and a bulk density of 1680[kg$/$m$^3$] for the liquid state. The velocity profiles and slip lengths are discussed considering the radial distributions of the fluid density by the finite difference-based velocity fitting method. It is shown that as the diameter of the CNT increases, the slip length and the flow rate enhancement generally become smaller while irregular tendencies (discontinuity points) are observed in the distribution profiles. Between the (7,7) and (8,8) CNTs, a steep drop can be seen in the profiles. Between the (9,9) and (11,11) CNTs, and between the (12,12) and (14,14) CNTs transitional profiles are observed. It is confirmed that those phenomena are caused by an instability of the fluid molecule cluster due to the discontinuous confinement of the CNTs.   

The investigation of contact line effect on nanosized droplet wetting behavior with solid temperature condition

In many multi-phase fluidic systems, there are essentially contact interfaces including liquid-vapor, liquid-solid, and solid-vapor phase. There is also a contact line where these three interfaces meet. The existence of these interfaces and contact lines has a considerable impact on the nanoscale droplet wetting behavior. However, recent studies have shown that Young's equation does not accurately represent this behavior at the nanoscale. It also emphasized the importance of the contact line effect.Therefore, We performed molecular dynamics simulation to imitate the behavior of nanoscale droplets with solid temperature condition. And we find the effect of solid temperature on the contact line motion. Furthermore, We figure out the effect of contact line force on the wetting behavior of droplet according to the different solid temperature condition. With solid temperature condition variation, the magnitude of contact line friction decreases significantly. We also divide contact line force by effect of bulk liquid, interfacial tension, and solid surface.   

Determination of the shear and bulk viscosity from equilibrium molecular-dynamics simulations

Determining fluid properties accurately is essential for large-scale fluid dynamics simulations where only a few parameters determine the behaviour of an entire system. Even though many properties are well known, others are more obscure and difficult to determine experimentally. One such property is the bulk viscosity which plays a particularly large role in compressible fluids but is rarely considered in fluid-dynamics simulations. We determine both the shear and bulk viscosity using equilibrium methods within the molecular-dynamics framework using both atomistic and coarse-grained models with a view of assessing both the accuracy of coarse-grained models for transport-property calculations and the necessity of including such properties at various scales and scenarios.   

Transport properties at fluids interfaces: a molecular study for a macroscopic modelling

Rapid developments in the field of micro- and nano-fluidics require detailed analysis of the properties of matter at the molecular level. But despite numerous works in the literature, appropriate macroscopic relations able to integrate a microscopic description of fluid and soft matter properties at liquid-vapour and multi-fluid interfaces are missing. As a consequence, studies on interfacial phenomena and micro-device designs often rely on oversimplified assumptions, e.g. that the viscosities can be considered constant across interfaces. In our work, we present non-equilibrium MD simulations to scrutinise efficiently and systematically, through the tools of statistical mechanics, the anisotropic properties of fluids, namely density variations, stress tensor, and shear viscosity, at the fluid interfaces between liquid and vapour and between two partially miscible fluids. Our analysis has led to the formulation of a general relation between shear viscosity and density variations validated for a wide spectrum of interfacial fluid problems. In addition, it provides a rational description of other interfacial quantities of interest, including surface tension and its origins, and more generally, it offers valuable insight of molecular transport phenomena at interfaces.   

Water imbibition by mica pores: what happens when capillary flow is suppressed?

The imbibition of liquids into porous media plays a critical role in numerous applications. Most prior studies focused on imbibition driven by capillary flows. In this work, we study the imbibition of water into slit-shaped mica pores filled with pressurized methane using molecular simulations. Despite that capillary flow is suppressed by the high gas pressure, water is imbibed into the pore as monolayer liquid films. Since the classical hydrodynamic flow is not readily applicable for the monolayer water film propagating on the mica wall and the imbibition is driven by the strong affinity of water molecules to the mica walls, the observed imbibition is best taken as surface hydration. We show that the dynamics of water's imbibition front follows a simple diffusive scaling law. The effective diffusion coefficient of the imbibition front, however, is more than ten times larger than the diffusion coefficient of the water molecules in the water film adsorbed on the mica walls. Using a molecular theory originally developed for the spreading of monolayer films on solid substrates, we clarify the mechanism underlying the rapid water imbibition observed here.   

Storage and recovery of methane-ethane mixtures in single shale pores.

Natural gas production from shale formations has received extensive attention recently. While great progress has been made in understanding the adsorption and transport of single-component gas inside shales' nanopores, the adsorption and transport of multicomponent shale gas under reservoir conditions (CH4 and C2H6 mixture) has only begun to be studied. In this work, we use molecular simulations to compute the storage of CH4 and C2H6 mixtures in single nanopores and their subsequent recovery. We show that surface adsorption contributes greatly to the storage of CH4 and C2H6 inside the pores and C2H6 is enriched over CH4. The enrichment of C2H6 is enhanced as the pore is narrowed, but is weakened as the pressure increases. We show that the recovery of gas mixtures from the nanopores approximately follows the diffusive scaling law. The ratio of the production rates of C2H6 and$_{\mathrm{\thinspace }}$CH4 is close to their initial mole ratio inside the pore despite that the mobility of pure C2H6 is much smaller than that of pure CH4 inside the pores. By using scale analysis, we show that the strong coupling between the transport of CH4 and C2H6 is responsible for the effective recovery of C2H6 from the nanopores.   

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models.   

Investigating Nonexistence of the reversed flow characteristics in a Falkner-Skan equation.

Existence of a class of similarity solutions for a nonlinear differential equation were considered in the case of accelerating and decelerating flows, in this article we proposed nonexistence of reversed flows in a Falkner Skan equation. A new converted nonlinear ordinary differential system is studied for reversed flows. Numerical results for various instances are calculated related to velocity profile, shear stress and their behaviors. In aeronautics, we can use these reversed flow solutions to estimate the critical value of separation.