Deterministic and Diffusive Mass Transfer Mechanisms in the Capture of Vapors and Particles.
Several analytical methods, some classical and some new, are employed to study the motion of dilute mixtures of particles or heavy molecules in a host gas. In the (particle) limit of negligible Brownian diffusivity, Robinson's extension of the potential flow theory to dust-laden fluids is re-introduced and more fully exploited. The generally overlooked but important phenomenon of particle phase compressibility is illustrated. It is shown that particle "inertial drift" and "pressure diffusion" are equivalent phenomena for host fluid deceleration times, (omega)('-1), which are large compared with the particle relaxation ("stopping") time (tau). Generalized phenomenological expressions, giving the particle velocity drift as a function of local fluid properties only (but valid for a much larger region of (omega)(tau) than the Chapman-Enskog expansion) are found. Although these phenomenological laws have been rigorously derived only for linear flows (in which the velocity field depends linearly on the spatial coordinates), it appears that the assumption of locally linear behavior leads to a valuable approximate description of the effects of inertia in particle motion even when the host fluid flow is not linear in the above sense. A useful analytical solution to the problem of the large Reynolds number motion of a dusty gas near the forward stagnation point of a cylinder in crossflow is derived, including inertial, diffusive (thermal and Brownian) and centrifugal effects. The analogous problem of a sphere in a low Reynolds number flow is also solved in the absence of thermophoresis. The generalized phenomenological laws obtained in the particle limit are extended to the case of non-negligible Fick diffusivity (heavy molecule limit) with the help of a Fokker-Planck kinetic equation. Owing to its great practical interest, we conclude with a treatment of the thermophoretic deposition of particles in turbulent boundary layer flow. Available, but limited, experimental data have been used to test our predictions, and the agreement is found to be generally good.
- Pub Date:
- Physics: Fluid and Plasma