The dynamic interaction between a rigid porous structure (porosity ϕ) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by for example Lévy, Auriault and Burridge & Keller is used, from which we reformulate the theory by Johnson, Koplik & Dashen. The macroscopic equations then serve to describe the high-frequency behaviour of an oscillating fluid within a porous sample. This behaviour may be characterized by the length parameter Λ and by the tortuosity parameter α∞. It is shown that Λ and α∞, which describe an oscillatory flow behaviour, may be evaluated on the basis of steady potential flow theory. Numerical results are then presented for several pore geometries, and for these geometries, the steady-state permeability k0 is computed numerically also. The parameter 8α∞ k0/ϕΛ2, first introduced by Johnson et al., is then evaluated and appears to be weakly dependent on pore geometry. This implies that for many porous media the dynamic interaction is described by an approximate scaling function. New experimental data, concerning oscillating flows through several porous media, are presented. Within limits of accuracy, these data are in agreement with the approximate scaling function.
We have measured homogeneous nucleation rates of water at 200-240 K in the carrier gas helium, in the range of 10 13 −10 17 m −3 s −1 using an expansion wave tube. The rates agree well with the results of Wölk and Strey ͓J. Phys. Chem. B 105, 11683 ͑2001͔͒ in the range of overlap ͑220-240 K͒, and are summarized by the empirical fit J = S exp͓4.6+ 0.244T − ͑906.8− 2.914T͒ / ͑ln S͒ 2 ͔, with J the nucleation rate in m −3 s −1 , S the supersaturation, and T the temperature in K. We find that the supersaturation dependence of both our rates and those of Wölk and Strey is lower than classical theory predicts, and that the critical cluster is smaller than the classical critical size. These deviations are explained in the framework of the Tolman theory for surface tension, and the "Tolman length" is estimated from our experimental results. We find a positive Tolman length that increases with decreasing temperature, from about 0.1 Å at 260 K to ͑0.6± 0.4͒ Å at 200 K. We present a nucleation rate expression that takes the Tolman length into account and show that both the supersaturation and temperature dependence are improved, compared to the classical theory.
Nucleation rate measurements of water in the presence of nitrogen as a carrier gas are reported at total pressures near 10, 25, and 40 bar, and temperatures of 230 and 250 K. The results were obtained using our pulse-expansion wave tube, particularly suited for high pressure nucleation research. Enhanced fugacity of water vapor in the mixture, due to the presence of nitrogen, was quantitatively taken into account. Values of the enhancement factors as a function of pressure and temperature were correlated from accurate gravimetric measurements available in literature. The results demonstrate a strong influence of nitrogen pressure on the nucleation behavior of water, when temperature and supersaturation are kept fixed. The effect is associated with a decrease of the surface tension of water, due to the adsorption of nitrogen onto the liquid surface. A tentative model is presented that qualitatively describes this decreasing surface tension with pressure. The competition between the opposing effects of enhanced fugacity and decreasing surface tension is identified as a complicating factor in detecting pressure effects on nucleation. This conclusion is expected to hold for other vapor/carrier gas systems as well.
The influence of a small amount of gas within the saturating liquid of a porous medium on acoustic wave propagation is investigated. It is assumed that the gas volumes are spherical, homogeneously distributed, and that they are within a very narrow range of bubble sizes. It is shown that the compressibility of the saturating fluid is determined by viscous, thermal, and a newly introduced Biot-type damping of the oscillating gas bubbles, with mean gas bubble size and concentration as important parameters. Using a super-saturation technique, a homogeneous gas-liquid mixture within a porous test column is obtained. Gas bubble size and concentration are measured by means of compressibility experiments. Wave reflection and propagation experiments carried out in a vertical shock tube show pore pressure oscillations, which can be explained by incorporating a dynamic gas bubble behaviour in the linear Biot theory for plane wave propagation.
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