Interfaces, diffuse motion

Equihbrium concentrations which tend to develop at solid-liquid, gas-liquid, or hquid-liquid interfaces are displaced or changed by molecular and turbulent diffusion between biilk fluid and fluid adjacent to the interface. Bulk motion (Taylor diffusion) aids in this mass-transfer mechanism also. 

Segmental Dynamics. Two types of dynamics can be considered-segmental motion, and diffusion of the polymer from the surface. Previously we have seen that at the solid-liquid interface segmental motion in loops appears to differ little from that in dilute, dissolved polymer, unless the loops are held close to the polymer surface. In the dry state temperature studies indicated that segmental motion of loops differed little from segmental motion in bulk polymer. 

The presence of the interface restricts the diffusive motion to a half space. More important is the presence of particle-surface interactions, which can modify the transport properties. 

Lin et al. [17] studied the dynamics of copolymers adsorbed on an air-water interface. These measurements complemented the static measurements described above and in Fig. 4. The extent of the polymer films perpendicular to the surface is small compared to penetration distance and wavelength so that EWDLS is most sensitive to variation of composition in the plane of the interface. Figure 7 shows the measured normalized autocorrelation I (/) for different surface pressures. Frames a-d were taken during the first compression of the monolayer, and frames e-h were taken during the second compression. The difference between the two sets of measurements is an indication of structural changes induced by compression cycling. The frames e-g can be compared to the data in Fig. 4. The solid lines in the three frames are fits to a sum of two exponential functions, each with a characteristic decay time. The fast decay constant has a characteristic associated with diffusive motion of the disks. The slow decay constant ( several seconds) was ascribed to the dynamics of the associations of disks. 

Previous studies about dynamics of water near interfaces by quasi-elastic neutron scattering involved measurements of the mobility of water on the surface of Nafion membranes [63,64], the diffusive motions and the density of states of water in silica gels [65], and the interfacial melting of ice in graphite and talc pow-... 

In the case of fractal interfaces, the anomalies in diffusive motion are localized within a thin section located close to the interface and referred to as the fractal layer, since diffusion is perfectly regular (Fickian) in the bulk fluid phase. 

Xu, R., Chu, B., Dynamic Light Scattering of Thin Disks Coupling of Diffusive Motion, J. Colloid Interface Set, 1987, 117,22-30. 

If the diffusion coefficient of species A is less tlian tliat of B (D < D ) tlie propagating front will be planar. However, if is sufficiently greater than tire planar front will become unstable to transverse perturbations and chaotic front motion will ensue. To understand tire origin of tire mechanism of tire planar front destabilization consider tire following suppose tire interface is slightly non-planar. We would like to know if tire dynamics will tend to eliminate this non-planarity or accentuate it. LetZ)g The situation is depicted schematically in figure... 

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

To estimate the slumping motion of the kiln bed which periodically exposes a fresh, vapor saturated surface at the bed—freeboard interface must be considered. Based on Pick s second law in a bed of porosity, S, and for an effective diffusion coefficient, the mass-transfer coefficient on the bed side is... 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

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