Knudsen effect, effective thermal

Just as microporous foams present better properties than conventional foams, it is expected that nanoporous foams will present enhanced properties because of their lower pore size. For instance, they could have better mechanical properties, such as better toughness, higher impact energies, and strain to failure [26], In addition, they could present an improved thermal insulation behavior because of the Knudsen effect [27], More details about the expected properties of nanoporous polymer foams will be provided in the last section of this chapter. 

The effective thermal conductivity k in the dried material has been found to vary significantly with the total pressure and with the type of gas present. Also, the type of material affects the value of k (SI, Kl). The effective diffusivity D of the dried material is a function of the structure of the material, Knudsen diffusivity, and molecular diffusivity (Kl). 

The low gas thermal conductivity Agas of aerogels in general can be explained by the Knudsen effect, expressing the gas conduction in a porous media as function of the air pressure and the characteristic pore size and written in a simplified way as follows (see also Figure 45.3) [31,69-71] ... 

Research is also ongoing to develop new high-performance thermal insulation materials, for example, nano insulation materials (NIM) [31,69,70,103-114] that utilize the Knudsen effect to achieve their low thermal conductivity without applying a vacuum in the pores. One possible pathway toward NlMs is to... 

Consider the mass, thermal and momentum balance equations. The key assumption of the present analysis is that the Knudsen number of the flow in the capillary is sufficiently small. This allows one to use the continuum model for each phase. Due to the moderate flow velocity, the effects of compressibility of the phases, as well as mechanical energy, dissipation in the phases are negligible. Assuming that thermal conductivity and viscosity of vapor and liquid are independent of temperature and pressure, we arrive at the following equations ... 

Summarizing it can be stated that the separation by gas phase transport (Knudsen diffusion) has a limited selectivity, depending on the molecular masses of the gases. The theoretical separation factor is decreased by effects like concentration-polarization and backdiffusion. However, fluxes through the membrane are high and this separation mechanism can be applied in harsh chemical and thermal environments with currently available membranes (Uhlhorn 1990, Bhave, Gillot and Liu 1989). 

This inaccuracy stems from their calculation of molecular transport effects, such as viscous dissipation and thermal conduction, from bulk flow quantities, such as mean flow velocity and temperature. This approximation of microscale phenomena with macroscale information fails as the characteristic length of the (gaseous) flow gradients approaches the average distance travelled by molecules between collisions - the mean path. The ratio of these quantities is referred to as Knudsen number. 

Effects of the main governing dimensionless parameters on the momentum and heat flow transfer will be analyzed. Pure analytical correlations for Nusselt number as a function of the Brinkman number and the Knudsen number are developed for both hyrodynamically and thermally fully developed flow. In fact, this work will be a summary view of our recent studies [12-15]. 

The experimental results have been obtained almost entirely from LEED, UPS and LEELS measurements for coverages ranging from a fraction of a monolayer to 20 monolayers, but an important point has been the use of molecular beam techniques for metal deposition to minimze contamination effects. (The metal was effused from clean Knudsen sources.) If we consider first the LEED observations, the initial state is a thermally produced 111 7 x 7 structure. The 7x7 periodicity is retained up to 1 monolayer of metal deposit, but as an extrinsic 7x7 pattern induced by the metal rather than a simple decrease in intensity of the Si 7 x 7 reflections. This was quoted as evidence of an essentially two-dimensional morphology for the metal deposit, since the formation of three-dimensional nuclei with clean silicon between them would have only reduced the intensity of the intrinsic 7x7 pattern. Beyond one monlayer, growth could follow a Stranski-Krastanov mode, however. 

Figure 9.37 Effect of the pore (cell) size on the gas thermal conductivity in open-pore polymeric foams together with the theoretical predictions obtained from the Knudsen equation and some of the previous results in aerogels. PMMA, poly(methyl methacrylate).

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