Gradient, concentration continuously

Where a, b, and c = van Deemter coefficients, dp = particle size of column, L = column length, Dm = diffusion coefficients of analytes, t = column dead time (depends on flow rate F), tg= gradient time (determines analysis time via tA = tg + t0), Ac = difference in concentrations of the organic modifier at the end and the beginning of the gradient (a continuous linear gradient is assumed), and B = slope of the linear relationship between the logarithm of the retention factor and the solvent composition. 

For the first and third layers the equations are rather simple whereas for the second layer, with the gradient concentration of PAA, the equation is more complex as it takes into account the continuous linear variation of the polyacid content across the layer. 

Amino acids are absorbed from the gut into the bloodstream by active transport and transferred to the cells. This requires a supply of energy, since the concentration of amino acids in the cell may be up to 100 times that in the blood and transfer into the cell has to take place against a very considerable concentration gradient. A continuous exchange takes place between the blood and cellular amino acids, but not between the free amino acids and those of the tissue proteins. The tissue proteins themselves undergo breakdown and resynthesis, but their stability varies between different tissues. For example, hver protein has a half-life of 7 days whereas collagen is so stable that it may be considered to be almost completely inert. 

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

We have used the fact that the concentration gradient grad c, or equivalently the pressure gradient, tends to zero as the permedility tends to infinity. Nevertheless, these vanishingly small pressure gradients continue to exert a nonvanishing influence on the flux vectors, and the course of Che above calculation Indicates explicitly how this comes about. 

When electrons are injected as minority carriers into a -type semiconductor they may diffuse, drift, or disappear. That is, their electrical behavior is determined by diffusion in concentration gradients, drift in electric fields (potential gradients), or disappearance through recombination with majority carrier holes. Thus, the transport behavior of minority carriers can be described by a continuity equation. To derive the p—n junction equation, steady-state is assumed, so that = 0, and a neutral region outside the depletion region is assumed, so that the electric field is zero. Under these circumstances,... 

Bubble Fractionation Figure 22-45 shows continuous bubble fractionation. This operation can be analyzed in a simplified way in terms of the adsorbed cariy-up, which furthers the concentration gradient, and the dispersion in the liquid, which reduces the gradient [Lemhch, Am. Inst. Chem. Fng. J., 12, 802 (1966) 13, 1017 (1967)]. 

The concentration gradient normal to the outside of the catalyst particle. The rate is expressed on catalyst-filled reactor volume, with e void fraction for this smaller volume the rate must be higher to keep Vrr=Vcr< . This is calculated from the continuity requirement that was mentioned above ... 

Concentration gradient inside the catalyst particle. The continuity statement, at the catalyst surface, is similar to Pick s first law for diffiasion. The reaction rate is equal to the diffusion rate at the outside layer of the catalyst... 

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