Stagnant point

The results in the present paragraph have limits of applicability, in particular those connected with the application of the boundary layer method. It is well known that results obtained by this method are unsuitable in the neighbourhood of the rear stagnant point. 

It was shown by Harper (1974, 1988) that the solution representing the distribution of the surface concentration diverges in the neighbourhood of the rear stagnant point (RSP) as... 

Free Surface Zone near Front Stagnant Point... 

Particle Deposition on the Free Zone near the Front Stagnant Point. Contaminated Water... 

In the preceding sections the possibility of the strong influence of the fi-ee surface zone near the front stagnant point on the transport stage of microflotation was emphasised. Eq. (10.40) enables us to estimate the critical condition of the appearance of an f.s.f.z. The parameters v and Re relate to the bubble with a completely retarded surface and can be described by equations derived for solid spheres. 

Example 93-7 Spatially resolved mass spectrometry as a fast semi-quantitative tool for testing heterogeneous catalyst libraries under reducing stagnant-point flow conditions (Eckhard et al., 2005). 

Eckhard, K., Schlueter, O., Hagen, V., Wehner, B., Erichsen, Schuhmann, W. And Muhler, M. (2005). Spatially resolved mass spectrometry as a fast semi-quantitative tool for testing heterogeneons catalyst libraries under reducing stagnant-point flow conditions. AppZ. Catal. A General 281, 1-2, 115-120. 

The experimental setup employs stagnant point flow hydrodynamics in a wall jet, shown in the inset of Figure 8.9. There is no convection at the stagnation point, so transport of surfactant to and from the surface is by diffusion only. The hydrodynamics associated with stagnation point flow have been investigated by Dabros and Van de Ven, who showed that the diffusion-limited flux, J, of an adsorbate to the surface is given by... 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

If q is negligibly small a stagnant diffusion layer in aqueous phase is a rate-limiting step. This case is often the most useful from an analytical point of view. The well-known equation for a reversible polarographic wave can be obtained as ... 

Consider the transport of gaseous species A from a bulk gas to a bulk liquid, in which it has a measurable solubility, because of a difference of chemical potential of A in the two phases (higher in the gas phase). The difference may be manifested by a difference in concentration of A in the two phases. At any point in the system in which gas and liquid phases are in contact, there is an interface between the phases. The two-film model (Whitman, 1923 Lewis and Whitman, 1924) postulates the existence of a stagnant gas film on one side of the interface and a stagnant liquid film on the other, as depicted in Figure 9.4. The concentration of A in the gas phase is represented by the partial pressure, pA, and that in the liquid phase by cA. Subscript i denotes conditions at the interface and 8g and are the thicknesses of the gas and liquid films, respectively. The interface is real, but the two films are imaginary, and are represented by the dashed lines in Figure 9.4 hence, Sg and 8( are unknown. 

Fig. 16.42 Atrazine degradation in sterilized aquifer material (Al, Bl, Cl) and in natural (unamended) aquifer material (A2, B2, C2) for reactors under stagnant (15°C), stagnant (25°C), and recirculating (15°C) conditions. Data points are the mean of three replications. The least significant difference between these treatments at the p < 0.05 level is 0.075. Figures are identified as (A) Topeka, (B) Ashland, and (C) Hutchinson aquifers. (Schwab et al. 2006)...

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