Modeling of Knudsen Layer Effects in the Micro-Scale Backward-Facing Step in the Slip Flow Regime.

The effect of the Knudsen layer in the thermal micro-scale gas flows has been investigated. The effective mean free path model has been implemented in the open source computational fluid dynamics (CFD) code, to extend its applicability up to slip and early transition flow regime. The conventional Navier-Stokes constitutive relations and the first-order non-equilibrium boundary conditions are modified based on the effective mean free path, which depends on the distance from the solid surface. The predictive capability of the standard `Maxwell velocity slip-Smoluchwoski temperature jump' and hybrid boundary conditions `Langmuir Maxwell velocity slip-Langmuir Smoluchwoski temperature jump' in conjunction with the Knudsen layer formulation has been evaluated in the present work. Simulations are carried out over a nano-/micro-scale backward facing step geometry in which flow experiences adverse pressure gradient, separation and re-attachment. Results are validated against the direct simulation Monte Carlo (DSMC) data, and have shown significant improvement over the existing CFD solvers. Non-equilibrium effects on the velocity and temperature of gas on the surface of the backward facing step channel are studied by varying the flow Knudsen number, inlet flow temperature, and wall temperature. Results show that the modified solver with hybrid Langmuir based boundary conditions gives the best predictions when the Knudsen layer is incorporated, and the standard Maxwell-Smoluchowski can accurately capture momentum and the thermal Knudsen layer when the temperature of the wall is higher than the fluid flow.

Breakdown parameter for kinetic modeling of multiscale gas flows.

Multiscale methods built purely on the kinetic theory of gases provide information about the molecular velocity distribution function. It is therefore both important and feasible to establish new breakdown parameters for assessing the appropriateness of a fluid description at the continuum level by utilizing kinetic information rather than macroscopic flow quantities alone. We propose a new kinetic criterion to indirectly assess the errors introduced by a continuum-level description of the gas flow. The analysis, which includes numerical demonstrations, focuses on the validity of the Navier-Stokes-Fourier equations and corresponding kinetic models and reveals that the new criterion can consistently indicate the validity of continuum-level modeling in both low-speed and high-speed flows at different Knudsen numbers.

Dynamics of nanoscale droplets on moving surfaces.

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.