Knudsen number

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

Gas transport in unsaturated porous media: The adequacy of Fick's law

Abstract: The increasing use of natural unsaturated zones as repositories for landfills and disposal sites for hazardous wastes (chemical and radioactive) requires a greater understanding of transport processes in the unsaturated zone. For volatile constituents an important potential transport mechanism is gaseous diffusion. Diffusion, however, cannot be treated as an independent isolated transport mechanism. A complete understanding of multicomponent gas transport in porous media (unsaturated zones) requires a knowledge of Knudsen transport, the molecular and nonequimolar components of diffusive flux, and viscous (pressure driven) flux. The constitutive equations relating these flux components are available from the “dusty gas” model of Mason et al. (1967). This review presents a brief discussion of the underlying principles and interrelationships among each of the above flux mechanisms. Some aspects of these transport mechanisms are, to our knowledge, generally unrecognized in the Earth science literature. The principles underlying the transport mechanisms are illustrated with binary systems; the constitutive equations are then cast in forms thought to be most useful for the study of natural unsaturated zones. The viscous and diffusive fluxes are coupled in the constitutive equations through the Knudsen diffusivities; a knowledge of Knudsen diffusivities is necessary to calculate the viscous component of flux and pressure gradients. The Knudsen diffusivities can be calculated from measurements of the Klinkenberg effect. Two examples are presented showing that in natural systems, very small pressure gradients (1 Pa/m or less) can produce viscous fluxes greater than or equal to diffusive fluxes and that, conversely, pressure gradients of this magnitude can be generated by diffusive processes. The example calculations show that major concentration gradients can be developed for stagnant (zero flux, nonreactive) gases. A method is presented for approximating the viscous and diffusive flux components of gases in a multicomponent system from a knowledge of the concentration profiles of stagnant gases. In subsoil environments, argon and nitrogen are considered to be stagnant gases. Fick's laws are essentially, by definition, inadequate to deal with stagnant gases. In the examples presented, the error associated with estimating the total fluxes of nonstagnant gases by Fick's law, relative to stationary coordinates, ranges from a few percent to orders of magnitude.

Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid

Abstract: In real systems there is always a certain amount of slip, which, however, is hard to detect experimentally because of the required space resolution. In this paper, we analyze the effect of slip boundary conditions on the dynamics of fluids in porous media by studying the flow of a Newtonian and non-Newtonian Maxwellian fluid in an axisymmetric cylindrical tube (pore), in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the pore. The viscosity as well as the compressibility of the liquid is taken into account. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves and studies of blood flow dynamics in living creatures. The Navier-Stokes equations for an axisymmetric cylindrical pore are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the pore is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and Knudsen number. The calculations disclose that the compressibility of the liquid, Knudsen number of slip flow and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. The effects of all parameters of the problem are numerically discussed and graphically explained.

Hydrodynamic origin of diffusion in nanopores.

Abstract: We study the transport of a subcritical Lennard-Jones fluid in a cylindrical nanopore, using a combination of equilibrium and nonequilibrium as well as dual control volume grand canonical molecular dynamics methods. We show that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. We also demonstrate that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities.