Radial diffusion method

Hagerman AE (1987) Radial diffusion method for determining tannin in plant extracts. J Chem Ecol 13 437-449... 

MIO. Mancini, G., Vaerman, J. P., Carbonara, A. O., and Heremans, J. F., A single-radial-diffusion method for the immunological quantitation of proteins. Protides Biol. Fluids, Proc. CoUoq. 11, 370-373 (1964). 

A two-point kinetic turbidimetric technique using commercially available monospecific antisera has been used for the determination of immunoglobulins G, A, and M in sera. The accuracy of the method when measuring idiotypic monoclonal proteins is greater than that of the radial diffusion method. 

Espinel-Ingroff et al. [97] described a radial diffusion bioassay method for miconazole, which employs Candida stellatoidea as the indicator organism. Results from... 

This problem, in which a radiogenic element is allowed to leak out of its host mineral as it forms, has found important applications in geochronology, particularly for the K-Ar method (Wasserburg, 1954) and the U-Pb method (Tilton, 1960 Wasserburg, 1963) with the so-called continuous loss model. The equation for radial diffusion of a radiogenic element in a sphere with radius a and uniform parent isotope concentration P = P0 at t = 0 can be written... 

Guesdon JL, Avrameas S. An immunoenzymatic method for measuring low concentrations of antigens by single radial diffusion. Immunochemistry 1974 11 595. 

Although convection, axial diffusion, and radial diffusion actually occur simultaneously, a multistep procedure was adopted in the finite-difference calculation. For each 5-cm increment in tidal volume and for each time increment At, the differential mass-balance equations were solved for convection, axial difihision, and radial diffusion in that order. This method may slightly underestimate the dosage for weakly soluble gases, because the concentration gradient in the airway may be decreased. 

Lawrence and Sanderson proposed another micro-method for measuring chymosin and other proteolytic enzymes. Measurement of concentration was based on the rate of radial diffusion of the enzyme through a thin layer of caseinate-agar gel. The limit of diffusion was marked by a zone of precipitated casein (Emstrom and Wong 1974). Holmes et al (1977) developed a microdiffusion assay for residual proteolytic enzymes in curd and whey that is more sensitive than the method of Lawrence and Sanderson or the clotting-time assay of Reyes (1971). 

Rowe DS. Radioactive single radial diffusion A method for increasing the sensitivity of immunochemical quantitation of proteins in agar gel. Bull WHO 1969 40 613-6. 

An approximate method of allowing for radial diffusion is given in ... 

Equations 8.37 and 8.38 impose a very severe restriction on the axial increment. If Ar is halved, Az must be decreased by a factor of more than 8. The net effect on convergence is that Az will be far smaller than necessary for convergence in the z direction while Ar is still too large for accurate results. The situation becomes worse when the radial diffusion rate, 0J/R, is large. The method of false transients discussed in Chapter 16 can be used, but there is no perfect method for solving PDEs. All methods are computationally intensive. 

This model has been applied to vacuum coalers where the material being vapor deposited is evaporated from one or more point sources. Note that and Dr are empirical parameters that account for both convection and diffusion. Rotary vacuum coalers avoid any dependence in the 6 direction by rotating the substrate as it is coated. The false-transient method works here as in Section 16.2.4, but the axial and radial diffusivities are now separate and empirical. 

An alternative approach to decrease the time constant of electrochemical systems rests on the use of the miniaturized ITIES. Micron-scale ITIES use a micropipette to support the aqueous phase [98]. Subsequently an alternative approach, using micro-holes formed by laser ablation of thin polymer films, was reported [99]. The advantage of the micron-scale approach is that the radial diffusive flux to such an inlaid interface reaches a steady state, so the problems of transient current methods due to the double-layer charging constant are avoided. The low currents measured at such interfaces, due to their small size,... 

The third variation that exploits unsliced gels is based on the following principle the gel is, after isoelectric focusing, incubated with antiserum and the non-precipitated proteins are eluted. Further processing, e.g., staining and destaining is conventional. Methods that use slicing can be also modified in at least three different ways the individual sections can be tested by double gel diffusion, radial diffusion or immunoelectrophoresis. 

Another approximate method of solution of Eq. (6.118) that covers both longitudinal and radial diffusion of substance was proposed in [15]. The essence of the method is to reduce the diffusion equation to a system of equations for the moments, which have a simple physical meaning. Introduce the following dimensionless variables ... 

Derive steady-state and nonsteady-state mass and energy balances for a catalyst monolith channel in which several chemical reactions take place simultaneously. External and internal mass transfer limitations are assumed to prevail. The flow in the chaimel is laminar, but radial diffusion might play a role. Axial heat conduction in the solid material must be accounted for. For the sake of simplicity, use cylindrical geometry. Which numerical methods do you recommend for the solution of the model ... 

Pipe reactors can be operated in laminar or turbulent flow. In laminar flow radial diffusivity is molecular only, which is very slow, particularly if the viscosity is high. In turbulent flow the radial fluctuating velocity component produces the radial turbulent diffusivity which is much faster than molecular diffusivity. Many devices have been developed to promote fast radial mixing in laminar flow, such as static mixers, which are discussed below and in Chapter 7. Besides static mixers, a number of methods exist to promote faster radial mixing in turbulent flow, since even in turbulent flow it takes 50 to 100 pipe diameters to achieve... 

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