Numerical solutions of the Lamm equation. III. Velocity centrifugation

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Abstract
We have generated solutions to the Lamm equation to examine the effects of concentration dependence on velocity experiments. Two forms of c dependence are considered: s/s0 = 1 – kc and s/s0 = (1 + kc)−1. Features of these solutions are discussed. The magnitude of the errors resulting from the usual procedure of measuring the rate of movement of schlieren maxima or of the position at which the concentration is one half the plateau value have been examined. These errors are usually negligible after sufficient centrifugation time. The errors in using the half‐plateau concentration are less than those using the movement of the peak. We have also examined a technique due to Fujita for determining D from boundary spreading when s/s0 = (1+kc)−1. This method is satisfactory when s/s0 is actually of this form, or under certain limitations when s/s0 = (1 + kc)−1. Creeth has shown that under certain conditions the concentration gradient, curve remains virtually unchanged in shape after separating from the meniscus. When this occurs it is possible to estimate s/D from the data. The condition for such a steady state is that kc0 be sufficiently large. Numerical confirmation of this method is presented in the final section.

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