Nishanth Dongari

Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows

We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.

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.

Molecular free path distribution in rarefied gases

We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Levy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices.

Thermal transpiration of nanoscale gas flow

We present a molecular dynamics (MD) methodology to investigate temperature-driven gas flow through a nanochannel connecting two reservoirs at different temperatures. The temperature gradient along the channel drives the macroscopic movement of gas molecules from the cold to the hot regions, in the phenomenon known as thermal transpiration. Temperature, density and pressure profile variations along the axial direction are measured at various rarefaction conditions, from the slip flow to the free molecular regimes. Pressure and density evolutions are monitored as a function of time in both the hot and cold reservoirs. The normalized thermo molecular pressure difference (TMPD) values are calculated and compared with kinetic theory results. Comparisons show good agreement up to the early transition regime, although beyond this our numerical experiments over-predict the theoretical results. These numerical experiments are useful because experimental data is scarce for nano devices and these molecular simulati...

Effects of curvature on rarefied gas flows between rotating concentric cylinders

The gas flow between two concentric rotating cylinders is considered in order to investigate non-equilibrium effects associated with the Knudsen layers over curved surfaces. We investigate the nonlinear flow physics in the near-wall regions using a new power-law (PL) wall-scaling approach. This PL model incorporates Knudsen layer effects in near-wall regions by taking into account the boundary limiting effects on the molecular free paths. We also report new direct simulation Monte Carlo results covering a wide range of Knudsen numbers and accommodation coefficients, and for various outer-to-inner cylinder radius ratios. Our simulation data are compared with both the classical slip flow theory and the PL model, and we find that non-equilibrium effects are not only dependent on Knudsen number and accommodation coefficient but are also significantly affected by the surface curvature. The relative merits and limitations of both theoretical models are explored with respect to rarefaction and curvature effects. The PL model is able to capture some of the nonlinear trends associated with Knudsen layers up to the early transition flow regime. The present study also illuminates the limitations of classical slip flow theory even in the early slip flow regime for higher curvature test cases, although the model does exhibit good agreement throughout the slip flow regime for lower curvature cases. Torque and velocity profile comparisons also convey that a good prediction of integral flow properties does not necessarily guarantee the accuracy of the theoretical model used, and it is important to demonstrate that field variables are also predicted satisfactorily.

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular microchannels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Velocity Inversion In Cylindrical Couette Gas Flows

We investigate a power-law probability distribution function to describe the mean free path of rarefied gas molecules in non-planar geometries. A new curvature-dependent model is derived by taking into account the boundary-limiting effects on the molecular mean free path for surfaces with both convex and concave curvatures. In comparison to a planar wall, we find that the mean free path for a convex surface is higher at the wall and exhibits a sharper gradient within the Knudsen layer. In contrast, a concave wall exhibits a lower mean free path near the surface and the gradients in the Knudsen layer are shallower. The Navier-Stokes constitutive relations and velocity-slip boundary conditions are modified based on a power-law scaling to describe the mean free path, in accordance with the kinetic theory of gases, i.e. transport properties can be described in terms of the mean free path. Velocity profiles for isothermal cylindrical Couette flow are obtained using the power-law model. We demonstrate that our model is more accurate than the classical slip solution, especially in the transition regime, and we are able to capture important non-linear trends associated with the non-equilibrium physics of the Knudsen layer. In addition, we establish a new criterion for the critical accommodation coefficient that leads to the non-intuitive phenomena of velocity-inversion. Our results are compared with conventional hydrodynamic models and direct simulation Monte Carlo data. The power-law model predicts that the critical accommodation coefficient is significantly lower than that calculated using the classical slip solution and is in good agreement with available DSMC data. Our proposed constitutive scaling for non-planar surfaces is based on simple physical arguments and can be readily implemented in conventional fluid dynamics codes for arbitrary geometric configurations.

Molecular dynamics simulations of high speed rarefied gas flows

To understand the molecular behaviour of gases in high speed rarefied conditions, we perform molecular dynamics (MD) numerical experiments using the open source code Open FOAM. We use shear-driven Couette flows as test cases, where the two parallel plates are moving with a speed of Uw in opposite directions with their temperatures set to Tw. The gas rarefaction conditions vary from slip to transition, and compressibility conditions vary from low speed isothermal to hypersonic flow regimes, i.e. Knudsen number (Kn) from 0.01 to 1 and Mach number (Ma) from 0.05 to 10. We measure the molecular velocity distribution functions, the spatial variation of gas mean free path profiles and other macroscopic properties. Our MD results convey that flow properties in the near-wall non-equilibrium region do not merely depend on Kn, but they are also significantly affected by Ma. These results may yield new insight into diffusive transport in rarefied gases at high speeds.

Rarefaction effects in gas flows over curved surfaces

The fundamental test case of gas flow between two concentric rotating cylinders is considered in order to investigate rarefaction effects associated with the Knudsen layers over curved surfaces. We carry out direct simulation Monte Carlo simulations covering a wide range of Knudsen numbers and accommodation coefficients, and for various outer-to-inner cylinder radius ratios. Numerical data is compared with classical slip flow theory and a new power-law (PL) wall scaling model. The PL model incorporates Knudsen layer effects in near-wall regions by taking into account the boundary limiting effects on the molecular free paths. The limitations of both theoretical models are explored with respect to rarefaction and curvature effects. Torque and velocity profile comparisons also convey that mere prediction of integral flow parameters does not guarantee the accuracy of a theoretical model, and that it is important to ensure that prediction of the local flowfield is in agreement with simulation data.

Behaviour of microscale gas flows based on a power-law free path distribution function

We investigate a power‐law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry‐dependent effective molecular mean free path (MFP) model is then derived for a planar wall confinement, by taking into account the boundary limiting effects on the molecular paths. The power‐law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier‐Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure‐driven Poiseuille gas flows in micro‐channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data.