Thermal Diffusion and Effusion

We begin this chapter with a comparison of the mechanisms responsible for mass and heat transfer. The mathematical similarities suggested by these mechanisms are discussed in Section 21.1, and the physical parallels are explored in Section 21.2. The similar mechanisms of mass and heat transfer are the basis for the analysis of drying, both of solids and of sprayed suspensions. However, the detailed models differ, as shown by the examples in Section 21.3. In Section 21.4, we outline cooling-tower design as an example based on mass and heat transfer coefficients. Finally, in Section 21.5, we describe thermal diffusion and effusion. 

We shall consider in detail the predictions of the hard-sphere model for the viscosity, thermal conductivity, and diffusion of gases indeed, the kinetic theory treatment of these three transport properties is very similar. But first let us consider the simpler problem of molecular effusion. 

Hindered diffusion, the primary transport mechanism in porous solids, can be qualitatively described as a series of hops by the analyte, via gas-phase diffusion, from one surface site to the next. Thus, hindered diffusion is composed of two main components a pure diffusion-related term, often Fickian in nature, associated with movement of the analyte in the gas phase and a term describing the noninstantaneous equilibration between gas-phase analyte and the solid surface at each point where the analyte touches down (adsorbs). In extended porous solids (e.g., a chromatographic column tightly packed with porous beads), transport is often more complex, requiring the consideration of such factors as eddy diffusion and Knudsen effusion. This is important if there is a significant pressure drop along the path of the analyte [109]. Finally, the presence of any external fields (thermal, electric, etc.) must be considered as well. 

Indices i and j refer to adjacent layers, kj and kj (W m s ) are thermal conductivities, and D, and Dj are the thermal diffusivities. Thermal effusivity is analogous to a refractive index for thermal waves. Reflection and absorption may be evaluated by the thermal reflection coefficient ... 

The major thermal constants of solids are the thermal conductivity a (W/mK) and the heat capacity per unit volume, C (J/m K). Related thermal parameters are the thermal diffusivity D = a/C (m /s) and the thermal effusivity e = (Ws /m K). As a dynamic factor, the thermal penetration... 

Problems associated with specimen 4- container reactions become serious as the temperature of vapour pressure measurement is increased towards 2000 K. For example, in effusion measurements it becomes difficult to find a cell material which is inert to the more refractory metals and which is not itself volatile. In transpiration and isopiestic studies, thermal diffusion errors are very difficult to avoid, although they can be considerably reduced by suitable precautions. 

Thermal diffusion, which has just been discussed, occurs in mixtures in which molecules of solute and solvent interact with each other. Thermal effusion, the effect discussed next, occurs when the molecules of a pure gas react largely with surroundings. 

The pressure on the hot side will be greater than the pressure on the cold side. The key to this process is that the holes in the diaphragm are very small. Thus thermal effusion is to Knudsen diffusion as thermal diffusion is to ordinary diffusion. Both thermal effusion and diffusion are illustrated in the following examples. 

Mandelis has reviewed photothermal TA techniques. Thermal waves may be optically induced in solid samples by modulated irradiation. These thermal waves then interact directly with the sample and such interaction is detected by suitable sensors. Acoustic waves may be simultaneously induced and detected. These techniques have specialized application to solid-state systems to determine thermal transport properties such as thermal conductivity, diffusivity/effusivity, and specific heat capacity. These techniques are of particular significance in the determination of mechanisms of solid-state phase transitions. 

Ryu et al. [151] employed GaAs substrates as an arsenic source for p-type doping of ZnO by PLD. In this case, a p-type ZnO layer was produced at the ZnO/GaAs interface after thermal armealing. The p-type ZnO films were grown on different substrates, ZnO, SiG, and sapphire, rather than on GaAs and As was supplied from an effusion cell in the PLD system. Thus, the postarmealing process was not deemed necessary to diffuse As into ZnO film [152, 153]. 

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