Abstract
The important practical problem of the dispersion of a passive contaminant in a fluid flowing through a pipe or channel of uniform cross-section is usually analysed in terms of the distribution of concentration. In this paper however a different though approximate approach is adopted which both illustrates the essential statistical nature of the process and may be quicker to employ when approximate answers are acceptable in a practical problem. A simple statistical model is proposed for the motion of a single molecule of contaminant and leads to an expression for the covariance of the velocity of the molecule in terms of the fluid velocity, and hence to a value of Taylor's longitudinal diffusivity. The model is applied to two simple flows in a channel, one of which illustrates the effect of the viscous sub-layer. Despite the number of simplifying assumptions made in constructing the model it gives results which are close to those obtained by conventional means. Ways in which the model could be adapted to give even better results are discussed.
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