Diffusion through stationary film

Consider the problem of the unidirectional, steady state flow of A through a stationary film B. It is assumed that the quantity of A diffus-... 

In most forms of gas chromatography (GC) and in some forms of liquid chromatography (LC) at high flowrates, the slow (and therefore controlling) step for solute transfer is diffusion through a stationary film or droplet of depth d. Under these circumstances, Eq. 9.17 applies. Assuming AV/V l, and using V= R(v), we get... 

This particular case exists for example in the diffusion of a substance through a film with thickness d (Fig. 7-3) if the concentrations at the two surfaces Cj at x = 0 and c2 at x = d remain constant (stationary case) ... 

Consider the cross-sectional view shown in Figure 1, B, and for ease of illustration assume that the barrel is rotating with a linear velocity ttDN with respect to the stationary screw. Depletion of a volatile component from the polymer phase takes place by molecular diffusion through the immediate surface layers of the wall film, abc (formed by the clearance between the screw land and barrel wall), and the nip film, dc, followed by evaporation from their respective interfaces into the vapor space and out of the svstem. The wall film is continually regenerated by the wiping action of the screw land, and the nip film by the circulatory fluid motion in the advancing helical nip. The following three important assumptions are made ... 

There are at least two main sources of resistance to mass transfer (Figure 5.4 [96]) external film mass transfer resistance and intrapartide diffusion that is composed of pore and surface diffusion. The latter diffusion is insignificant in numerous adsorbents but plays an important role in most adsorbents used in RPLC. For particles having micropores, there is an additional mass transfer resistance, the resistance to diffusion through micropores which is often important. This explains why considerable attention is paid in the preparation of stationary phases for FIPLC to avoid the formation of micropores. This explains also why graphi-tized carbon black, which tends to be plagued by a profusion of micropores, has not been a successful stationary phase for HPLC. 

The self-diffusion part of the behavior is taken to occur by means of a stationary intergranular watery film. This film allows quartz to dissolve at sites of high compression, travel through the film as a solute, and reprecipitate as quartz at sites of low compression. Interest attaches to (i) the mathematics and (ii) the comparison with natural examples of real rocks in analogous situations. 

During constant-rate period, the free moisture leaves the saturated surface of the material by diffusion through a stationary air film into air stream. GiUiland[3] showed that the drying rate for this period for variety of material is essentially the same (around 2.0-2.8 kg/rrP/K). 

Thus, during solute transfer between the phases, (t) is now the average diffusion time (to) and (o) is the mean distance through which the solute diffuses, Le., the depth or thickness of the film of stationary phase (df). Thus,... 

During the constant rate period, it is assumed that drying takes place from a saturated surface of the material by diffusion of the water vapour through a stationary air film into the air stream. Gilliland(8) has shown that the rates of drying of a variety of materials in this stage are substantially the same as shown in Table 16.1. 

Ceramic materials in contact with aqueous liquids are also susceptible to attack. This is of particular importance in the realm of civil engineering, where materials of con-strnction that contain minerals routinely come in contact with groundwater and soil. Minerals dissolve into aqueous solutions through the diffusion of teachable species into a stationary thin film of water, about 110 ttm thick... 

Liquid water on one side of a silicone contact lens permeates through the lens by a solution-diffusion mechanism and evaporates on the other side quickly according to the permeability of water, whereas the solubility of water in silicone polymer is low [1]. The high water vapor permeability was speculated to be one of the reasons causing the suction cup effect that makes the lens stationary on one spot and tenaciously stick to the cornea this may damage the corneal epithelium and result in other complications. However, the high permeability per se cannot be the reason for the suction cup effect if the exterior surface is covered by the tear film, i.e., if there is no driving force for water permeation. 

Band broadening and temperature The five terms of Equation (24-14) can be examined in the context of the influence of temperature on flow rates, retention volumes, and diffusion coefficients to obtain an estimate of the overall influence of temperature on band broadening. Through thermal expansion, temperature also influences such factors as thickness of a liquid film and particle and column diameters, and it may also influence slightly the empirical constants in (24-14). With a liquid mobile phase, flow velocity (with the same inlet and outlet pressures) is strongly dependent on temperature. But with flow velocity u maintained constant the first term of (24-14) becomes smaller as diffusion coefficients increase in the mobile phase. For flow rates near the optimum the first term is approximately inversely proportional to The second and third terms increase in direct proportion to the diffusion coefficients in the mobile and stationary phases D and D, whereas the fourth and fifth... 

Either side of the phase boundary two stationary laminar fluid layers (films) are formed with thicknesses (5g and dt, through which the gas can only pass by diffusion. 

In general, two well separated kinetic processes are observed and were identified by Bertrand et al. [172] as a first fast nucleation of domains followed by a second slower reorganization of the polymer chains in the multilayer. A more detailed picture allows one to describe the first step as a diffusive process coupled to the adsorption through an electrostatic or steric barrier [166, 173], whereas the second step implies aU the reorganization steps that lead to the multilayer till the stationary state [167]. This latter step includes both in plane reorganization of the polymeric chains and the interdififusion of the polyelectrolyte chains along the whole multilayer structure [99]. Figure 13 shows the adsorption kinetics of a PDADMAC layer onto a (PDADMAC - - PSS)n film. 

An initially non-linear pressure increase in the transient state is followed by a linear increase in the steady state when an equilibrium concentration profile in the film is reached. From the slope of the steady state pressure increase it is possible to calculate the permeability of a penetrant through a polymeric sample.The time to reach the stationary flux conditions is called lag-time and it allows us to determine the diffusivity of the system. Alternatively, in the pressure decay methods, a polymer sample and a gas are closed in a eonstant volume. The pressure decreases in time due to the sorption of the gas into the polymer are monitored. 

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