Knudsen number

About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.

Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition

Abstract: It has long been recognized that the fluid mechanics of gas-phase microflows can differ significantly from the macroscopic world. Non-equilibrium effects such as rarefaction and gas-surface interactions need to be taken into account, and it is well known that the no-slip boundary condition of the Navier-Stokes equations is no longer valid. Following ideas proposed by Maxwell, it is generally accepted that the Navier-Stokes equations can be extended into the slip-flow regime, provided the Knudsen number is less than 10− 1. Improvements in micro-fabrication techniques, however, are now enabling devices to be constructed with sub-micron feature sizes. At this scale, the flow will depart even further from equilibrium and will enter the transition regime. In recent years, there has been considerable success in the implementation of second-order slip-boundary conditions to extend the Navier-Stokes equations into the transition regime. Unfortunately, as yet, no consensus has been reached on the correct form of h...

Fluid flow in nanopores: An examination of hydrodynamic boundary conditions

Abstract: Steady-state Poiseuille flow of a simple fluid in carbon slit pores under a gravity-like force is simulated using a realistic empirical many-body potential model for carbon. In this work we focus on the small Knudsen number regime, where the macroscopic equations are applicable, and simulate different wetting conditions by varying the strength of fluid–wall interactions. We show that fluid flow in a carbon pore is characterized by a large slip length even in the strongly wetting case, contrary to the predictions of Tolstoi’s theory. When the surface density of wall atoms is reduced to values typical of a van der Waals solid, the streaming velocity profile vanishes at the wall, in accordance with earlier findings. From the velocity profiles we have calculated the slip length and by analyzing temporal profiles of the velocity components of particles colliding with the wall we obtained values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall.

Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions

Abstract: The lattice Boltzmann method is developed to study gaseous slip flow in microchannels. An approach relating the Knudsen number with the relaxation time in the lattice Boltzmann evolution equation is proposed by using gas kinetic equation resulting from the Bhatnagar–Gross–Krook collision model. The slip velocity at the solid boundaries is obtained with kinetic theory boundary conditions. The two-dimensional micro-Couette flow, micro-Poiseuille flow, and micro-lid-driven cavity flow are simulated using the present model. It is found that the numerical results agree well with available analytical and benchmark solutions.