Gas Transport During Oscillatory Flow in a Network of Branching Tubes

Abstract

A transport coefficient was measured for a range of oscillatory flow conditions in a branching network of tubes. Measurements were made both across the first generation of a three-generation network and the second generation of a four-generation network. The results for these two series of tests were similar, indicating that there was no significant effect due to the system boundaries. The results are cast in terms of an effective axial diffusion coefficient of the form (Formula: see text) where kappa is the molecular diffusivity, Vt is the local stroke volume (cc); and f is the oscillation frequency (Hz). These results are compared to those obtained by other investigators in branching systems of similar geometry. At low frequency, this result is found to be in approximate agreement with the steady flow result of Scherer, et al. [15]. This expression differs from the oscillatory flow results of Tarbell, et al. [19] for liquids, primarily in terms of the effects of oscillation frequency.

Streamline crossing: An essential mechanism for aerosol dispersion in the pulmonary acinus

“…These models predict that for a low dimensionless frequency parameter (i.e. Womersley number, Wo = a ( ω / ν ) 1/2 with ω the angular frequency and ν the fluid’s kinematic viscosity) the ratio D eff / D mol will return to unity (Elad et al, 1992; Gaver et al, 1992); a trend different from our observations for Wo = O (10 −2 ) where the ratio D eff / D mol yields ~10 3 and Pe values are intrinsically much larger (Kamm et al, 1984). While these results call for further investigation, we note as a final remark that net particle displacements per cycle scale approximately according to a modified Fick’s law, i.e.…”

“…Such dispersion regime would only be met for L ≫ O (10 −1 m ) which is not the present case. Theoretical and experimental works have extended such works to quantify axial diffusivity under oscillatory laminar flows both in straight pipes (Joshi et al, 1983; Watson, 1983) and branching tube networks (Kamm et al, 1984). These models predict that for a low dimensionless frequency parameter (i.e.…”

Toward improved methods of high frequency ventilation: a study of gas transport mechanisms

“…Several experimental studies have been published using gases (2)(3)(4)(5)(6)(7) and liquids (8,9). The physical models used have included a single straight tube (4,7), a straight tube connected to a large reservoir (6), and branching networks (2,3,5,8,9).…”

“…Several experimental studies have been published using gases (2)(3)(4)(5)(6)(7) and liquids (8,9). The physical models used have included a single straight tube (4,7), a straight tube connected to a large reservoir (6), and branching networks (2,3,5,8,9). In most of these, particularly those in branching networks, the results indicated that gas transport could be described by an "efTective diffusivity", Der, defined through an expression having the form of Fick's law for molecular diffusion: Vx = -D,rrA(dc/dx) where 0, is the rate of transport of gas 'x', A is the local cross-sectional area, and dc/dx is the local concentration gradient.…”