Knudsen number

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

Drag Force and Slip Correction of Aggregate Aerosols

Abstract: The drag force on aggregate particles of uniform spheres was measured in a Millikan apparatus as a function of Knudsen number. Our experiment was designed to study the effect of particle orientation on the slip correction factor of nonspherical particles. The velocities of charged particles in a gravitational field with and without an applied electrical field were measured. An electrical field strength of 2000 V/cm was used to align doublet and triplet particles. Results showed that an aggregate particle moved in random orientation while in the gravitational field. The same particle moved with its polar axis parallel to the electric field (doublets) or with its plane of centers parallel to the electrical field (triangular triplets). Using a nonlinear regression method, both the dynamic shape factor and slip correction factor could be determined separately from the data. The dynamic shape factors at different orientations were in good agreement with those obtained previously in a sedimentation tank. The sl...

Navier-Stokes Simulations of a Novel Viscous Pump

Abstract: A numerical study of flow in a novel viscous-based pumping device appropriate for microscale applications is described. The device, essentially consisting of a rotating cylinder eccentrically placed in a channel, is shown to be capable of generating a net flow against an externally imposed pressure gradient. Navier-Stokes simulations at low Reynolds numbers are carried out using a finite-volume approach to study the influence of various geometric parameters. Slip effects for gas flows are also briefly investigated. The numerical results indicate that the generated flow rate is a maximum when the cylinder is in contact with a channel wall and that an optimum plate spacing exists. These observations are in excellent agreement, both qualitatively and quantitatively, with a previous experimental study. Furthermore, it is shown that effective pumping is obtained even for considerably higher Reynolds numbers, thereby extending the performance envelope of the proposed device to non-microscale applications as well. Finally, slip-flow effects appear to be significant only for Knudsen numbers greater than 0.1, which is important from the point of view of microscale applications.

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation.

Abstract: In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g., Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity with unknown boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup compared to the standard training process (e.g., Adam plus L-BFGS-B) for the two-dimensional flow problems considered in our work.

Unipolar Diffusion Charging of Small Aerosol Particles

Abstract: A theory for unipolar ``diffusion charging'' of small aerosol particles is developed for the free‐molecule and transition regions. The free‐molecule theory is, of course, exact within the restrictions imposed on the physical system. The theory for the transition region is based on the Knudsen iteration solution of a relaxation model of the Boltzmann equation. Insufficient experimental data are available to permit detailed comparison with the developed theories.

Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics

Abstract: In this paper we present a new semilagrangian scheme for the numerical solution of the BGK model of rarefied gas dynamics, in a domain with moving boundaries, in view of applications to Micro Electro Mechanical Systems (MEMS). The source term is treated implicitly, which makes the scheme Asymptotic Preserving in the limit of small Knudsen number. Because of its Lagrangian nature, no stability restriction is posed on the CFL number, which is determined only by accuracy requirements. The method is tested on a one dimensional piston problem. The solution for small Knudsen number is compared with the results obtained by the numerical solution of the Euler equation of gas dynamics.